ALBERT

Notes: X-ray diffraction (XRD) patterns from nominally β-SiC specimens often differ from those expected for the cubic crystal structure. These differences include the presence of additional peaks, enhanced background intensities, peak broadening, changes in relative peak heights, and shifts in peak positions. It has long been recognized that they are due to the presence of stacking faults, and models relating the experimental observations to stacking fault population have continued to evolve. The presence and relative magnitude of these features vary among different β-SiC specimens. In this work, computer simulations were used to show that the variations are closely related to differences in the type and spatial distribution of stacking faults in each specimen. In these simulations, stacking sequences were generated using a selectively activated 1-D Ising model with a Boltzmann-type probability function for specifying errors, which allows a wide variety of fault configurations to be generated. Direct correlations between different features in the XRD data to the underlying fault population are demonstrated, which are discussed in this paper. It is also shown that this computer model is general, in the sense that many of the models presented in prior work can be interpreted as limiting cases of it.

Notes: The electromagnetic array profiling (EMAP) exploration method can be combined with a direct one-dimensional inversion process for conversion to depth to produce a subsurface resistivity cross-section. This cross-section may then be interpreted in parallel with a seismic cross-section to enhance the prediction of rock type and structure. In complex thrust environments and areas of shallow carbonate rocks, the EMAP method is often used to provide additional data either to help the seismic processor and/or to aid the seismic interpretation. In particular, the electromagnetic (EM) data can be used to build an independent seismic velocity file for depth migration.Three EMAP test areas in the western United States are used to demonstrate such a use of EMAP as an expioration tool. The first shows how a velocity file is estimated from resistivity data for seismic depth migration processing in a complex thrust environment. In the second example, the method is applied in layer-cake geology with high seismic velocity rocks at the earth's surface. The third example is another complex thrust environment, but in this case the velocity file derived from the resistivity data is used for stacking the seismic data.

Notes: A fast inversion technique for the interpretation of data from resistivity tomography surveys has been developed for operation on a microcomputer. This technique is based on the smoothness-constrained least-squares method and it produces a two-dimensional subsurface model from the apparent resistivity pseudosection. In the first iteration, a homogeneous earth model is used as the starting model for which the apparent resistivity partial derivative values can be calculated analytically. For subsequent iterations, a quasi-Newton method is used to estimate the partial derivatives which reduces the computer time and memory space required by about eight and twelve times, respectively, compared to the conventional least-squares method. Tests with a variety of computer models and data from field surveys show that this technique is insensitive to random noise and converges rapidly. This technique takes about one minute to invert a single data set on an 80486DX microcomputer.

Notes: High-speed photography has been used visually to study the shape, surface, turbulence and behaviour of an underwater oscillating bubble generated by an airgun. The source was a BOLT airgun with a chamber volume of 1.6cu.in., placed in a 0.85m3 tank at 0.5m depth. Near-field signatures were also recorded in order to compare the instant photographs of the oscillating bubble with the pressure field recorded about 25 cm from the gun. Estimations of the bubble-wall velocity and bubble radius estimated from high-speed film sequences are also presented, and are compared with modelled results. The deviation between the modelled and measured bubble radii was at most 9%. In order to check the capacity for transmission of light through the bubble, a concentrated laser beam was used as illumination. We found that the air bubble is a strong scattering medium of laser light, hence the bubble is opaque.

Notes: Full-wavefield inversion for distributions of acoustic velocity, density and Q on a vertical slice through a25D model is implemented for common-source gathers in a cross-hole geometry. The wavefield extrapolation used is 3D, so all geometrical spreading, scattering, reflection, and transmission effects are correctly and automatically compensated for. In order to keep the number of unknowns tractable, application was limited to 2.5D models of known geometry; the latter assurnes a prior step, such as tomography, to fix the layer geometries. With the model geometry fixed, reliable solutions are obtained using synthetic data from only two independent source locations. Solutions from data with noisy and missing traces are comparable to those from noise-free data, but with higher residuals. When the source locations are spatially widely separated, conunon-source gathers may be summed and treated as a single wavefield to yield the same model estimates as when the individual source wavefields are treated separately, at substantially reduced cost. Inversions for full 3D parameter distributions can be handled with the same software, requiring only solution for more unknowns.

Notes: It is seen that the apparent chargeability (Ma)L anomaly over a 2D graphite body splits into two distinct (Vs)L anomalies which closely follow the apparent resistivity profile. This suggests that the electric field amplitude is distorted due to a superficial inhomogeneity creating a (Vs)L anomaly, which bears no relation to the polarized body. The target depth obtained by continuation of such a profile is therefore, not acceptable.

Notes: The improvement in accuracy and efficiency of wave-equation migration techniques is an ongoing topic of research. The main problem is the correct imaging of steeply dipping reflectors in media with strong lateral velocity variations. We propose an improved migration method which is based on cascading phase-shift and finite-difference operators for downward continuation. Due to these cascaded operators we call this method‘Fourier finite-difference migration’(FFD migration).In our approach we try to generalize and improve the split-step Fourier migration method for strong lateral velocity variations using an additional finite-difference correction term. Like most of the current migration methods in use today, our method is based on the one-way wave equation. It is solved by first applying the square-root operator but using a constant velocity at each depth step which has to be the minimum velocity. In a second step, the approximate difference between the correct square-root operator and this constant-velocity squareroot operator (the error made in the first step) is implemented as an implicit FD migration scheme, part of which is the split-step Fourier correction term.Some practical aspects of the new FFD method are discussed. Its performance is compared with that of split-step and standard FD migration schemes. First applications to synthetic and real data sets are presented. They show that the superiority of FFD migration becomes evident by migrating steeply dipping reflectors with complex overburden having strong lateral velocity variations. If velocity is laterally constant, FFD migration has the accuracy of the phase-shift method. The maximum migration angle is velocity adaptive, in contrast to conventional FD migration schemes. It varies laterally depending on the local level of velocity variation. FFD migration is more efficient than higher-order implicit FD schemes. These schemes use two cascaded downward-continuation steps in order to attain comparable migration performance.

Notes: Simulated annealing is a stochastic combinatorial optimization technique, based on ideas from statistical mechanics, thermodynamics and multivariable probability theory. This paper presents the use of simulated annealing as a means of inversion for both linear magnetics and non-linear resistivity problems. The subsurface is viewed as being constructed of smaller elemental blocks which possess either uniform internal magnetization or conductivity, enabling larger structures to be modelled. Simulated annealing is employed to calculate the distribution of the particular physical property which causes a measured anomalous field curve.A general description of simulated annealing and its application is given, followed by specific descriptions of its application to the magnetics and resistivity cases.For the magnetics case the subsurface consists of 2D prismatic elements as the basis for the forward model. Synthetic model data is used to test the algorithm and an example of actual field data; a survey across an igneous dike is used to demonstrate the use of the method with real data. In the resistivity case, the finite-element method is used to generate the forward models. Synthetic vertical profiling data is used to test the application of the simulated annealing method to the resistivity case. Actual data from an archaeological survey is used to show again the use of the method with real data.Simulated annealing is shown to be capable of inverting both the linear and non-linear methods of magnetic surveying and resistivity surveying respectively.

Notes: We consider the problem of computing the most probable location of a target based on radar measurements of the subsurface. Our algorithm makes use of the maximum likelihood estimator (MLE), which represents a correlation between the measured data and synthetic data generated for the object of interest at different locations. Previous studies assume a plane-wave acquisition geometry and target object(s) embedded in a uniform background. In this paper, a generalization of the MLE method is presented which is valid for discrete point sources (and receivers) and a 2D model (i.e. a 2.5D acquisition geometry). Within this formulation the treatment of a non-uniform background model is also possible. We concentrate on geotechnical ground investigations and assume that the characteristic dimensions of the target object are in the range 1–2λ, (λ being the wavelength). The potential of the method is demonstrated employing cross-hole radar data acquired in a controlled field experiment. The MLE result is also compared with the image obtained employing a full reconstruction method such as diffraction tomography.

Notes: We present a simple method for estimating an effective source wavelet from the first arrival in marine vertical seismic profiling (VSP) data. The method, which utilizes the free-space Green's function of the Helmholz equation, is simple and very computer efficient. We show examples from synthetic and real offset and walkaway VSP data.In the synthetic examples, we show that data modelled with the estimated wavelet give small residuals when subtracted from the reference data. In the real data examples, we show that when modelling with the wavelet estimated from the real data, in a smooth macromodel, we obtain a good fit between the first arrivals in the real and modelled data.

Notes: An expression which is optimum with respect to the simplicity of the numerical computations is obtained for the magnetic field of a polyhedron with constant magnetization. The high accuracy of the results is illustrated using a realistic numerical model.The existence of the magnetic field at points inside the source and on its boundary is discussed and related to real magnetic data modelling.

Notes: The posterior probability density function (PPD), σ(m|dobs), of earth model m, where dobs are the measured data, describes the solution of a geophysical inverse problem, when a Bayesian inference model is used to describe the problem. In many applications, the PPD is neither analytically tractable nor easily approximated and simple analytic expressions for the mean and variance of the PPD are not available. Since the complete description of the PPD is impossible in the highly multi-dimensional model space of many geophysical applications, several measures such as the highest posterior density regions, marginal PPD and several orders of moments are often used to describe the solutions. Calculation of such quantities requires evaluation of multidimensional integrals. A faster alternative to enumeration and blind Monte-Carlo integration is importance sampling which may be useful in several applications. Thus how to draw samples of m from the PPD becomes an important aspect of geophysical inversion such that importance sampling can be used in the evaluation of these multi-dimensional integrals. Importance sampling can be carried out most efficiently by a Gibbs' sampler (GS). We also introduce a method which we called parallel Gibbs' sampler (PGS) based on genetic algorithms (GA) and show numerically that the results from the two samplers are nearly identical.We first investigate the performance of enumeration and several sampling based techniques such as a GS, PGS and several multiple maximum a posteriori (MAP) algorithms for a simple geophysical problem of inversion of resistivity sounding data. Several non-linear optimization methods based on simulated annealing (SA), GA and some of their variants can be devised which can be made to reach very close to the maximum of the PPD. Such MAP estimation algorithms also sample different points in the model space. By repeating these MAP inversions several times, it is possible to sample adequately the most significant portion(s) of the PPD and all these models can be used to construct the marginal PPD, mean) covariance, etc. We observe that the GS and PGS results are identical and indistinguishable from the enumeration scheme. Multiple MAP algorithms slightly underestimate the posterior variances although the correlation values obtained by all the methods agree very well. Multiple MAP estimation required 0.3% of the computational effort of enumeration and 40% of the effort of a GS or PGS for this problem. Next, we apply GS to the inversion of a marine seismic data set to quantify uncertainties in the derived model, given the prior distribution determined from several common midpoint gathers.

Notes: The long-wavelength propagation and attenuation characteristics of three geological structures that frequently occur in reservoir environments are investigated using a theoretical model that consists of a stack of fine and viscoelastic plane layers, with the layers being either solid or fluid. Backus theory properly describes fine layering and a set of fluid-filled microfractures, under the assumption that interfaces between different materials are bonded. The effects of saturation on wave attenuation are modelled by the relative values of the bulk and shear quality factors.The anisotropic quality factor in a fine-layered system shows a variety of behaviours depending on the saturation and velocities of the single constituents. The wave is less attenuated along the layering direction when the quality factors are proportional to velocity, and vice versa when inversely proportional to velocity. Fractured rocks have very anisotropic wavefronts and quality factors, in particular for the shear modes which are strongly dependent on the characteristics of the fluid filling the microfractures.When the size of the boundary layer is much smaller than the thickness of the fluid layer, the stack of solid-fluid layers becomes a layered porous media of the Biot type. This behaviour is caused by the slip-wall condition at the interface between the solid and the fluid. As in Biot theory, there are two compressional waves, but here the medium is anisotropic and the slow wave does not propagate perpendicular to the layers. Moreover, this wave shows pronounced cusps along the layering direction, like shear waves in a very anisotropic single-phase medium.

