ALBERT

Notes: The changes in porosity and elastic moduli of YSZ-containing nickel-based anode materials for solid oxide fuel cells were studied as a function of the fraction of reduced NiO. Anode samples were reduced in a gas mixture of 4% hydrogen and 96% argon for different periods of time at 800°C and their Young's and shear moduli were determined afterward at room temperature using resonant ultrasound spectroscopy and impulse excitation. It was found that the magnitude of Young's and shear moduli decreased significantly with increasing fraction of reduced NiO and that the magnitude of the elastic moduli of a fully reduced Ni–YSZ anode was ∼45% lower than that of unreduced NiO–YSZ. Because the elastic moduli of NiO are close to those of Ni, the observed decrease in the magnitude of the elastic moduli was found to be caused mainly by the significant increase in the porosity of the sample as a result of NiO reduction. Expressions are presented for the amount of porosity and the magnitude of the elastic moduli as a function of the fraction of reduced NiO.

Notes: Two- and three-dimensional SiCr/SiC composites have been prepared starting from Tyranno SA(tm) fiber preforms. Preform densification has been performed by a modified preceramic polymer impregnation and pyrolysis (PIP) process consisting of filling the preform large interbundle voids with SiC powder before the PIP process. This step was accomplished by low-pressure infiltration of a SiC powder dilute slurry through the preform thickness. Specimens were further processed with polymer impregnation and pyrolysis to determine the effects on structural, thermal, and mechanical properties of the obtained composites. High-temperature pyrolysis treatment, which promoted polymer derived SiC matrix crystallization, markedly increased thermal diffusivity.

Notes: Carbon is commonly added to sulfate-fined silicate-glass batches to enhance the fining process. Reactions between carbon and Na2SO4 modify the SOx emissions from Na2SO4 decomposition. Fourier-transform infrared (FTIR) spectrometry is used to analyze the emission of air pollutants from the isothermal decomposition of Na2SO4 + C undertaken using thermogravimetric analysis (TGA). The FTIR spectrometer is calibrated using standard gas mixtures containing CO, CO2, SO2, NO, and NO2. The collected spectra are quantified using the classical least-squares (CLS) approximation. The TGA-FTIR system provides SOx, and COx, concentrations versus time data from the isothermal decomposition of Na2SO4, in the presence of a carbon black. Mass spectrometry (MS) complements FTIR by being able to detect SO(g).

Notes: Different ratios of the precursor phases of SrFeO3–x (SFO) and SrMoO4 (SMO) were used to prepare Sr2FeMoO6 (SFMO) by a solid-state reaction. X-ray diffraction was used to identify the phases. A residual SMO was observed to exist in the sample with an SFO/SMO ratio of 0.9:1. The sample with a residual SMO phase had higher resistivity, lower magnetization, but higher low-field magnetoresistance (LFMR). High-resolution transmission electron microscopy was used to identify the compositions and phases. Nanometer-sized amorphous-like clusters of SMO phase were located inside the grains rather than at grain boundaries; however, some boundaries were rich in the strontium ion. The possible mechanisms for the conduction and the increase of LFMR of SFMO are discussed.

Notes: Submicro- and nano-sized liquid-phase-sintered SiC ceramics were mechanically tested by nanoindentation in the peak load range 5–400 mN. The submicro-sized sample showed a marked indentation size effect which the nano-sized samples did not exhibit. The relevance of indentation depth with respect to the microstructural scale has been outlined. In the investigated grain-size range, the hardness dependence on the grain size could be described by a load-dependent inverse Hall–Petch relation. Young's modulus was less microstructure- and load-dependent. Because of the very fine microstructure, the nano-sized SiC materials gave lower elastic values than the submicro-sized SiC ceramic.

Notes: Samples of composition Ba1−xLaxTi1−x/4O3, x= 0, 0.003, 0.03, and 0.10, were prepared by an alkoxide sol–gel route with final firing of ceramics at 1100°C, 2 h in air. All samples showed bulk insulating behavior with no evidence of semiconductivity caused by either direct donor doping or oxygen loss.