Notes: Responses of a multifrequency, multicoil airborne electromagnetic (AEM) system were modelled numerically for 3D electrical conductors embedded in a resistive bedrock and overlain by an overburden of low to moderate conductivity. The results cover a horizontal coplanar coil configuration and two frequencies, 7837 Hz and 51 250 Hz. The models studied are single or multiple, poor conductors (conductance lower than 0.1 S) embedded in a host rock of high but finite resistivity (5000 Ωm) and overlain by a layer of overburden with finite thickness and low to moderate conductivity (conductance up to 2 S).On the basis of the modelling results, limits of detectability for poor conductors have been studied for the various model structures. The results indicate that the anomaly from a steeply dipping, plate-like conductor will decrease significantly when the conductor is embedded in a weakly conductive host rock and is overlain by a conductive overburden. However, an anomaly is obtained, and its magnitude can even increase with increasing overburden conductivity or frequency. The plate anomaly remains practically constant when only the overburden thickness is varied. Changes in overburden conductivity will cause the plate-anomaly values to change markedly. If the plate conductance is less than that of the overburden, a local anomaly opposite in sign to the normal type of anomaly will be recorded. Another major consequence is that conductors interpreted with free-space models will be heavily overestimated in depth or underestimated in conductance, if in reality induction and current channelling in the host rock and overburden make even a slight contribution to the anomalous EM field.The lateral resolution for the horizontal coplanar coil system was found to be about 1.7 times the sensor altitude. Similarly, the lateral extension of a horizontal conductive ribbon, required to reach the semi-infinite (half-space) behaviour, is more than three times the sensor altitude. Finally, screening of a steeply dipping plate, caused by a small, conductive horizontal ribbon, is much more severe than screening of the same plate by an extensive horizontal layer.

Notes: We consider the problem of determining and predicting how the wave speeds in particular directions for a transversely isotropic (TI) medium depend on particular combinations of the density-normalized moduli Aij. The expressions for the qP and qSV velocities are known to depend on four moduli. Normally, we can only determine three independent parameters from qP data, or two from qSZ data, as the others have much lower sensitivity. The resolvable parameters are conveniently described by axial and off-axis parameters: for qP rays, P0°= A11, P90°= A33 and P45°=(A11+ A33)/4 + (A13+2A55)/2; and for qSV rays, S0°= S90°=A55 and S 45°= (A11+ A 33)/4- A13/2. These parameters control the magnitude of the squared-velocities on the axes and at approximately 45°. For an arbitrary TI medium, if the medium is perturbed in a way that preserves a particular parameter, then slowness points in the associated direction and mode witl be approximately preserved in the new medium. we refer to these parameters as ‘push-pins’, i.e. if a parameter is fixed, the associated part of the slowness surface is pinned in place.Because, these five push-pins only contain four independent moduli, we can only fix at most three push-pins. Perturbing one of the other parameters inevitably perturbs the other. Numerical results illustrating the linkage between two push-pins, when three are fixed, are presented.So-called anomalous TI media occur when the roles of the qP and qSV waves are reversed: in some directions the faster ray has transverse polarization. That, in turn, requires anomalous velocities at the push-pins, i.e. S0° 〉 P0°, S45° 〉 P45° and/or S90° 〉 P90° (equivalent to the usual anomalous conditions A11 〈 A55, 〈 0 and/or A33 〈 A55). In the Appendix, we confirm that anomalous sensitivities of the velocities at the five push-pins only occur in such media, although the push-pins still apply if interpreted appropriately. Truly anomalous sensitivities, in which push-pins play no role, only occur in media near the boundary between normal and anomalous.

Notes: Electrical conductivity mapping is a prerequisite tool for hydrogeological or environmental studies. Its interpretation still remains qualitative but advantages can be expected from a quantitative approach. However a full 3D interpretation is too laborious a task in comparison with the limited cost and time which are involved in the majority of such field studies. It is then of value to define the situations where lateral variations are sufficiently smooth for a 1D model to describe correctly the underlying features.For slingram conductivity measurements, criteria allowing an approximate 1D inversion are defined: these mainly consist of a limited rate of variation over three times the intercoil spacing.In geological contexts where the weathering has generated a conductive intermediate layer between the underlying sound rock and the soil, this processing can be applied to determine the thickness of the conductive layer from the apparent resistivity map when the other geoelectrical parameters are known. The examples presented illustrate this application.

Notes: A method to determine the position and magnetization vector of buried objects producing a magnetic anomaly is described. The data used were collected in boreholes. Since the anomaly is due to a number of objects, a ‘stripping’ procedure is employed for finding them, and therefore the process of inversion for finding all objects causing the anomaly consists of a few inversion steps.In each inversion step, two dipoles are considered as a model which approximates an object. The position and magnetic moments of the dipoles are the unknown parameters. The initial parameters are optimized by minimization of an objective function. The optimization procedure consists of a combination of linear and non-linear inversion. The solution of the linear inversion is obtained by singular value decomposition and that of the non-linear inversion by a six-dimensional simplex method (polytope algorithm). After finding one object, its effect is subtracted (‘stripped’) from the data and a new inversion step is started with new initial models and with a reduced data set. The inversion steps for finding different objects are continued until the absolute norm of the data becomes less than some adjustable value.The data will also be inverted assuming a three-dipole model in order to find the effect of using a more complex model in the inversion.The efficiency of the method is demonstrated using synthetic and real borehole data.

Notes: A simple numerical procedure is described for measuring the distance XY in the generalized reciprocal method when there are significant measurement errors in the refracted arrival times. It is applicable when the XY value is of similar magnitude to or less than the receiver spacing. Such conditions frequently occur in using the reciprocal or generalized reciprocal methods to estimate static corrections from first-break times measured in multifold seismic reflection profiling. The use of the method is illustrated with data from both deep and high-resolution seismic reflection profiles.

Notes: An analytical transient solution is obtained for propagation of compressional waves in a homogeneous porous dissipative medium. The solution, based on a generalization of Biot's poroelastic equations, holds for the low- and high-frequency ranges, and includes viscoelastic phenomena of a very general nature, besides the Biot relaxation mechanism. The viscodynamic operator is used to model the dynamic behaviour associated with the relative motion of the fluid in the pores at all frequency ranges. Viscoelasticity is introduced through the standard linear solid which allows the modelling of a general relaxation spectrum. The solution is used to study the influence of the material properties, such as bulk moduli, porosity, viscosity, permeability and intrinsic attenuation, on the kinematic and dynamic characteristics of the two compressional waves supported by the medium. We also obtain snapshots of the static mode arising from the diffusive behaviour of the slow wave at low frequencies.

Notes: The application of McClellan transformations considerably reduces the computational cost of 3D wavefield depth extrapolation by explicit convolutional methods. The accuracy of migration methods based on McClellan transformation depends on how well the transformation filter (cos !;κ!;) is approximated; errors in this approximation cause anisotropy in the extrapolation operator and frequency dispersion in the migrated results. The anisotropy can be greatly reduced by rotating the approximate filter by 45° and averaging the rotated filter with the original filter. The application of the rotated filter yields a migration method that correctly images very steep dips, with little or no additional computational cost. McClellan migration with the improved circular response enhances the imaging of synthetic and real data.

Notes: It is often very useful to be able to smooth velocity fields estimated from exploration seismic data. For example seismic migration is most successful when accurate but also smooth migration velocity fields are used. Smoothing in one, two and three dimensions is examined using North Sea velocity data.A number of ways for carrying out this smoothing are examined, and the technique of locally weighted regression (LOESS) emerges as most satisfactory. In this method each smoothed value is formed using a local regression on a neighbourhood of points downweighted according to their distance from the point of interest. In addition the method incorporates ‘blending’ which saves computations by using function and derivative information, and ‘weighting and robustness’ which allows the smooth to be biased towards reliable points, or away from unreliable ones.A number of other important factors are also considered: namely, the effect of changing the scales of axes, or of thinning the velocity field, prior to smoothing, as well as the problem of smoothing on to irregular subsurfaces.

Notes: A fast imaging technique is developed to deduce the spatial conductivity distribution in the earth from low-frequency (〉 1 MHz) cross-well electromagnetic measurements. A sinusoidally oscillating, vertically orientated, magnetic dipole employed as a source, and it is assumed that the scattering bodies are azimuthally symmetric about the source dipole axis. The use of this model geometry reduces the 3D vector problem to a more manageable 2D scalar form. Additional efficiency is obtained by using the Born series approximation which is derived from nonlinear integral equations that account for the scattered magnetic fields generated by inhomogeneities embedded in a layered earth. Stabilization of the inversion problem is accomplished through the use of bounding constraints and a regularization method which results in a smooth model that fits the data to the desired noise level.The applicability of cross-well electromagnetics for imaging and monitoring changes caused by subsurface processes has been tested by simulating plumes of conductive fluid with 2D models. The images that result from inverting these synthetic data indicate that the vertical resolution of the method is better than the horizontal, increasing the noise decreases the image resolution, and incorporating a priori knowledge in the form of positivity constraints improves the results. Although higher operating frequencies are usually associated with better resolution, frequencies as low as 100 Hz can produce acceptable images in simulated oilfield environments.The imaging scheme has been applied to data collected during a salt-water injection experiment at the Richmond Field Station test site in Richmond, California. Both the data and the resulting images clearly reveal the presence of the plume and indicate that it is migrating towards the north-northwest rather than spreading symmetrically about the injection well. Applying the imaging code to synthetic data generated by a 3D sheet model verifies the interpretation of these results.

Notes: An accurate analytical expression for shot-gather dip-moveout (DMO) in the timespace log-stretch domain has until now not been published. We present a simpler, alternative derivation of the exact DMO relationships of Black et al. which correctly take account of the repositioning of the midpoint. A new computationally efficient frequency-wavenumber (F-K) DMO operator for shot profiles is then derived, based on these DMO relationships in the time-space log-stretch domain. The newly derived DMO operator is, unlike most other log-stretch DMO operators) accurate for the full range of reflector dips. Along with other schemes which are performed in the log-stretch domain, it offers considerable time savings over conventional DMO processing. We have compared numerically the impulse response of the new operator with those of a number of other shot-gather DMO operators, and found it to be superior and well match to the theoretical elliptical DMO response.

Notes: In order to investigate the possibility of using low-frequency electromagnetic waves to detect and monitor oil contamination of soils, a series of laboratory measurements were performed. A new measurement system to monitor the resistivities of soil and sand samples while samples are being contaminated by diesel oil is presented. The frequency used in measurements is 100 kHz. Since the measurement system is composed of coil-type transmitters and receivers, there is no need for electrodes to be in contact with samples. The contamination process is simulated using diesel oil dripping on top of soil and sand samples. The conductivity distributions in samples along the sample length are recorded as a function of time. Water-wet sand and soil samples were measured during diesel oil contamination. The measured data show that the conductivities of soil and sand samples change during the contamination process. The change in resistivity for measured samples before and after diesel oil contamination is in the range of 20% to 50%, giving a reflection coefficient change in the low-frequency limit of 4.7% to 7%. This amount of change in the reflection coefficient makes it very challenging to detect and monitor oil contamination based on EM reflection from the contaminants. The results suggest that EM methods based on propagation and induction, such as tomography and borehole induction, could be used for this purpose.