Notes: We have studied the rheological property evolution and hydration behavior of white and ordinary portland cement (type I) pastes and concentrated cement–polyelectrolyte suspensions. Cement composition had a marked effect on the elastic property evolution (G′(t)) and hydration behavior of these suspensions in the presence of poly(acrylic acid)/poly(ethylene oxide) copolymer (PAA/PEO), even though their affinity to adsorb such species was nearly identical. Both white and ordinary portland cement pastes exhibited G′0 values of ∼104 Pa and fully reversible G′(t) behavior until the onset of the acceleratory period (t= 2 h), where the pastes stiffened irreversibly. In contrast, cement–PAA/PEO suspensions exhibited G′0 values of ∼1 Pa and G′(t) behavior comprised of both reversible and irreversible features. Interestingly, ordinary portland cement–PAA/PEO suspensions experienced a gel-to-fluid transition on high shear mixing at short hydration times (〈1 h), and the particle network did not rebuild until ∼24 h of hydration. In sharp contrast, white portland cement–PAA/PEO suspensions remained weakly gelled throughout the initial stage of hydration even after high shear mixing. At longer hydration times (〉1 h), both cement–PAA/PEO suspensions exhibited G′i(t) ∼ exp(t/τc) with τc values of 5.6 and 1.3 h for ordinary and white portland cement, respectively. Our observations suggest that hydration phenomena impact interparticle forces during early stage hydration and, ultimately, lead to initial setting through the formation of solid bridges at the contact points between particles within the gelled network.

Notes: A new ceramic freeze-casting technique capable of manufacturing near room temperature with a sublimable vehicle was accomplished. Fluid-concentrated slurries of Al2O3 powder in molten camphene (C10H16) were prepared at 55°C. These slurries were quickly solidified (frozen) at room temperature to yield rigid solid green bodies, followed by frozen camphene removal by sublimation (freeze-drying) with negligible shrinkage. Sintering without any special binder burnout process yielded sintered bodies with over 98% theoretical density. The proposed advantages include (1) elimination of extremely cold temperatures, (2) elimination of troublesome binder burnout process, and (3) fast manufacturing cycle due to quick solidification.

Notes: Dense composites in the Ti-B-N system have been produced by reactive hot pressing of titanium and BN powders. The effect of the addition of a small amount of nickel (1–3 wt%) on the reaction kinetics and densification of TiN–TiB2 (40 vol%) composite has been studied. Composites of ∼99% of theoretical density have been produced at 1600°C under 40 MPa for 30 min with 1% nickel. The hardness and fracture toughness of these composites are 24.5 ± 0.97 GPa and 6.53 ± 0.27 MPa·m1/2, respectively. The microstructural studies on samples produced at lower temperatures indicate the formation of a transient liquid phase, which enhances the kinetics of the reaction and densification of the composite.

Notes: This paper presents new findings on ultrasonic spray pyrolysis of zirconium hydroxyl acetate precursor drops whose sizes were precisely measured using laser light diffraction technique. Precursor concentration plays a predominant role in determination of product particle size. At 0.01 wt% precursor concentration, conventional spray pyrolysis at 750°C using precursor drops 5–8 μm in diameter, generated by an ultrasonic nebulizer at 2.66 MHz, yielded uniform spherical yttria-stabilized zirconia (YSZ) particles 73 nm in diameter measured by scanning electron microscopy. The YSZ particle diameters were much smaller than those predicted by the one-particle-per-drop mechanism. Under similar reaction conditions, the high-throughput ultrasound-modulated two-fluid (UMTF) spray pyrolysis of larger precursor drops (28-μm peak diameter) also yielded spherical dense particles; they were significantly smaller in size than those produced by the low-throughput conventional ultrasonic spray pyrolysis of smaller drops (6.8-μm peak diameter).

Notes: Thermoelectric elements consisting of the layered polycrystalline materials of Al-doped ZnO and NaCo2O4 were prepared using the pulse electric-current sintering (PECS) method at 900°C for 3 min. Direct contact between the polycrystalline Al-doped ZnO and the NaCo2O4 was obtained in a single-step process for the stacked powders. The electrical conductivities of the polycrystalline materials prepared by PECS were higher than those of materials prepared by conventional sintering, despite their porous structure. The thermoelectric voltage of the 1-mol%-Al-doped ZnO and NaCo2O4 polycrystalline element (measuring ∼6 mm × 3 mm × 15 mm) was 83 mV at dT= 500 K, when the junction of the elements was at 800°C.