Notes: A simple expression ties the midpoint of a surface spread to reflection points on a dipping plane. If we use two coordinate systems, an unprimed one with a z-axis perpendicular to the surface and a primed one with a z-axis perpendicular to the reflector, we have 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR831:GPR_831_mu1"/〉where θ is the dip angle, φ is the profile angle, X is the source-to-receiver separation, and D is the depth of the reflector. The reflection point is (x, yp, D) and the surface midpoint is (xc, yc, 0).Using the expression, I show that if complete azimuthal coverage is required at a CMP position, the reflection points lie on an ellipse. Similarly, a fixed reflection point generates a circle of surface midpoints. A circle of CMP positions for fixed θ and φ becomes an ellipse of reflection points and a circle of reflection points becomes an ellipse of midpoints. A user can easily find the shape and location of the reflection area generated by a surface aperture.

Notes: An integrated electromagnetic and nuclear magnetic resonance (NMR) method is proposed for investigating highly conductive soil areas. Using a simple model of a homogeneous half-space and the same antenna for both methods, a significant improvement in the NMR data interpretation is obtained. A case study has shown fair agreement between the results from computer modelling, field tests, and data from a nearby observation well. The electromagnetic method and the half-space model were selected for easy integration into an existing instrument used for the NMR method. A more accurate knowledge of the conductivity distribution with depth will further improve the final result.

Notes: A new method is proposed for the quantitative interpretation of SP field data produced by a polarized ore body and simulated by an inclined sheet. The theoretical concept is based on the study of the amplitude Spectrum. It is shown that the SP amplitude Spectrum is not continuous at zero frequency; this leads to the dip angle determination of the inclined sheet. It is also shown that the SP amplitude spectrum is practically nullified at a characteristic amortization frequency that depends on the depth of the polarized body. The maximum amplitude Spectrum value of the SP gradient is used to estimate the depth to the bottom of the polarized body. Thus, the geometrical parameters h and H, the depths to the top and bottom, respectively, as well as the dip angle of the inclined sheet, can be satisfactorily determined. Some problems may arise in the determination of these parameters, affecting their accuracy, whenever unwanted frequency noise is present.

Notes: Twelve ground penetrating radar (GPR) experiments were conducted on the modern, wave-influenced William River delta, on the Southern shore of Lake Athabasca in northern Saskatchewan, Canada. The delta is a well-sorted, quartzoserich, clean, sand-dominated, water-saturated geomorphic feature which provided an ideal site to test GPR. Penetration depths, resolution and continuity of reflections were compared for different antennae frequencies (25, 50, 100, 200 MHz) and transmitter powers (pulser voltage: 400 V, 1000 V). The data show significant variations in vertical resolution from 0.15 m to 0.76 m (200-25 MHz), depth of penetration from 14 m-28 m (200-25 MHz), and continuity of reflections. Increasing the transmitter power from 400 V to 1000 V increases the depth of penetration by 5 to 14% and improves the continuity of reflections with little effect on the resolution.

Notes: Biot's poroelastic differential equations are modified for including matrix–fluid interaction mechanisms. The description is phenomenological and assumes a solid–fluid relaxation function coupling coefficient. The model satisfies basic physical properties such as, for instance, that P-wave velocities at low frequencies are lower than those predicted by Biot's theory. In many cases, the results obtained with the Biot (two-phase) modelling are equal to those obtained with single-phase elastic modelling, mainly at seismic frequencies. However, a correct equivalence is obtained with a viscoelastic rheology, which requires one relaxation peak for each Biot (P and S) mechanism. The standard viscoelastic model, which generalizes compressibility and shear modulus to relaxation functions, is not appropriate for modelling the Biot complex moduli, since Biot's attenuation is of a kinetic nature (i.e. it is not related to bulk deformations). The problem is solved by associating relaxation functions with each wave modulus. The equivalence between the two modelling approaches is investigated for a homogeneous water-filled sandstone and a periodically layered poroelastic medium, alternately filled with gas and water. The simulations indicate that, in the homogeneous case, particle velocities in the solid skeleton, caused by a source applied to the matrix, are equivalent to viscoelastic particle velocities. In a finely layered medium, viscoelastic modelling is not, in principle, equivalent to porous modelling, due to substantial mode conversion from fast wave to slow static mode. However, this effect, caused by local fluid-flow motion, can be simulated by including an additional relaxation mechanism similar to the squirt-flow.

Notes: An algorithm for modelling and migrating ground penetrating radar (GPR) data in moderately heterogeneous dispersive media is presented. The method is based on wavefield extrapolation in the frequency–wavenumber (f–k) domain, from the solution of the 2D Maxwell's equations. The wavefield is extrapolated by a phase-shift technique using a constant relative permittivity K and a quality factor Q. It is then modified by a correction term to handle the lateral K and Q variations. The spatial distribution of the K and Q-factor values, representing the given model parameters, is introduced into the algorithm by a regular grid parametrization. The radar wave dispersion and attenuation, induced by relaxation processes, are taken into account by a linear frequency-dependent Q model, and expressed by a complex wavenumber in the propagation equation.A synthetic case and a field data set illustrate the potential of the method for frequencies of 300, 500 and 900 MHz. In the first case, a typical civil engineering problem is considered. The frequency dependence of the wave velocity and attenuation is well illustrated. The synthetic data are afterwards migrated using the initial model parameters. The results show the importance of using spatially varying model parameters in the migration processes. The second case concerns an application of the method to a real data set. In order to adjust the model parameters, a forward modelling sequence is performed until the best match between the measured and the synthetic data is achieved. A depth migration is then applied to the data, and the result is compared with the initial model parameters.In conclusion, we assess the contributions of the method to industrial applications, by discussing the performance of the algorithm compared with its limitations.

Notes: Vibroseis data recorded at short source–receiver offsets can be swamped by direct waves from the source. The signal-to-noise ratio, where primary reflections are the signal and correlation side lobes are the noise, decreases with time and late reflection events are overwhelmed. This leads to low seismic resolution on the vibroseis correlogram. A new precorrelation filtering approach is proposed to suppress correlation noise. It is the ‘squeeze-filter-unsqueeze’ (SFU) process, a combination of ‘squeeze’ and ‘unsqueeze’ (S and U) transformations, together with the application of either an optimum least-squares filter or a linear recursive notch filter. SFU processing provides excellent direct wave removal if the onset time of the direct wave is known precisely, but when the correlation recognition method used to search for the first arrival fails, the SFU filtering will also fail. If the tapers of the source sweeps are badly distorted, a harmonic distortion will be introduced into the SFU-filtered trace. SFU appears to be more suitable for low-noise vibroseis data, and more effective when we know the sweep tapers exactly. SFU requires uncorrelated data, and is thus cpu intensive, but since it is automatic, it is not labour intensive.  With non-linear sweeps, there are two approaches to the S,U transformations in SFU. The first requires the non-linear analytical sweep formula, and the second is to search and pick the zero nodes on the recorded pilot trace and then carry out the S,U transformations directly without requiring the algorithm or formula by which the sweep was generated. The latter method is also valid for vibroseis data with a linear sweep. SFU may be applied to the removal of any undesired signal, as long as the exact onset time of the unwanted signal in the precorrelation domain is known or determinable.

Notes: Accurate well ties are essential to practical seismic lithological interpretation. As long as the geology in the vicinity of the reservoir is not unduly complex, the main factors controlling this accuracy are the processing of the seismic data and the construction of the seismic model from well logs. This case study illustrates how seismic data processing to a near-offset stack, quality control of logs and petrophysical modelling improved a well tie at an oil reservoir. We demonstrate the application of a predictive petrophysical model in the preparation and integration of the logs before building the seismic model and we quantify our improvements in well-tie accuracy. The data for the study consisted of seismic field data from a 3D sail line through a well in a North Sea oilfield and a suite of standard logs at the well. A swathe of fully processed 3D data through the well was available for comparison. The well tie in the shallow section from first-pass seismic data processing and a routinely edited sonic log was excellent. The tie in a deeper interval containing the reservoir was less satisfactory: the phase errors within the bandwidth of the seismic wavelet were of the order of 20°, which we consider too large for subsequent transformation of the data to seismic impedance. Reprocessing the seismic data and revision of the well-log model reduced these phase errors to less than 10° and improved the consistency of the deep and shallow well ties. The reprocessing included densely picked iterative velocity analysis, prestack migration, beam-forming multiple attenuation, stacking the near-offset traces and demigration and remigration of the near-offset data. The petrophysical model was used to monitor and, where necessary, replace the P-wave sonic log with predictions consistent with other logs and to correct the sonic log for mud-filtrate invasion in the hydrocarbon-bearing sand. This editing and correction of the P-wave transit times improved the normal-incidence well tie significantly. The recordings from a monopole source severely underestimated the S-wave transit times in soft shale formations, including the reservoir seal, where the S-wave velocity was lower than the P-wave velocity in the drilling mud. The petrophysical model predicted an S-wave log that matched the valid recordings and interpolated between them. The subsequent seismic modelling from the predicted S-wave log produced a class II AVO anomaly seen on the CDP gathers around the well.

Notes: We design a velocity–porosity model for sand-shale environments with the emphasis on its application to petrophysical interpretation of compressional and shear velocities. In order to achieve this objective, we extend the velocity–porosity model proposed by Krief et al., to account for the effect of clay content in sandstones, using the published laboratory experiments on rocks and well log data in a wide range of porosities and clay contents.The model of Krief et al. works well for clean compacted rocks. It assumes that compressional and shear velocities in a porous fluid-saturated rock obey Gassmann formulae with the Biot compliance coefficient. In order to use this model for clay-rich rocks, we assume that the bulk and shear moduli of the grain material, and the dependence of the compliance on porosity, are functions of the clay content.Statistical analysis of published laboratory data shows that the moduli of the matrix grain material are best defined by low Hashin–Shtrikman bounds. The parameters of the model include the bulk and shear moduli of the sand and clay mineral components as well as coefficients which define the dependence of the bulk and shear compliance on porosity and clay content. The constants of the model are determined by a multivariate non-linear regression fit for P- and S-velocities as functions of porosity and clay content using the data acquired in the area of interest.In order to demonstrate the potential application of the proposed model to petrophysical interpretation, we design an inversion procedure, which allows us to estimate porosity, saturation and/or clay content from compressional and shear velocities.Testing of the model on laboratory data and a set of well logs from Carnarvon Basin, Australia, shows good agreement between predictions and measurements. This simple velocity-porosity-clay semi-empirical model could be used for more reliable petrophysical interpretation of compressional and shear velocities obtained from well logs or surface seismic data.

Notes: Gravity data are often acquired over long periods of time using different instruments and various survey techniques, resulting in data sets of non-uniform accuracy. As station locations are inhomogeneously distributed, gravity values are interpolated on to a regular grid to allow further processing, such as computing horizontal or vertical gradients. Some interpolation techniques can estimate the interpolation error. Although estimation of the error due to interpolation is of importance, it is more useful to estimate the maximum gravity anomaly that may have gone undetected by a survey. This is equivalent to the determination of the maximum mass whose gravity anomaly will be undetected at any station location, given the data accuracy at each station. Assuming that the maximum density contrast present in the survey area is known or can be reasonably assumed from a knowledge of the geology, the proposed procedure is as follows: at every grid node, the maximum mass whose gravity anomaly does not disturb any of the surrounding observed gravity values by more than their accuracies is determined. A finite vertical cylinder is used as the mass model in the computations. The resulting map gives the maximum detection error and, as such, it is a worst-case scenario. Moreover, the map can be used to optimize future gravity surveys: new stations should be located at, or near, map maxima. The technique is applied to a set of gravity observations obtained from different surveys made over a period of more than 40 years in the Abitibi Greenstone Belt in eastern Canada.

Notes: Restoration of missing offsets and trace interpolation is an interesting and important problem in seismic data processing. Based on the parabolic Radon transform, a method is presented for missing offset restoration, resampling and regularization of prestack individual CMP gathers. The method is also valid for resampling spatially aliased seismic data.The method is based on the parabolic assumption of the seismic events which is generally verified after a partial NMO correction in the CMP organization of the data. The essence of the method consists of a band-limited forward parabolic Radon transform of the data containing zero traces at the missing offset locations. The curvature range is chosen to map properly the coherent energy while the zero traces map beyond that range. After inverse transform the originally zero traces are partly filled with information. Several iterations of forward and inverse transform, every time replacing the zero traces in the original gather with the partially reconstructed ones, almost fully restore the zero traces.Efficient and fast algorithms can be built up to process data having a uniform geometry. Examples on synthetic as well as on field data demonstrate clearly the robustness of the method.

Notes: Sedimentary rocks beneath the Columbia River Basalt Group are recognized as having potential for oil and gas production, but the overlying layered basalts effectively mask seismic reflections from the underlying sediments. Four electromagnetic (EM) methods have been applied on profiles crossing Boylston Ridge, a typical east–west trending anticline of the Yakima Fold Belt, in an attempt to map the resistivity interface between the basalts and the sediments and to map variations in structure and resistivity within the sediments. The EM surveys detected strong variations in resistivity within the basalts, and in particular the continuous magnetotelluric array profiling (EMAP) revealed resistivity lows beneath the surface anticlines. These low resistivity zones probably coincide with fracturing in the core of the anticlines and they appear to correlate well with similar zones of low seismic velocity observed on a nearby seismic profile.The controlled-source EM surveys (in-loop transient, long-offset transient, and variable-offset frequency-domain) were designed in anticipation of relatively uniform high resistivity basalts, and were found to have been seriously distorted by the intrabasalt conductors discovered in the field. In particular, the resistivity sections derived from 1D inversions were found to be inconsistent and misleading. The EMAP survey provided the most information about the subsurface resistivity distribution, and was certainly the most cost-effective. However, both controlled-source and EMAP surveys call for accurate 2D or 3D inversion to accommodate the geological objectives of this project.

Notes: Five examples, obtained during exploration for hydrocarbons in the Pannonian Basin of Hungary, are used to show how the interpretation of seismic sections can be usefully complemented by results from MT surveys.Selection of the most appropriate MT quantities, considered to be proper ‘MT attributes’ for the purpose of visualization as well as recognition of the subsurface structures and the different inversions of MT data is essential for practical integration of seismic and MT surveys.A new technique providing a semiquantitive MT-attribute pseudosection for the purpose of visualization of the subsurface structures is proposed. The procedure utilizes derivative functions of the phase of MT impedance for visualization and derives estimated depths from the Bostick transformation of Cagniard apparent resistivities.On the basis of the MT-attribute pseudosections, constructed from the phase derivatives and transformed resistivity data, depths are estimated for interfaces between geological formations with significant resistivity contrast. In particular examples, the interface between the Tertiary sediments and the older basement rocks as well as tectonic fracture zones with decreased resistivity can be resolved.

Notes: A new 3D wavefield modelling approach based on dynamic ray tracing is presented. This approach is called wavefront construction, and it can be used in 3D models with constant or smoothly varying material properties (S- and P-velocity and density) separated by smooth interfaces. Wavefronts consisting of rays arranged in a triangular network are propagated stepwise through the model. At each time step, the differences in a number of parameters are checked between each pair of rays on the wavefront. New rays are interpolated whenever this difference between pairs of rays exceeds some predefined maximum value. A controlled sampling of the wavefront at all time steps is thus obtained. Receivers are given multiple-event values by interpolation when the wavefronts pass them. The strength of the wavefront construction method is that it is robust and efficient.

Notes: This work presents a new modelling scheme for the simulation of electromagnetic radio waves, based on a full-field simulator. Maxwell's equations are modified in order to include dielectric attenuation processes, such as bound- and free-water relaxation, ice relaxation and the Maxwell–Wagner effect. The new equations are obtained by assuming a permittivity relaxation function represented by a generalized Zener model. The convolution integral introduced by the relaxation formulation is circumvented by defining new hidden field variables, each corresponding to a different dielectric relaxation. The equations are solved numerically by using the Fourier pseudospectral operator for computing the spatial derivatives and a new time-splitting integration algorithm that circumvents the stiffness of the differential equations. The program is used to evaluate the georadar electromagnetic response of a Japanese burial site, in particular, a stone coffin-like structure.

Notes: The clay-sand mixture model of Xu and White is shown to simulate observed relationships between S-wave velocity (or transit time), porosity and clay content. In general, neither S-wave velocity nor S-wave transit time is a linear function of porosity and clay content. For practical purposes, clay content is approximated by shale volume in well-log applications. In principle, the model can predict S-wave velocity from lithology and any pair of P-wave velocity, porosity and shale volume. Although the predictions should be the same if all measurements are error free, comparison of predictions with laboratory and logging measurements show that predictions using P-wave velocity are the most reliable. The robust relationship between S- and P-wave velocities is due to the fact that both are similarly affected by porosity, clay content and lithology. Moreover, errors in the measured P-wave velocity are normally smaller than those in porosity and shale volume, both of which are subject to errors introduced by imperfect models and imperfect parameters when estimated from logs.Because the model evaluates the bulk and shear moduli of the dry rock frame by a combination of Kuster and Toksöz’ theory and differential effective medium theory, using pore aspect ratios to characterize the compliances of the sand and clay components, the relationship between P- and S-wave velocities is explicit and consistent. Consequently the model sidesteps problems and assumptions that arise from the lack of knowledge of these moduli when applying Gassmann's theory to this relationship, making it a very flexible tool for investigating how the vP-vs relationship is affected by lithology, porosity, clay content and water saturation. Numerical results from the model are confirmed by laboratory and logging data and demonstrate, for example, how the presence of gas has a more pronounced effect on P-wave velocity in shaly sands than in less compliant cleaner sandstones.

Notes: A publicly available and maintained electromagnetic finite-difference time domain (FDTD) code has been applied to the forward modelling of the response of 1D, 2D and 3D geophysical targets to a vertical magnetic dipole excitation. The FDTD method is used to analyse target responses in the 1 MHz to 100MHz range, where either conduction or displacement currents may have the controlling role. The response of the geophysical target to the excitation is presented as changes in the magnetic field ellipticity.The results of the FDTD code compare favourably with previously published integral equation solutions of the response of 1D targets, and FDTD models calculated with different finite-difference cell sizes are compared to find the effect of model discretization on the solution. The discretization errors, calculated as absolute error in ellipticity, are presented for the different ground geometry models considered, and are, for the most part, below 10% of the integral equation solutions.Finally, the FDTD code is used to calculate the magnetic ellipticity response of a 2D survey and a 3D sounding of complicated geophysical targets. The response of these 2D and 3D targets are too complicated to be verified with integral equation solutions, but show the proper low- and high-frequency responses.

Notes: The applications of electromagnetics have increased in the past two decades because of an improved understanding of the methods, improved service availability, and the increased focus of exploration in the more complex reservoir characterization issues. For electromagnetic methods surface applications for hydrocarbon Exploration and Production are still a special case, while applications in borehole and airborne research and for engineering and environmental objectives are routine.In the past, electromagnetic techniques, in particular deep transient electromagnetics, made up a completely different discipline in geophysics, although many of the principles are similar to the seismic one. With an understanding of the specific problems related to data processing initially and then acquisition, the inclusion of principles learned from seismics happened almost naturally. Initially, the data processing was very similar to seismic full-waveform processing. The hardware was also changed to include multichannel acquisition systems, and the field procedures became very similar to seismic surveying. As a consequence, the integration and synergism of the interpretation process is becoming almost automatic.The long-offset transient electromagnetic (LOTEM) technique will be summarized from the viewpoint of its similarity to seismics. The complete concept of the method will also be reviewed. An interpretation case history that integrates seismic and LOTEM from a hydrocarbon area in China clearly demonstrates the limitations and benefits of the method.

Notes: A correspondence principle is derived that relates the Green's functions (point-receiver responses to point-source excitations) for 2D transient diffusive electro-magnetic fields with electric field in the vertical plane to 2D seismic waves (in the acoustic approximation) with particle velocity in the vertical plane in arbitrarily inhomogeneous media. The constituent medium parameters in the two cases are related via two global proportionality constants. The kernels in the integral operators that express the diffusion phenomenon in terms of the wave phenomenon are of a smoothing nature. The fact that they are explicitly known can be of importance to the inverse operation. The correspondence principle is the fundamental tool in comparing the spatial resolving powers in the two methods of geophysical prospecting.

Notes: A case history is presented where electromagnetic (EM) methods were applied as a complement to seismic, for structural mapping in basin-and-range-like geology: 366 five-component magnetotelluric (MT) soundings were carried out together with 331 transient soundings (TDEM) along seismic lines.Due to high structural complexity, seismic shows a number of limitations. For the same reasons, MT is highly perturbed and three specific interpretation techniques were comprehensively applied:1. a classical correction of static effect using TDEM sounding, to determine the high-frequency nondistorted apparent resistivities and thus the corrected tensor;2. a so-called regional correction based upon the same concept as the static effect, to transform distorted resistivity curves due to the horst/graben situation into plausible 1D curves, through the use of nomograms built for 2D H-polarization situations;3. a stripping technique which made it possible to map areas where a deep conductive Mesozoic shale was present below carbonates, at a depth of 3 km.After the best MT interpretation was obtained along each line, it was integrated with seismic and with the results from two boreholes. A crude empirical law relating resistivity and acoustic velocity was established and the MT horizons were plotted on the two-way traveltime seismic sections.The final integrated cross-sections obtained are undoubtedly of greater use to the explorationist than the initial seismic sections alone and two wells were accurately predicted.

Notes: We investigate the magnetotelluric response of two-dimensional bodies, characterized by the presence of low-frequency dispersion phenomena of the electrical parameters. The Cole-Cole dispersion model is assumed to represent the frequency dependence of the ‘impedivity’ complex function, defined as the inverse of Stoyer's ‘admittivity’ complex parameter. To simulate real geological situations, we consider three structural models, representing a sedimentary basin, a geothermal system and a magma chamber, assumed to be partially or totally dispersive. From a detailed study of the frequency and space behaviours of the magnetotelluric parameters, taking known non-dispersive results as reference, we outline the main peculiarities of the local distortion effects, caused by the presence of dispersion in the target media. Finally, we discuss the interpretative errors which can be made by neglecting the dispersion phenomena. The apparent dispersion function, which was defined in a previous paper to describe similar effects in the one-dimensional case, is again used as a reliable indicator of location, shape and spatial extent of the dispersive bodies. The general result of this study is a marked improvement in the resolution power of the magnetotelluric method.