Notes: Pb(Zr,Ti)O3–Pb(Mn1/3 Nb2/3)O3 (PZT–PMnN) system has been studied for high-power piezoelectric applications. This study investigates this system to find out the composition with high-power density piezoelectric characteristics and low tem-perature coefficient of resonance frequency (TCF). It was found that the composition 0.9PZT–0.1PMnN (Zr/Ti = 0.51/0.49) modified with 6 mol% Sr exhibits a TCF of −8 ppm/°C (−20 to +80°C). Further, the dielectric and piezoelectric properties of this composition are as follows: kp= 0.53; Qm= 800; d33= 274; ε33/ε0= 1290 and tan δ=1.1%, which shows the suitability of this composition for ultrasonic devices used under fluctuating thermal environment.

Notes: Beam bending is an excellent method for measuring low permeabilities (≤10−18 m2) in homogeneous materials, because it is fast, requires no high pressure, and provides a concurrent measurement of the modulus of the material. The method was previously analyzed and substantiated for cylindrical or square beams. Recently, the analysis was extended to include isotropic and transversely isotropic rectangular beams. In this paper, the analysis is applied to measurements performed on cement paste, and it is shown that the solution for isotropic rectangular beams accounts for changes in the hydrodynamic behavior caused by changing the aspect ratio of the sample. The permeability and elastic modulus results are verified through comparison to previous measurements on cylindrical beams.

Notes: The deformation behavior of boron- and carbon-doped β-silicon carbide (B,C-SiC) with an average grain size of 260 ± 18 nm containing 1 wt% boron was investigated by compression testing at elevated temperatures. Extensive grain growth during deformation was observed. The stress–strain curves were compensated for grain growth by assuming power-law type of dependence on grain size and strain rate. The stress exponent n was ∼1.3 and the grain size exponent p was ∼2.7 at temperatures ranging from 1593° to 1758°C. The apparent activation energy of deformation Qd was ∼760 kJ/mol, which was lower than the activation energy for lattice diffusion of silicon and carbon in SiC and higher than that for grain-boundary diffusion of carbon in SiC. These results suggest that the deformation mechanism of the fine-grained B,C-SiC is grain-boundary sliding accommodated by the grain-boundary diffusion.

Notes: Chromium-containing stainless steel (SS) is a prospective material for use as an interconnect in solid oxide fuel cells (SOFCs). However, during operations at high temperatures, the growth of oxide scales causes the performance of the interconnect and SOFC as a whole to deteriorate. The coating of SS 446 with a conducting perovskite is a potential method of slowing the growth of oxide scale and, therefore, improving overall SOFC performance. In the present research, the structural characterization of a pure LaCrO3 thin film on the SS 446 substrates has been performed as a model material that can be used as a barrier coating for the metallic interconnect. The deposition of an amorphous La-Cr-O thin film on SS 446 was performed using radio-frequency (rf) magnetron sputtering. The deposited amorphous film was annealed in air to form the desired perovskite phase. The film underwent an amorphous to LaCrO4 phase transition during annealing at 500°C with further transformation to LaCrO3 orthorhombic phase during annealing at 700°C. A self-organized dendritic structure was reported as a result of the perovskite-phase formation. Although formation of various oxides, such as Fe2O3 and Fe3O4, was observed during the annealing of uncoated SS 446 in air, the coating of SS 446 surface with LaCrO3 film prevented formation of various oxide phases at the interconnect surface. The structural characterization of the films and SS 446 surfaces was accomplished using scanning electron microscopy with energy-dispersive X-ray analysis, X-ray diffractometry, micro-Raman spectroscopy, and nanoindentation.

Notes: The density, surface tension, and viscosity of the melts from the PbO-B2O3-SiO2 system have been measured at temperatures in the range 1073–1473 K. The effect of composition on these properties was also investigated. The density of the melt was found to increase linearly with increasing PbO content. Molar volume was derived from the density data, and its deviation from the additivity of partial molar volumes was calculated. These deviations in molar volume from those obtained from additivity rules have been used along with the ratio of various coordination numbers of boron (as reported by Bray) to discuss the structure of the melts. The surface tension was found to decrease with decreasing SiO2/B2O3 ratio, and to increase in the range of the PbO content between 30 and 60 mol%, showing a maximum at ∼60 mol% PbO, and then decreased with further additions. This result suggested that the surface tension would be affected primarily by the B2O3 content in the range of the PbO content between 30–60 mol%, and mainly by the PbO content in the range of the PbO content 〉60 mol%, respectively. The viscosity of the melt was found to decrease linearly with increasing PbO content. The results obtained indicate that the increase in viscosity with B2O3 was half that of SiO2 (on a molar basis), and an empirical equation has been proposed for the viscosity as a function of mole fraction.