Notes: Highly non-linear seismic trace inversion problems can be solved efficiently by an implementation of Tabu Search, a meta-heuristic method related to artificial intelligence. The implementation under consideration is a deterministic, global search that combines the advantages ofa local search, giving a quick descent to local misfit minima, with an ability to cross misfit barriers in the model space. Once Tabu Search has found an area of low misfit, it performs an extensive exploration of its deepest points. This property makes it possible to use Tabu Search for a semiquantitative resolution and uncertainty analysis of the inverse problem.

Notes: A first-order one-way wave system has been created based on characteristic analysis of the acoustic wave system and optimization of the dispersion relation. We demonstrate that this system is equivalent to a third-order scalar partial-differential equation which, for a homogeneous medium, reduces to a form similar to the 45° paraxial wave equation. This system describes accurately waves propagating in a 2D heterogeneous medium at angles up to 75°.The one-way wave system representing downgoing waves is used for a modified reverse time migration method. As a wavefield extrapolator in migration, the downgoing wave system propagates the reflection events backwards to their reflectors without scattering at the discontinuities in the velocity model. Hence, images with amplitudes proportional to reflectivity can be obtained from this migration technique. We present examples of the application of the new migration method to synthetic seismic data where P-P reflections P-SV converted waves are present.Absorbing boundaries, useful in the generation of synthetic seismograms, have been constructed by using the one-way wave system. These boundaries absorb effectively waves impinging over a wide range of angles of incidence.

Notes: The filter for wave-equation-based water-layer multiple suppression, developed by the authors in the x-t, the linear τ-p, and the f-k domains, is extended to the parabolic τ-2 domain. The multiple reject areas are determined automatically by comparing the energy on traces of the multiple model (which are generated by a wave-extrapolation method from the original data) and the original input data (multiples + primaries) in τ-p space. The advantage of applying the data-adaptive 2D demultiple filter in the parabolic τ-p domain is that the waves are well separated in this domain. The numerical examples demonstrate the effectiveness of such a dereverberation procedure. Filtering of multiples in the parabolic τ-p domain works on both the far-offset and the near-offset traces, while the filtering of multiples in the f-k domain is effective only for the far-offset traces.Tests on a synthetic common-shot-point (CSP) gather show that the demultiple filter is relatively immune to slight errors in the water velocity and water depth which cause arrival time errors of the multiples in the multiple model traces of less than the time dimension (about one quarter of the wavelet length) of the energy summation window of the filter. The multiples in the predicted multiple model traces do not have to be exact replicas of the multiples in the input data, in both a wavelet-shape and traveltime sense. The demultiple filter also works reasonably well for input data contaminated by up to 25% of random noise. A shallow water CSP seismic gather, acquired on the North West Shelf of Australia, demonstrates the effectiveness of the technique on real data.

Notes: We have monitored changes in seismic velocity due to longwall coal-mining in the Selby coalfield, Yorkshire, England by. ten repeated surveys of a surface seismic reflection profile. The direction of face advance in the Barnsley Seam, at 550 m depth, was parallel to the orientation of the profile. The traveltime of a strong reflection event from an anhydrite bed at 150 m depth was measured after processing the data with standard techniques. As the face advanced, the traveltime increased by about 4% overall. In detail, the progressive increase in traveltime correlates well with empirical calculations of differential subsidence between the surface and the anhydrite. However, the magnitude of the change must principally be accounted for by a decrease in seismic velocity, which we attribute to a reduction in the vertical effective stress.

Notes: Inversion for S-wave velocities from the amplitude variation with offset of P-wave data is far from being a standard routine in the seismic processing sequence. However, the need for tracking the amplitude versus offset (AVO) occurs in several situations, for example in order to estimate the zero-offset amplitude, to reveal areas with particular AVO characteristics, or to compress the AVO so that it is more easily obtainable at a later stage of the seismic processing. Furthermore, weak reflections can occasionally, due to the effect of the angle-dependent reflectivity, have a polarity-shift with offset, resulting in a very poor, or even vanishing, stack response. In such cases, the reflection event has to be represented by some other property than its mean amplitude or stack value.We outline how the AVO of seismic data may be extracted and classified by the use of orthogonal polynomials. The main advantage of this method compared to a general polynomial fit is that the AVO may be classified by a unique Spectrum of polynomial coefficients. This is in analogy to Fourier coefficients where the orthogonal basis is harmonic functions. The set of orthogonal polynomials is constructed entirely from the set of offset coordinates, and these polyno-mials are defined only on the offset window considered. Compared to a Fourier transform, this is a major advantage since there is no effect of a limited spatial bandwidth.The AVO of normal-moveout corrected data may be represented by a data gather where the orthogonal polynomial coefficients are given as time traces with each trace revealing a certain AVO characteristic. For instance, the stack is proportional to the zeroth-order coefficient, the mean gradient is given by the firstorder coefficient, while the second-order coefficient indicates whether the AVO increases and then decreases, or vice versa.

Notes: The Belvedere Spinello salt mine is located in the Catanzaro Province of Calabria in Southern Italy. An extensive mining program has caused the development of Underground cavities filled with brine and the migration of this brine has been of great environmental concern to the mine owners. This paper presents the results of a multidimensional interpretation of a two-phase resistivity and magnetotelluric (MT) survey that was performed in an attempt to determine the complex conductivity structure of the mine area and to gain information on brine development and migration pathways. Key resistivity soundings were interpreted using a 2.5D algorithm based on the Polozhii decomposition method. The MT data were interpreted using a 2D finite-element code. A conductivity model was developed, integrating available geological and drill-hole information. The interpretation of the MT data, collected five years after the acquisition of the resistivity data, shows a conductive feature of depth that is not resolved in the resistivity interpretation. This feature has been interpreted as a thick brine zone that has developed as a result of mining during the interval between the resistivity and the MT measurements.

Notes: Following a previous paper in which the principles of a 3D ground-surface tomographic processing of self-potential data were established, we extend the method to active source geoelectric surveying. The main purpose of the new tomographic approach is to obtain a physical image reconstruction of the induced electric charges distributed over buried resistivity discontinuities. The information is produced in a probabilistic sense, as the mathematical formulation underlying the method treats only the intrinsic physical nature of the generated electric field underground and the method of its ground-surface detection, independently of the geometry of the unknown structures. In practice, a 3D tomography is realized by cross-correlating a set of distributed electric-field ground-surface data with a scanning function, representing a unit positive point charge located anywhere in the lower half-space. The resolution of the method is tested on the synthetic response of a 3D structural simulation of an archaeological target, consisting of an infinitely resistive prismatic body immersed in a half-space, including surface inhomogeneities and layering. Finally, the field response of a 3D structure consisting of a hypogeal dromos-chamber tomb inside the Sabine Necropolis at Colle del Forno, close to Rome, is presented and discussed.

Notes: A guided wave along a borehole is often observed in borehole radar measurements. These guided waves deform the antenna pattern and can cause artefacts in radar measurements. A water-filled borehole or a conducting logging cable can function as a waveguide for electromagnetic waves under some conditions. We describe the theoretical characteristics of such a guided wave in a borehole and compare them with our experiments. The measured signal discussed was obtained with a directional borehole radar. This radar uses a cylindrical conformal array antenna as receiver and is a model of a conducting structure in a borehole. The induced field around the borehole was compared with the theory. The most fundamental symmetrical and asymmetrical modes were TM01 and HE11, and they were identified in the measured signals using time–frequency distribution analysis and by observation of the azimuthal field distribution of the magnetic field.

Notes: The electrical method presented is used for determining the resistivity of lake-bottom sediments and is based on the d.c. electrical sounding principles. The electrode array, called the fishing rod (FR), is of pole-pole type and is orientated vertically on a line perpendicular to the surface of the water. The technique is used for mapping resistivity anomalies located deep underwater. This paper presents an analysis of the resolution capabilities of the FR method and the results of a case study carried out in Lake Geneva, where measurements were interpreted using a one-dimensional (1D) multilayer earth model. The analysis of the uncertainty in the model parameters of a 1D multilayer earth model is carried out using the covariance matrix of the linearized inversion problem. The results of the analyses show that when the thickness and resistivity of the water layer is known, the resistivity of the sediment layer is well determined under most circumstances. The thickness of the sediment layer is well determined when resistivity contrasts are not too low. In Lake Geneva the FR method has been used to study an old depression with a resistive channel. This application shows the efficiency of the method compared with conventional electrical methods, where water depth becomes a limiting factor. The use of an automated iterative inversion scheme in this particular case is advantageous, as a joint interpretation of the three different data sets measured with the FR method can be carried out. Finally, the result of the inversion is compared with the trial-and-error interpretations of a previous study.

Notes: Minimum variance unbiased (MVU) beamforming is a type of multichannel filtering which extracts coherent signals without distortion, whilst minimizing residual noise power. Adaptive beamforming estimates signal and noise characteristics as part of the extraction process. The adaptive beamformer used here is designed from models of primary and multiple reflection signals having parametrically specified moveout and amplitude variation with offset (MVO and AVO). Phase variation with offset (PVO) can also be included but it is not usually justified in practice. The resulting analysis provides data for input into AVO and PVO schemes for obtaining lithological information. Synthetic data examples illustrate details of implementation of parametric adaptive MVU beamforming and the response characteristics of the resultant design. Real data examples show that data-adaptive beamforming is more flexible and more effective in attenuating multiples in prestack common-midpoint seismic data than Radon transform methods. In common with other prestack multichannel processes, the advantages of beamforming are shown to best effect in data with a good signal-to-noise ratio.

Notes: Known mineral occurrences in northern Vancouver Island are typically hosted in volcanic units of the Bonanza Group. At a local scale, the mineralization is associated with advanced argillic bedrock alteration and is often intimately related to porphyry intrusions. On a larger scale, faults are thought to exert the most significant control on the distribution of mineralized host rocks. Poor exposures and a complex glacial history limit the use of traditional methods of geological mapping and mineral exploration in this region and to date geophysical methods have been under-utilized. Here we present findings from four standard geophysical (gravity, magnetics, electromagnetics and seismic refraction) methods, recently deployed here to elucidate the subsurface geology, as well as to identify new targets for base metal exploration.Results at two different sites show that the integrated interpretation of geophysical data, constrained by physical rock property measurements, yields detailed images of the subsurface at a fraction of the cost of drilling. At one site, east of Rupert Inlet, the final subsurface model shows that the Bonanza Group is not nearly as extensive as previously presumed. An extension of the Holberg Fault is identified some 50 km east of the visibly mapped outcrop and an extensive zone of alteration around the fault is recognized. Furthermore, a number of the methods provide support for the existence of a porphyry dike at this site. At the second site, north of Rupert Inlet, magnetic and electromagnetic data prove effective at mapping alteration and locating shear zones beneath a relatively thin drift cover. Together, these results help outline a strategy for exploration in drift-covered terrains and show that a redirection of exploration effort is warranted in the case of northern Vancouver Island.

Notes: The significant development in acoustic full waveform logging during the last ten years has made it increasingly possible for log analysts to determine the physical properties of a rock formation in situ.Parallel to the methods applied to a single wavetrain during seismic processing, the new techniques, used for sets of wavetrains, have been successfully tested with acoustic full waveforms. Instantaneous characteristics analysis is included in this group of methods. This approach, leading to qualitative and quantitative interpretation, reveals the influence of small changes in physical properties on acoustic full wavetrains.Applications of complex acoustic waveform analysis for the determination of inhomogeneous zones are presented. Colour diagrams of instantaneous characteristics are used for the detection of fractured regions and slow formations with increased attenuation of acoustic waves.Results of the interpretation of individual acoustic full waveforms, based on cross-correlation and spectral analysis, using the IDNP and IDNS computer programs, e.g. velocities of compressional waves, shear and Stoneley waves, are presented. Since the bulk density of the rocks was known, it was possible, using the velocities of P- and S-waves obtained, to calculate the dynamic elastic moduli. We used the interpretation of acoustic full wavetrains to calculate porosity. The sonic porosity is compared to the porosity obtained from other logs and to that obtained from core sample analysis.The examples of acoustic full wavetrains were recorded in the Miocene sulphur-bearing limestones in central Poland. Field measurements were made using the domestic prototype equipment for well log recordings in shallow boreholes.

Notes: A tomographic imaging technique combined with coherence inversion is proposed for constructing a near-surface model from refraction events. A model obtained from coherence inversion serves as a good background model for the tomographic reconstruction. A simultaneous iterative reconstruction technique (SIRT) algorithm was used for this purpose. This is a simple algorithm and can be easily adapted to irregular acquisition geometry and limited angular aperture. Using synthetic data it was shown that the proposed procedure can be used for determination of local velocity anomalies in a shallow subsurface. The technique was also tested on a real data set.

Notes: A deterministic near-surface correction procedure is developed for multicomponent VSP data, shot using directional sources and recorded using three-component receivers. The method is capable of removing unwanted effects of acquisition such as unequal source strengths or misorientations, but may also remove near-surface multiples and anisotropy. This is of considerable benefit for obtaining accurate and consistent estimates of subsurface anisotropy from different source combinations. Application of the technique is illustrated using a dataset from the Romashkino reservoir in Russia, where three or four different directional sources are used at the same source locations. The technique corrects for the large discrepancies which exist between the estimates obtained using different source combinations. Application of the technique to three wells in the survey region reveals a nearly isotropic subsurface, except for a few isolated zones of moderate to high (2 to 8%) anisotropy which lie close to the expected depth for the reservoir. Although there is no significant correlation with the production figures for each well, the qS1 polarization azimuth within the reservoir does vary at each well location, suggesting that this may be a more sensitive indicator of reservoir Drocess.

Notes: Computational seismic modelling (CSM) plays an important role in the geophysical industry as an established aid to seismic interpreters. Numerical solution of the elastic wave equations has proved to be a very important tool for geophysicists in both forward modelling and migration. Among the techniques generally used in CSM, we consider the finite-element method (FEM) and investigate its computational and visualization requirements. The CSMFEM program, designed for this purpose and developed on an IBM 3090 computer with vector facility, is described in detail. It constitutes a numerical laboratory for performing computer experiments. Two Newmark type algorithms for time integration are compared with other time integration schemes, and both direct and iterative methods for solving the corresponding large sparse system of linear algebraic equations are analysed. Several numerical experiments to simulate seismic energy propagation through heterogeneous media are performed. Synthetics in the form of common shot gathers, vertical seismic profiles and snapshots are suitably displayed, since with the large amounts of data obtained from CSM research, methods for visualization of the computed results must be developed. The FEM is compared with other numerical tools, such as finite-difference and pseudo-spectral methods.

Notes: A 2D reflection tomographic method is described, for the purpose of estimating an improved macrovelocity field for prestack depth migration. An event-oriented local approach of the ‘layer-stripping’ type has been developed, where each input event is defined by its traveltime and a traveltime derivative, taken with respect to one of four coordinates in the source/receiver and midpoint half-offset systems.Recent work has shown that the results of reflection tomography may be improved by performing event picking in a prestack depth domain. We adopt this approach and allow events to be picked either before or after prestack depth migration. Hence, if events have been picked in a depth domain, such as the common-shot depth domain or the common-offset depth domain, then a depth-time transformation is required before velocity estimation. The event transformation may, for example, be done by conventional kinematic ray tracingr and with respect to the original depth-migration velocity field. By this means, we expect the input events for velocity updating to become less sensitive to migration velocity errors.For the purpose of velocity estimation, events are subdivided into two categories; reference horizon events and individual events. The reference horizon events correspond to a fixed offset in order to provide basic information about reflector geometry, whereas individual events, corresponding to any offset, are supposed to provide the additional information needed for velocity estimation. An iterative updating approach is used, based on calculation of derivatives of event reflection points with respect to velocity. The event reflection points are obtained by ray-theoretical depth conversion, and reflection-point derivatives are calculated accurately and efficiently from information pertaining to single rays. A number of reference horizon events and a single individual event constitute the minimum information required to update the velocity locally, and the iterations proceed until the individual event reflection point is consistent with those of the reference horizon events. Normally, three to four iterations are sufficient to attain convergence. As a by-product of the process, we obtain so-called uncertainty amplification factors, which relate a picking error to the corresponding error in the estimated velocity or depth horizon position.The vector formulation of the updating relationship makes it applicable to smooth horizons having arbitrary dips and by applying velocity updating in combination with a flexible model-builder, very general macro-model structures can be obtained. As a first step in the evaluation of the new method, error-free traveltime events were generated by applying forward ray tracing within given macrovelocity models. When using such ‘perfect’ observations, the velocity estimation algorithm gave consistent reconstructions of macro-models containing interfaces with differential dip and curvature, a low-velocity layer and a layer with a laterally varying velocity function.

Notes: The gas industry is continuing to concentrate its research and development efforts on new and advanced technology to improve reservoir descriptions through the producing life and development history of heterogeneous gas reservoirs. A very important aspect of this need is the ability to reduce the uncertainty of estimating probable reserves and to lower the operating costs to recover incremental reserves in producing and depleted gasfields. Established methods for reducing uncertainty in heterogeneous reservoir compartments, such as VSP and cross-well techniques may enhance resolution, but they are currently not economically justifiable in on-shore gasfields. Continuity logging using guided waves is an alternative approach to analysing inter-well seismic data to confirm the continuity of heterogeneous gas reservoir compartments; in particular, the continuity of sand and shale stratigraphy in gas reservoirs.The solution of a coupled system of differential equations based on Biot and homogenization theories is adapted to calculate guided seismic waves trapped in low-velocity layers. The general solution is for a 3D source in a horizontally layered poroviscoelastic medium having isotropic and laterally homogeneous material properties. A unified representation of the medium that includes fluid-solid interactions and viscoelastic losses is incorporated into the solution. The guided-wave part of the vector wave field and fluid-pressure of the complete wave motion in layered dissipative media is verified and used to simulate dispersion and attenuation of guided seismic waves for continuity logging applications. The results of this work suggest that the multimode wave solution is appropriate to simulate guided seismic wave signatures to indicate continuity of layered earth structures in poroviscoelastic reservoirs. In particular, the normal mode information can be used for planning continuity logging surveys and for interpreting the corresponding seismic data. Further, fluid-pressure waveforms show that maximum amplitude normal modes can be detected at layer interfaces in fluid-filled porous media, and the corresponding Airy phase wave groups may carry information on the formation permeability.

Notes: A concise derivation is given for the downward continuation of the tangential fields on the surface to yield expressions for the fields at a specified depth. A homogeneous slab region is assumed for the analysis.

Notes: The near-surface layer is modelled as a constant-velocity layer with varying thickness. The base of the layer is described by a B-spline curve. The optimum model is calculated by minimizing, with respect to the model parameters, the difference between traveltimes predicted by the model and those observed in the data. Once a model has been produced, corrections that are dependent on the raypath geometry through the near-surface layer can be calculated.The effect of the near-surface layer is normally considered to be consistent at each shot or geophone station for all traveltimes arriving at that location (the surface-consistent approximation). This assumption linearizes the problem, allowing timeshifts to be calculated and the traveltimes corrected to a chosen datum, representing static corrections. The single correction at each point is an averaged correction, based on an assumption that is particularly inaccurate in the presence of lateral variations of velocity or thickness of the surface layer, in the presence of large surface layer velocities or in the presence of a thick surface layer. The method presented considers the non-linear relationship between data and model explicitly, hence the correction that is dependent on the raypath. Linearization removes this dependence and reduces the problem to a surface-consistent approximation.The method is applied to synthetic data calculated from a model with surface layer variations. Comparisons are made between the corrected data resulting from the method described here and the conventional surface-consistent approach. From these results it becomes apparent that the near-surface layer inversion method presented here can reproduce accurate models and correct for near-surface layer effects in cases where conventional methods encounter difficulties. Additionally the method can be readily extended to 3D.

Notes: Refraction seismics and modern tomographic surveys were employed at the Platanovrissi dam site on the Nestos river in northern Greece in an effort to investigate the dynamic elastic properties and rockmass condition of gneiss-schist outcropping in the area under investigation. Six seismic refraction traverses were run on the ground surface, inside the exploratory tunnels and between tunnels and the ground surface. The results provided information about the low-velocity surface layer parameters and the stress relief zones on the walls of all the tunnels in which seismic tomography tests were performed. Ultrasonic tests, conducted both in situ and in the laboratory, enabled the determination of the ratio Vp/Vs and the Poisson's ratio calculation. From the tomography data analysis and the geological interpretation of the results, three main velocity zones, ranging between 3500 and 4000, 3000 and 3500 and less than 3000m/s, were detected in each tunnel. High-velocity zones were found to be compatible with the hard rockmass of gneiss-schist material, while moderate velocities are closely related to jointed and fractured zones. Finally, low-velocity zones were well correlated with weathered gneiss-schist material.

Notes: The prospecting of densely urbanized areas by the measurement of magnetic and electric natural fields is severely hampered by electromagnetic (EM) noise. Active man-made EM noise sources can generally be considered fixed in space, thus affecting the magnetotelluric (MT) signals of a measuring site mainly along their polarization directions.Taking advantage of the impulsive nature of polarized EM noise, a time-domain directional noise cancelling (DNC) technique is proposed. The comparison of noisy data with data predicted, using a low noise reference signal or with data interpolated whenever no reference is available, allows the detection of the most likely noise sources with prevailing directional patterns using a Bayes's criterion. The DNC approach is general and can be adapted, depending on the reference signal used (single-site or remote-reference).In field data, hodograms of the prediction residuals basically confirm the directional noise model assumed in DNC. An example is presented in which the DNC technique has been applied to a single-site MT survey carried out in northern Italy, where the signal was heavily corrupted by noise with prevailing directional properties due to the densely urbanized area. MT apparent resistivities and phases obtained at the site of the survey before and after DNC are presented and discussed.

Notes: A new approach to deconvolution has been developed to improve the attenuation of multiple energy. This approach to deconvolution is unique in that it not only eliminates the usual assumptions of a minimum phase lag wavelet and a random distribution of impulses, but also overcomes the noise limitation of the homomorphic deconvolution and its inherent instability to phase computation.We attempt to analyse the continuous alteration of the acoustic waveform during the propagation through a linear system. Based on the results of this analysis, the surface-related measurements are described as a convolution of the impulse response of the system with the non-stationary forward wavelet which includes all multiple terms generated within the system.The amplitude spectrum of the forward wavelet is recovered from the amplitude spectrum of the recorded signal, using the difference between the rate of decay of the source wavelet and the duration of the measurement.The phase spectrum of the forward wavelet is estimated using the Hilbert transform and the fact that the mixed phase lag wavelet can be presented as a convolution of the minimum and maximum phase lag wavelets.The multiples are discriminated from primaries by comparison of the phase spectrum of the seismic signal and the inverse of the forward wavelet. Therefore, the technique is called phase inversion deconvolution (PID). This approach requires no velocity information in order to recognize and attenuate multiple energy. Therefore, primary energy is recovered in the near-offset region where the velocity differential between primary and multiple energies is very small.