Notes: Core/shell structures have been prepared via a mechanofusion system by employing several kinds of spherical polymers as a core material and Al2O3 powder or a mixture of Al2O3 and SiO2 powders as a shell material. The effect of the kind of core polymers on the quality of the resulting hollow alumina microspheres has been discussed on the basis of the thermal decomposition behavior of spherical polymers used as a core material. A large fraction of hollow alumina microspheres reflecting the shape and the particle size distribution of the core polymer could be fabricated after sintering at 1600°3C for 3 h, when highly cross-linked poly(methyl methacrylate) (PMMA) microspheres with a gel fraction of 99.03% were used as a core polymer, and abrupt firing at temperatures higher than 500°3C was adopted to remove the PMMA microspheres. The addition of 5 mass% SiO2 to the Al2O3 shell layer was found to be useful for maintaining the spherical shell structure during the firing process and for fabricating a large fraction of hollow alumina microspheres after the sintering.

Notes: Well-defined and stoichiometric spherical particles of BaTiO3 of narrow size distribution were produced at 82° and 92°3C by precipitation from chloride solutions in a strong alkaline environment. The size of the particles can be tailored in the range from ≅103 to 70–80 nm by increasing the barium concentration from ≅0.07 to 0.7 mol/L. The particles are composed of tight aggregates resulting from the assembly of several nanocrystals. The size of the nanocrystals decreases from 200–300 to 30–40 nm by increasing reactant concentration. At low barium concentration (≤0.07 mol/L at 82°3C, ≤0.06 mol/L at 92°3C), formation of BaTiO3 is strongly slowed down and nonstoichiometric, Ti-rich powders are produced. Under these conditions, the particles have the tendency to develop a dendritic-like morphology.

Notes: Crystals of δ-Y2Si2O7 (space group P121/c1) were examined using high-temperature powder X-ray diffractometry to determine their unit-cell dimensions from 296 to 1473 K. The lattice deformation induced by thermal expansion was investigated using matrix algebra analysis to determine the directions and magnitudes of the principal distortions (Λi, i= 1,2, and 3). The directions of Λ1 and Λ3 were defined by the acute angle Λ1c, which linearly decreased from 5(2)° to —5.5(3)° with increased temperature from 504 to 1473 K. The Λ2-axis invariably coincided with the crystallographic b-axis. The magnitudes of Λ1 and Λ2 steadily increased to, respectively, 1.0061(1) and 1.0068(1) during heating to 1473 K, while Λ3 remained almost constant for the entire temperature range. The mean principal distortion, Λm (= (Λ1+Λ2+Λ3)/3), steadily increased to 1.0044(1) with increased temperature to 1473 K. The coefficient of mean linear thermal expansion (α) was derived from the mean principal strain (Λm - 1) as α= (Λm - 1)/ΔT. The temperature dependence was determined to be α= 2.03 times 103+ 1.36(T - 296) (10-9 K-1). Provided that the rule-of-mixtures holds for the Y2Si2O7/Y2SiO5 composites as protective coating on SiC substrates, the volume fractions of 0.72-0.77 (70–75 mass%) would be necessary for the Y2Si2O7 component to match the α-values of both materials.

Notes: Microcellular silicon oxycarbide open cell ceramic foams were fabricated from a silicone resin. Microcellular foams, with a cell size ranging from ∼1–80 μm, were fabricated using poly(methyl methacrylate) microbeads as sacrificial templates. The compression strength of the foams decreased with increasing cell size.

Notes: Electroconductive zirconia-toughened mullite (TiN/ZTM) intragranular nanocomposite was fabricated by hot-pressing a powder mixture of nano-sized TiN, ZrO2(2Y), and mullite gel. The material showed a good sinterability and could be highly densified at a low temperature of 1300°3C. Sintering temperature strongly influenced the microstructure and electrical resistivity of the material. The electrical resistivity increased monotonously from 20 Ω-cm to 1.5 times 106°3Cm, as the sintering temperature was increased from 1300° to 1500°3C. TEM results indicated that such a phenomenon could be ascribed to the changes in the microstructure of the material, which led to a decrease in the connectivity of the TiN network in the sample as the sintering temperature was increased.