Notes: The inversion of resistivity profiling data involves estimation of the spatial distribution of resistivities and thicknesses of rock layers from the apparent resistivity data values measured in the field as a function of electrode separation. The drawbacks of using traditional curve-matching techniques to solve this inverse problem have been overcome by iterative linear techniques but these require good starting models even if the shape of the causative body is asssumed known. In spite of the recent developments in inversion techniques, no robust method exists for the inversion of resistivity profiling data for the simple model of dikes and spheres which are the classical models of geophysical prospecting.We apply three different non-linear inversion schemes to invert synthetic resistivity profiling data for the classical models embedded in a uniform matrix of contrasting resistivity. The three non-linear algorithms used are called the Metropolis simulated annealing (SA), very fast simulated annealing (VFSA) and a genetic algorithm (GA). We compare the performance of the three algorithms using synthetic data for an outcropping vertical dike model. Although all three methods were successful in obtaining optimal solutions for arbitrary starting models, VFSA proved to be computationally the most efficient.

Notes: In order to detect underground cavities, we have designed a geophysical method based on the interaction of a monochromatic electromagnetic wave in the frequency band 100 MHz to 1 GHz with the ground situated between two boreholes.Three different approaches are involved in the design of this EM tomographic method.〈list xml:id="l1" style="custom"〉1The application of an ‘exact’ theory is used to calculate artificial data, based on an integral equation method. These data are inverted using a tomographic algorithm whose basic assumptions are rather coarse. The results show that, however, cavities can very well be detected and their position recovered.2Data are obtained with a physical reduced-scale model in a water tank, in which all parameters are known in advance. The inversion process confirms the validity of the method.3Underground cavities are actually detected.The above approaches are described and discussed and results are shown. The equipment involved and its operation is quite simple: the surface devices are commercially available and only the transmitter and receiver antennae must be specially built. The method is shown to be quite efficient and its cost should be reasonably low.

Notes: The stable-beam method for forward modelling of seismic data is introduced. The method is applicable to geometries which may be approximated by a series of single-valued (in depth) interfaces separating constant-velocity layers. For models of this restricted type, the results are of similar accuracy to those from waveequation-based methods whilst the run times are similar to, or better than, those for simple ray-tracing approaches. The basis of the method is to approximate interfaces by a series of straight-line segments. This allows very rapid and stable ray tracing through the model. Pseudodiffractions are then added from all of the interface discontinuities formed between adjacent segments. These pseudodiffractions have the effect of correcting for the phase, amplitude and wavefront continuity errors introduced by the interface approximation. Comparison of the stable-beam results to analytical, Kirchhoff, finite-difference and physical model results confirm the accuracy ofthe technique.

Notes: A migration algorithm appropriate for moderately varying lateral velocity changes is developed as an extension of phase-shift migration by using a variable-length spatial transform. This process significantly reduces the number of lateral wave-numbers necessary to downward continue the data, and it replaces the spatial FFT with a simple recursion relationship. For a given frequency and position x, ten lateral wavenumbers are typically sufficient, and the migration algorithm produces accurate images when the velocity structure V (X, z) changes over a few depth intervals of thickness Δz, with lateral velocity gradients up to 1.4 to 1.0.

Notes: A method is reported for the production of synthetic porous sandstones containing cracks of known dimensions and geometry with respect to the matrix. A synthetic sandstone was manufactured from Sand cemented with an epoxy glue. The cracks of known geometry were introduced into the material in the manufacturing stage, by emplacing thin metallic discs in the Sand-epoxy matrix. These discs were chemically leached out of the consolidated porous sandstone. Acoustic anisotropy. and shear-wave splitting were observed in the synthetic sandstones. For the dry sample the observed angular dependence of the P- and S- wave velocities (at 100 kHz) compares well, qualitatively, with the theoretical models of Hudson and of Thomsen. Quantitatively, however, the experimental data fits Hudson's model better. For the case of a saturated sample the experimental results are in excellent agreement with Thomsen's model. Hudson's model, on the other hand, predicts a different angular dependence for P-waves. This demonstrates that the concept of fluid transfer between cracks and the ambient porosity can be a significant process. The results reported here are from the first successful experiment in which the theoretical models were tested on a porous material containing a known crack geometry.

Notes: All theoretical expressions which relate the characteristics of saturated aligned cracks to the associated elastic anisotropy are restricted in some important way, for example to the case of stiff pore fluids, or of the absence of equant porosity, or of a moderately high frequency band. Because of these restrictions, previous theory is not suitable for application to the upper crust, where the pore fluid is brine (Kf≅ K820), the equant porosity is often substantial (φp 〉 0.1), and the frequency band is sonic to seismic. This work removes these particular restrictions, recognizing in the process an important mechanism of dispersion. A notable feature of these more general expressions is their insensitivity, at low frequency, to the aspect ratio of the cracks; only the crack density is critical. An important conclusion of this more general model is that many insights previously achieved, concerning the shear-wave splitting due to vertical aligned saturated cracks, are sustained. However, conclusions on crack orientation or crack aspect ratio, which were derived from P-wave data or from shear-wave‘critical angles’, may need to be reconsidered. Further, the non-linear coupling between pores and cracks, due to pressure equalization effects, means that the (linear) Schoenberg-Muir calculus may not be applied to such systems. The theory receives strong support from recent data by Rathore et al. on artificial samples with controlled crack geometry.

Notes: The aim of this work is to consider the phenomenon of negative response and its detectability in a polarizable half-space formed of Clay-water mixture which commonly exists in water aquifers and which can be used as a simple indicator of the presence of Underground water.We make use of an analytical treatment for the transient voltage induced in a coincident loop lying on a half-space as a basis for our computations. A Cole-Cole model is used to represent the Clay with appropriate parameters.As saturated Clay is characterized by high conductivity and moderate chargeability, it is hardly detectable relative to the practical noise level. However, there are optimum Clay parameters that offer a maximum negative response. It is also observed that for a very short time constant τ in the Cole-Cole model, the amplitude of the negative response decreases with the decrease of the time constant due to the fast decay of the polarization current.Finally, it is found that there is an optimum value for the loop radius which gives the largest value of the negative response and this loop radius depends on the model parameters.

Notes: Laboratory measurements of soil samples are necessary to assess the effect of mineralogy, grain size distribution, moisture content, and electrolyte composition on the resistivity spectrum of soil material. Laboratory results are also required for the interpretation of field data. Induced polarization phenomena in glacial soils are poorly understood and so far no convenient laboratory techniques are available for its measurement. Coarse grain size and the need to measure unsaturated samples and to monitor the homogeneity of the sample require a sample holder–electrode construction that differs from those presented in Clay mineral Studies.This study presents a spectral induced polarization laboratory system that is suitable for measuring fine- and coarse-grained and both saturated and unsaturated soil samples. The noise caused by the electrode–electrolyte interface is studied in detail. It is shown that easy-to-use platinum or acid-free steel potential electrodes are convenient over a broad frequency band ranging from 0.016Hz up to more than 1000 Hz. The laboratory experiments and comparisons between laboratory and field results also indicate that sampling and sample packing procedures have only a minor influence on the phase spectrum of glacial soils.

Notes: Source-generated energy in seismic vibrator records includes ultraharmonics, subharmonics, ultra-subharmonics and possibly chaotic oscillatory behaviour. Nonlinear behaviours can be modelled using a ‘hard-spring’ form of the Duffing equation. Modelling indicates that a qualitatively similar harmonic resonance structure is present for a broad range of possible mathematical descriptions. Qualitative global system behaviours may be examined without knowledge of actual earth parameters. Non-linear resonances become stronger, relative to fundamental sweep frequencies, as the driving force increases or damping decreases. System response energy levels are highest when non-linear resonances are strong. The presence of chaotic energy can indicate the highest energy state of a system reponse. Field data examples are consistent with behaviours predicted by modelling. Conventional correlation and stack uses a fraction of the energy produced in the earth-vibrator system. A correlation and filtering process that uses a representation of the source dynamics based on the system response can reduce signal degradation due to non-linear resonance.

Notes: Results from walkaway VSP and shale laboratory experiments show that shale anisotropy can be significantly anelliptic. Heterogeneity and anellipticity both lead to non-hyperbolic moveout curves and the resulting ambiguity in velocity analysis is investigated for the case of a factorizable anisotropic medium with a linear dependence of velocity on depth. More information can be obtained if there are several reflectors. The method of Dellinger et al. for anisotropic velocity analysis in layered transversely isotropic media is examined and is shown to be restricted to media having relatively small anellipticity. A new scheme, based on an expansion of the inverse-squared group velocity in spherical harmonics, is presented. This scheme can be used for larger anellipticity, and is applicable for horizontal layers having monoclinic symmetry with the symmetry plane parallel to the layers. The method is applied to invert the results of anisotropic ray tracing on a model Sand/shale sequence. For transversely isotropic media with small anisotropy, the scheme reduces to the method of Byun et al. and Byun and Corrigan. The expansion in spherical harmonics allows the P-phase slowness surface of each layer to be determined in analytic form from the layer parameters obtained by inversion without the need to assume that the anisotropy is weak.

Notes: Compressional and shear-wave velocities have been measured and a novel approach using digital processing employed to study wave attenuation for brine- and gas- saturated sandstones, over a range of effective stresses from 5 to 60 MPa. Also measured were the complex conductivity in the brine-saturated state and permeability in the gas-saturated state over the same range of stresses as for the velocity measurements. Broadband ultrasonic pulses of P- and orthogonally polarized S-waves in the frequency range 0.3–0.8 MHz are transmitted through the specimen to be characterized for comparison with a reference (aluminium) having low attenuation. The attenuation is calculated in terms of the quality factor Q from the Fourier spectral ratios, using the frequency spectral ratios technique. The corrections necessary for the effects of diffraction due to the finite size of the ultrasonic transducers have been carried out for the case of measurements under lower confining stress. To interpret the laboratory measured velocity and attenuation data under the physical conditions of this study and to estimate the effects of pore structure, numerical modelling of velocities and attenuation as functions of the confining stress have been performed, based on the MIT model. Theoretical models based on several hypothesized attenuation mechanisms are considered in relation to laboratory data of the effects of confining pressure, fluid saturation and pore structure on attenuation. Numerical calculations using these models with the experimental data indicate that friction on thin cracks and grain boundaries is the dominant attenuation mechanism for dry and brine-saturated sandstones at low effective stresses for the frequencies tested. However, for brine-saturated sandstones at moderately high effective stresses, fluid flow could play a more important role in ultrasonic S-wave attenuation, depending on the pore structure of the sample.

Notes: We consider the calculation of the electrical field quantities, electric potential and the vertical component of the total volume density of electric current, in a horizontally layered, piecewise homogeneous and arbitrarily anisotropic earth due to a system of direct current point sources. By applying Fourier transformation with respect to the horizontal space coordinates to the static field equations, the field quantities are obtained as the solutions of the system of transform-domain differential equations in the vertical (depth) coordinates. A recurrence scheme has been given to compute the tranform-domain field quantities at any depth. The corresponding space-domain quantities are then obtained by inverse Fast Fourier Transformation (FFT). A complete computer program has been developed for computing the electric potentials at any depth of the layered earth, which is composed of an arbitrary number of anisotropic layers with arbitrary conductivity tensors. By considering the point sources at different depths from the surface, equipotential contours on the surface of arbitrarily anisotropic layered earth models are given.