Notes: Effects of fluids on material removal rate, chipping damage, and surface roughness in the simulated clinical-dental machining of a dental-type glass ceramic were investigated. Significant differences in removal rate were obtained among the fluids investigated, but only a 4 wt% boric acid solution gave a higher removal rate than conventionally used water. Chipping damage was substantially lower for the boric acid and an oil-emulsion coolant compared with other fluids tested. Surface roughness was independent of the fluids used. The results indicate that improvement can be achieved in both material removal rate and machining damage by the appropriate selection of coolant chemistry.

Notes: This paper reviews the structures and properties of 10 binary, ternary, and quaternary crystals within the equilibrium phase diagram of the SiO2–Y2O3–Si3N4 system. They are binary compounds SiO2, Y2O3, Si3N4; ternary compounds Si2N2O, Y2Si2O7, and YSi2O5; and quaternary crystals Y2Si3N4O3 (M-melilite), Y4Si2O7N2, (N-YAM), YSiO2N (wallastonite), and Y10(SiO4)6N2 (N-apatite, N-APT). Although the binary compounds are well-known and extensively studied, the ternary and the quaternary crystals are not. Most of the ternary and the quaternary crystals simply have been referenced as secondary phases in the processing of nitrogen ceramics. Their crystal structures are complex and not precisely determined. In the quaternary crystals, there exists O/N disorder in that the exact atomic positions of the anions cannot be uniquely determined. It is envisioned that a variety of cation–anion bonding configurations exist in these complex crystals. The electronic structure and bonding in these crystals are, therefore, of great interest and are indispensable for a fundamental understanding of structural ceramics. We have used ab initio methods to study the structure and bonding properties of these 10 crystals. For crystals with unknown or incomplete structural information, we use an accurate total energy relaxation scheme to obtain the most likely atomic positions. Based on the theoretically modeled structures, the electronic structure and bonding in these crystals are investigated and related to various local cation–anion bonding configurations. These results are presented in the form of atom-resolved partial density of states, Mulliken effective charges, and bond order values. It is shown that Y–O and Y–N bonding are not negligible and should be a part of the discussion of the overall bonding schemes in these crystals. Spectroscopic properties in the form of complex, frequency-dependent dielectric functions, X-ray absorption near-edge structure (XANES), and the electron energy-loss near-edge structure (ELNES) spectra in these crystals also are calculated and compared. These results are discussed in the context of specific bonding configurations between cations (silicon and yttrium) and anions (oxygen and nitrogen) and their implications on intergranular thin films in polycrystalline Si3N4 containing rare-earth elements.

Notes: Simultaneous synthesis and sintering of hexagonal α-Ti1−x-Alx(N) (0 ≤x≤ 0.08) solid solutions, which contain a small amount of nitrogen, have been performed by a self-propagating high-temperature combustion method under a nitrogen pressure of 4 MPa. Dense materials (∼99% of theoretical) prepared directly from a mixture of elemental (Ti and Al) powders reveal homogeneous microstructure composed of fine grains (12–16 μm). α-Ti1−xAlx(N) (x= 0.02; Ti0.98Al0.02N0.26) exhibits a three-point bending strength σb of 390 MPa, a Vickers hardness Hv of 9.24 GPa, and a fracture toughness KIC of 4.89 MPa·m1/2; their mechanical properties are much improved by doping Al into α-Ti(N), in comparison with those (σb= 245 MPa, Hv= 9.02 GPa, and KIC= 3.77 MPa·m1/2) of α-Ti(N) fabricated under the same conditions.

Notes: Electrophoretic deposition has been used to synthesize nickel–alumina, functionally graded materials from NiO and alumina suspensions in ethanol. Suspension stability and the kinetics of deposition were studied to determine optimum conditions. Deposition starts with an alumina suspension into which a stream of NiO suspension is injected at various flow rates to obtain the desired profiles. The latter were controlled by varying the deposition current density and component flow rate. The green bodies obtained were sintered in Ar/H2 atmosphere to reduce the NiO to nickel. Various gradation profiles were obtained illustrating the facility of EPD to synthesize continuously graded materials. NiO was used as the precursor for nickel to alleviate settling and rough columnar deposit problems.

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: When a rather extensive network of short distance refraction profiles was shot the following two observations were made. Firstly, the wave velocity in the weathered layer showed a quite considerable fluctuation in horizontal direction, the extreme values being of the order of 300 and 700 m/sec. A practical result of this scattering of the velocities is that an uncertainty of about 10% is introduced in the computation of the weathering corrections. The second observation is that, in the majority of cases, the travel time curve does not pass through the origin. It could be ascertained that this observation was not caused by errors in the method of observation. A probable explanation of the phenomenon is found in a theory that has been developed by Gassmann, who derived the velocity distribution for a hexagonal packing of spherical solid bodies. According to this theory extremely low velocities would occur in the first few centimeters of the crust of the earth. Qualitatively, our observations are in agreement with the theory of Gassmann.

Notes: The geophysicists who attempted to evaluate elastic anisotropy of some bedded formations most often gave but little information about recording and interpretating the measurements.May be they did not lay enough stress on the fact that any determination of the anisotropy factor is a critical operation and that, to have some certainty. it must be made under good conditions and then discussed.Due to the very favourable conditions offered: undisturbed tectonics and topography, relatively regular series the Berriane district in Northern Sahara, is rather well suited to accurate measurements and to an anisotropy study down to 1,250 meters. Since measurements have been carried out in the wildcat drilled at Berriane by S. N. Repal, it seems interesting to communicate the results obtained and to discuss them according to the influence of high velocity layers.It can be noted that in the clay and sand series which have been investigated, anisotropy coefficient amounts to 1.09 or so.To conclude, it seems desirable that determinations made by numerous operators should allow a more accurate knowledge of the anisotropy factor in the main types of rocks.

Notes: The aim of the present investigation is to examine the significance of the second derivative for the purpose of the prospective determination of the geological properties of the district of Offenburg, which are relatively wellknown as a result of both reflection seismic and bore profile findings.The calculation of the second derivative is carried out by means of three approximation formulae, which are compared with each other. In contrast to the isogam map the second derivative shows some additional characteristics, whose structural significance illuminates the comparison with the results of reflection seismics.A geological profile constructed on the basis of 6 wells completely confirms the geophysical findings.

Notes: Using a comprehensive theory of the vertical force variometer, it is shown that the mean of the two readings taken in azimuths 180 degrees apart only eliminates the error of misorientation and of inclination of the knife edge if these factors are sufficiently small. The necessary accuracy in the 180 degree rotation and in the readjustment of the levels are investigated and a practical test is developed to allow the initial adjustments to be determined. Finally, a brief description of a new variometer tripod is given.

Notes: It is known that good use can be made of calculating the second vertical derivative of gravitational and magnetic fields. The first derivative, or Vertical Gradient, has the same properties, Like the second derivative, it does not depend on the locally linear regional anomaly. Moreover, the gradient is less affected by experimental errors.The report gives a practical method of calculating the vertical gradient. Its application is identical to that in general use for calculating the second derivative, except that the numerical coefficients are different. The method also allows the establishment of formulae for downward extension of the field and its derivatives.

Notes: In the region covered by the paper, electrical methods have been applied in four different zones:〈list xml:id="l1" style="custom"〉a) Ales-Maruejols Basin (resistive lower Oligocene blanketed by conductive Upper Oligocene);b) Ledignan and Vaunage-Lunel anticlines (faulted structures in the marly and limy Cretaceous, with different resistivities;c) Camargue (thick series of conductive sediments);d) Beziers Basin (highly complicated structures in the Mesozoic, widely blanketed by conductive Miocene).It may be assumed that electrical methods can yield valuable information enabling one to define the rugged subsurface topography of resistive strata burried under a reasonably thick cover of conductive sediments especially when a part of the lower formation outcrops even if the part exposed be small. Faults may be delineated and much, more information is obtainable than can be expected from gravity meter survey at a price not very much higher.