Notes: Seismic refractions have different applications in seismic prospecting. The travel- times of refracted waves can be observed as first breaks on shot records and used for field static calculation. A new method for constructing a near-surface model from refraction events is described. It does not require event picking on prestack records and is not based on any approximation of arrival times. It consists of the maximization of the semblance coherence measure computed using shot gathers in a time window along refraction traveltimes. Time curves are generated by ray tracing through the model. The initial model for the inversion was constructed by the intercept-time method. Apparent velocities and intercept times were taken from a refraction stacked section. Such a section can be obtained by appling linea moveout corrections to common-shot records. The technique is tested successfully on synthetic and real data. An important application of the proposed method for solving the statics problem is demonstrated.

Notes: A new method of numerical computation of elastic wavefields in regions containing caustics is tested. The method is an extension of the asymptotic ray theory (ART). The essential features of the method consist of the application of expressions which are well defined at caustics and expressed in terms of ray tracing combined with complex ray tracing in caustic shadows. The method and an outline of the underlying theory are briefly presented, followed by a comparison with finite differences on a test model involving a caustic cusp. The comparison reveals the unexpectedly high degree of accuracy of the new method.

Notes: An amplitude-preserving migration aims at imaging compressional primary (zero-or) non-zero-offset reflections into 3D time or depth-migrated reflections so that the migrated wavefield amplitudes are a measure of angle-dependent reflection coeffcients. The principal objective is the removal of the geometrical-spreading factor of the primary reflections. Various migration/inversion algorithms involving weighted diffraction stacks proposed recently are based on Born or Kirchhoff approximations. Here, a 3D Kirchhoff-type zero-offset migration approach, also known as a diffraction-stack migration, is implemented in the form of a time migration. The primary reflections of the wavefield to be imaged are described a priori by the zero-order ray approximation. The aim of removing the geometrical- spreading loss can, in the zero-offset case, be achieved by not applying weights to the data before stacking them. This case alone has been implemented in this work. Application of the method to 3D synthetic zero-offset data proves that an amplitude-preserving migration can be performed in this way. Various numerical aspects of the true-amplitude zero-offset migration are discussed.

Notes: Physical models give us a known geometry with which to compare our processed reflection images and therefore our imaging techniques. We show how this comparison may be quantified in order to evaluate processed images properly. A crosshole data set was acquired through a model interrogated at ultrasonic frequencies using Durham University's physical modelling system. Various reflectivity images were obtained using processing sequences which include deconvolution, wavefield separation and migration. An error-energy scheme was used to assess the quality of these images, by comparing them against a best-fit depth model. A synthetic data set was also used to evaluate the imaging capability of the crosshole geometry and the effectiveness of the different processing schemes.

Notes: The analysis of prestack reflections may have a high diagnostic potential in the evaluation of the petrophysical characteristics of subsurface targets. However, the recovery of reliable seismic responses, especially when examining amplitude versus offset (AVO) variations, is of the utmost importance and is strictly dependent on the acquisition and processing steps.In order to evaluate the impact of different processing sequences, we examine the AVO responses of three seismic events from a marine data set. Borehole data indicate that these events are related to a lignitic sand, a gas sand and a cineritic bed. The AVO analysis is focused mainly on the reflections from the gas sand. In particular, we compare the results of a standard processing sequence with results from a surface-consistent approach and with results from a processing sequence tailored to this specific case. A decreasing AVO trend of the gas-sand reflection results from the analyses of data that have undergone the standard and the surface-consistent processing sequences. This contrasts with both theory and borehole information, which both predict an energy increase with offset. A detailed study shows that the receiver array attenuation, neglected in previous Studies, plays a major role in attenuating the far-offset reflections. Other propagation factors, such as offset-dependent geometrical spreading and Q absorption, produce only minor effects.Taking into account the above factors, we apply a third processing sequence whose impact on the AVO trend is evaluated step by step and whose results are compared with the previously applied sequences. This new sequence leads to better agreement between the AVOs predicted from borehole data and those measured on surface seismic data.

Notes: Median filters may be used with seismic data to attenuate coherent wavefields. An example is the attenuation of the downgoing wavefield in VSP data processing. The filter is applied across the traces in the ‘direction’ of the wavefield. The final result is given by subtracting the filtered version of the record from the original record. This method of median filtering may be called ‘median filtering operated in subtraction’. The method may be extended by automatically estimating the slowness of coherent wavefields on a record. The filter is then applied in a time- and-space varying manner across the record on the basis of the slowness values at each point on the record.Median filters are non-linear and hence their behaviour is more difficult to determine than linear filters. However, there are a number of methods that may be used to analyse median filter behaviour: (1) pseudo-transfer functions to specific time series; (2) the response of median filters to simple seismic models; and (3) the response of median filters to steps that simulate terminating wavefields, such as faults on stacked data. These simple methods provide an intuitive insight into the behaviour of these filters, as well as providing a semiquantitative measurement of performance. The performance degradation of median filters in the presence of trace-to-trace variations in amplitude is shown to be similar to that of linear filters. The performance of median filters (in terms of signal distortion) applied obliquely across a record may be improved by low-pass filtering (in the t-dimension). The response of median filters to steps is shown to be affected by background noise levels. The distortion of steps introduced by median filters approaches the distortion of steps introduced by the corresponding linear filter for high levels of noise.

Notes: For the exploration of near-surface structures, seismic and geoelectric methods are often applied. Usually, these two types of method give, independently of each other, a sufficiently exact model of the geological structure. However, sometimes the inversion of the seismic or geoelectric data fails.These failures can be avoided by combining various methods in one joint inversion which feads to much better parameter estimations of the model than the independent inversions.A suitable seismic method for exploring near-surface structures is the use of dispersive surface waves: the dispersive characteristics of Rayleigh and Love surface waves depend strongly on the structural and petrophysical (seismic velocities) features of the near-surface Underground.Geoelectric exploration of the structure Underground may be carried out with the well-known methods of DC resistivity sounding, such as the Schlumberger, the radial-dipole and the two-electrode arrays.The joint inversion algorithm is tested by means of synthetic data. It is demonstrated that the geoelectric joint inversion of Schlumberger, radial-dipole and two-electrode sounding data yields more reliable results than the single inversion of a single set of these data. The same holds for the seismic joint inversion of Love and Rayleigh group slowness data. The best inversion result is achieved by performing a joint inversion of both geoelectric and surface-wave data.The effect of noise on the accuracy of the solution for both Gaussian and non-Gaussian (sparsely distributed large) errors is analysed. After a comparison between least-square (LSQ) and least absolute deviation (LAD) inversion results, the LAD joint inversion is found to be an accurate and robust method.

Notes: A new information criterion, the extended information criterion (EIC) was applied in order to determine an optimum solution in simultaneous iterative reconstruction technique (SIRT) P-wave velocity tomography. The EIC is derived from information theory and statistics, and it measures the goodness-of-fit between the true (unknown) data distribution and the observed data distribution: the former gives the probability of data realization from the true (unknown) model, whereas the latter gives a probability of data realization calculated from a particular model of which parameters are estimated. The EIC is calculated using bootstrap statistics, a numerical technique for calculating statistical estimators. Bootstrap statistics enables us to obtain the bias between the log likelihood and the expected log likelihood, and then to obtain the expected log likelihood from the log likelihood. Since the EIC is obtained numerically, we can use it for most problems of model parameter estimation without employing the maximum likelihood method. Taking weak anisotropy into account, we reconstructed the P-wave velocity structure of a rock sample during water infiltration under differential stress loading conditions. The results indicate that we can remove unrealistic solutions sometimes encountered when too many iterations are made. In spite of much computation time, the EIC is a promising technique for the near future, prompted by the rapid progress in current computer technology.

Notes: The effects of source and receiver motion on seismic data are considered using extensions of the standard convolutional model. In particular, receiver motion introduces a time-variant spatial shift into data, while source motion converts the effect of the source signature from a single-channel convolution in time to a multichannel convolution in time and space. These results are consistent with classical Doppler theory and suggest that Doppler shifting can introduce distortions into seismic data even at relatively slow acquisition speeds. It is shown that, while both source and receiver motion are known to be important for marine vibroseis acquisition, receiver motion alone can produce significant artifacts in marine 3D data. Fortunately, the convolutional nature of the distortions renders them amenable to correction using simple deconvolution techniques. Specifically, the effects of receiver motion can be neutralized by applying an appropriate reverse time-variant spatial shift, while those due to source motion can be addressed by introducing time-variant spatial shifts both before and after standard, deterministic, signature deconvolution or correlation.

Notes: Various applications of a new geophysical reconstruction method, generalized acoustical diffraction tomography (GADT), which is based on transmission data as input are considered. Conventional diffraction tomography methods normally require linearization with respect to a uniform reference medium and regular sampling along a straight line. Thus, these methods will not work well when the background is strongly non-uniform and/or the acquisition geometry is arbitrary. However, GADT can, in principle, handle both irregularly spaced data, curved acquisition lines, and non-uniform background models.A number of controlled model tank and field experiments, where the model and the test object(s) are known a priori, have been carried out. After acquiring the tomographic data in each experiment, these are used to compute a reconstruction of the model, which can then be compared with the actual, known model. The method's ability to yield high-quality images of the different targets is demonstrated.

Notes: Hydrocarbon exploration in the Papuan fold belt is made extremely difficult by mountainous terrain, equatorial jungle and thick karstified Miocene limestones at the surface. The high-velocity karstified limestones at or near the surface often render the seismic technique useless for imaging the subsurface. In such areas magnetotellurics (MT) provides a valuable capability for mapping subsurface structure. The main structural interface which can be mapped with MT, due to the large electrical contrast, is the contact between the resistive Darai limestone and the underlying conductive sediments of the Ieru Formation. In some areas the base of the Darai can be mapped with reasonable accuracy by fitting 1D models to the observed MT data. However, in many cases where 2D and 3D effects are severe, 1D interpretations can yield dramatically incorrect results. Numerical and field data examples are presented which demonstrate the severity of the 1D errors and the improvements in accuracy which can be achieved using a 2D inverse solution.Two MT lines over adjacent anticlines, both with well control and seismic data, are used to demonstrate the application of 1D and 2D inversions for structural models. In both cases the seismic data provide no aid in the interpretations. The example over the Hides anticline illustrates a situation where 1D inversion of either TE or TM mode provides essentially the same depth to base of Darai as 2D inversion of both TE and TM. Both models provide base Darai depth estimates which are within 10% of that measured in the well. The example over the Angore anticline illustrates the inadequacy of 1D inversion in structurally complex geology complicated by electrical statics. The TE mode fits a 1D Darai thickness of 800 metres while the TM mode fits a 1D Darai thickness of 3500 metres, bracketing the thickness of 2450 metres observed in the well. The final 2D inversion model provides a depth estimate of 2250 metres. Four MT lines along the Angore anticline have been interpreted using 2D inversion. A high degree of correlation exists between lineaments observed on an airborne radar image and zones of low resistivity within the high-resistivity material interpreted as Darai limestone. These low-resistivity zones are interpreted as fault zones.Three-dimensional modelling has been used to simulate 3D statics in an otherwise 2D earth. These data were used to test the Groom-Bailey (GB) decomposition for possible benefits in reducing static effects and estimating geoelectric strike in the Papua New Guinea (PNG) field data. It has been found that the GB decomposition can provide improved regional 2D strike estimates in 3D contaminated data. However, in situations such as PNG, where the regional 2D strike is well established and hence can be fixed, the GB decomposition provides apparent resistivities identical to those simply rotated to strike.