Notes: For the treatment of the problems involved in the interpretation of gravity pictures this paper gives a formula that holds generally for any potential function. It provides an extended applicability of the relation used by Elkins for the computation of the second derivative, and also yields an analogous relation to derivatives of higher order of the gravity field.This relation has not been utilized to determine in details the course of the derivatives of higher order in a plane, but is merely applied to points of comparatively extreme curvature of the isogams where the differential values present a ratio favourable to the “noise level”. By this method the values of the derivatives of higher order will not be determined themselves but only the ratio's responsible for the depth of divergence in comparison with the course of an anomaly of masses replaced by points.It is shown by examples of intercalated masses that the divergence points are important and by law related to the form and position of the density contrasts themselves.An analysis of the total gravity picture is made possible by progressing from elements close to the surface to deeper ones. In this way the fundamental features of the earth's crust will be obtained. The application of the analysis process to a gravity anomaly actually measured in Northwest Germany is given.

Notes: When refraction time signals are transmitted over a radio link between shooter and observer there is a serious risk of interference from electrical storms. This risk can be minimised by sending a series of signals at fixed time intervals and the paper describes a simple device which will do this with the required accuracy.

Notes: Seismic reflection, telluric and gravity results are given for the lifted area of Ferrara, in Northern Italy. The agreement is shown between the available shallow seismic data and the gravity evidences. For a portion of the above area where seismic results are particularly poor the vertical gradients method gives a resolution of a gravity anomaly and confirms the telluric information. The residual gravity values, the vertical gradients and the telluric data along a seismic line crossing the zone are compared with seismic results and with evidences from adjacent wells.

Notes: Investigations into reflection seismic on the salt structure of Heide raised the following questions:〈list xml:id="l1" style="custom"〉1) How can the different directions of trend of a series of layers be established?2) How are the contour maps of reflecting horizons to be constructed if there is no general trend of the layers?To answer these questions, the case of the subsoil consisting of a series of layers with plane reflecting beds and constant layer-velocities is treated strictly. The strike lines of the reflecting planes may be at any angle whatever. However, formulas for constructing contour maps of the reflecting planes have been derived. With these formulas, the problem quoted under 1) has also been solved.The construction of contour maps is given.For special cases, formulas are obtained which have already been proved by others.

Notes: The triple integral for the attraction of a mass on a point is transformed in a double sum. This double sum serves to construct a graph for the rapid determination of the gravimetric influence of structures given by depth contours. The influence of topography can also be computed with this graph.

Notes: The total mean-square error (MSE) of the estimated model, defined as the sum of the standard model variance and the bias variance, is used to define the truncation level of the singular-value decomposition to give a reasonable balance between model resolution and model variance. This balance is determined largely by the data and no further assumptions are necessary except that the bias terms are estimated sufficiently well. This principle has been tested on the 1D magnetotelluric inverse problem with special emphasis on high-frequency radio magnetotelluric (RMT) data. Simulations clearly demonstrate that the method provides a good balance between resolution and variance. Starting from a homogeneous half-space, the best solution is sought for a fixed set of singular values. The model variance is estimated from the sum of the inverse eigenvalues squared, up to a certain threshold, and the bias variance is estimated from the model projections on the remaining eigenvectors. By varying the threshold, the minimum of the MSE is found for an increasing number of fixed singular values until the number of active singular values becomes greater than or equal to the estimated number. As a side-effect, the depth of penetration of a given set of measurements can be estimated very efficiently by simply noting at which depth the final model deviates little from the starting homogeneous half-space model. A suite of synthetic data is inverted and an example of inversion of one site is shown to illustrate how the truncation is carried out as the non-linear inversion process proceeds. A field example with a profile across a plume of contaminated groundwater in the Netherlands shows good agreement with the electrical resistivity obtained in a nearby borehole.

Notes: Faithful recording of the elastic wavefield at the sea-bed is required for quantitative applications of 4C seismic. The accuracy of the recorded vectorial wavefield depends on factors that vary from deployment to deployment. This paper focuses on one such factor: the interaction of the acquisition system with the sea-bed, which is referred to here as coupling. We show, using multi-azimuth data recorded with a cable-based sea-bed acquisition system, whose sensor housing is cylindrically shaped and with the in-line geophone fixed to the cable, that coupling depends on the propagation direction and wave type (P- or S-waves) of the incident wavefield. We show that coupling is more critical for S-waves than for P-waves. Detection of inconsistent coupling using both P- and S-waves is therefore mandatory. A data-driven processing method to compensate for the frequency-dependent coupling response of the cross-line geophone is derived. Its application to field data verifies the effectiveness of the method.

Notes: The combined use of time-lapse PP and PS seismic data is analysed for optimal discrimination between pressure and saturation changes. The theory is based on a combination of the well-known Gassmann model and the geomechanical grain model derived by Hertz and Mindlin. A key parameter in the discrimination process is the opening angle between curves representing constant changes in PP and PS reflectivity plotted against pressure and saturation changes. The optimal discrimination angle in the pressure–saturation space is 90° and this is used to determine optimal offset ranges for both PP and PS data. For typical production scenarios, we find an optimal offset range corresponding to an angle of incidence of 25–30°, for both PP and PS data. For gas we find slightly different results. This means that conventional survey parameters used in marine multicomponent acquisition should be sufficient for the purpose of estimating pressure and fluid saturation changes during production.

Notes: Cross-hole anisotropic electrical and seismic tomograms of fractured metamorphic rock have been obtained at a test site where extensive hydrological data were available. A strong correlation between electrical resistivity anisotropy and seismic compressional-wave velocity anisotropy has been observed. Analysis of core samples from the site reveal that the shale-rich rocks have fabric-related average velocity anisotropy of between 10% and 30%. The cross-hole seismic data are consistent with these values, indicating that observed anisotropy might be principally due to the inherent rock fabric rather than to the aligned sets of open fractures. One region with velocity anisotropy greater than 30% has been modelled as aligned open fractures within an anisotropic rock matrix and this model is consistent with available fracture density and hydraulic transmissivity data from the boreholes and the cross-hole resistivity tomography data. However, in general the study highlights the uncertainties that can arise, due to the relative influence of rock fabric and fluid-filled fractures, when using geophysical techniques for hydrological investigations.

Notes: Shear-wave polarization and time delay are attributes commonly used for fracture detection and characterization. In time-lapse analysis these parameters can be used as indicators of changes in the fracture orientation and density. Indeed, changes in fracture characteristics provide key information for increased reservoir characterization and exploitation. However, relative to the data uncertainty, is the comparison of these parameters over time statistically meaningful? We present the uncertainty in shear-wave polarization and time delay as a function of acquisition uncertainties, such as receiver and source misorientation, miscoupling and band-limited random noise. This study is applied to a time-lapse borehole seismic survey, recorded in Vacuum Field, New Mexico. From the estimated uncertainties for each survey, the uncertainty in the difference between the two surveys is 31° for the shear-wave polarization angle and 4 ms for the shear-wave time delay. Any changes in these parameters greater than these error estimates can be interpreted with confidence. This analysis can be applied to any time-lapse measurement to provide an interval of confidence in the interpretation of shear-wave polarization angles and time splitting.

Notes: A series of downhole magnetometric resistivity (DHMMR) and downhole electromagnetic (DHEM) surveys were conducted near Broken Hill, New South Wales, Australia, and at Zinkgruvan, Sweden, to determine how probe and receiver equipment choices affect the amount of noise visible in borehole MMR and EM data. Noise analyses performed on the data, using the standard deviation to gauge the relative noise levels between different probes and receiver systems, indicate that high noise levels in MMR data result primarily from the use of a three-component EM probe, which has a reduced effective area and hence a higher noise floor compared with a single-component EM probe. High noise, attributable to cultural sources such as nearby power lines, in either MMR or EM data can be reduced through the use of full-waveform, multipurpose receiver systems. These systems allow for the use of tapered stacking, which is a more effective method of eliminating coherent noise associated with power-line transients than the boxcar-stacking method used by traditional receiver systems.

Notes: Interlayer slipping breccia-type gold deposit – a new type of gold deposit, defined recently in the northern margin of the Jiaolai Basin, Shandong Province, China – occurs in interlayer slip faults distributed along the basin margin. It has the features of large orebody thickness (ranging from 14 m to 46 m, with an average thickness of 30 m), shallow embedding (0–50 m thickness of cover), low tenor of gold ore (ranging from 3 g/t to 5 g/t), easy mining and ore dressing. This type of gold deposit has promising metallogenic forecasting and potential for economic exploitation.A ground gamma-ray survey in the Pengjiakuang gold-ore district indicates that the potassium/thorium ratio is closely related to the mineralization intensity, i.e. the larger the potassium/thorium ratio, the higher the mineralization. The gold mineralized alteration zone was defined by a potassium/thorium ratio of 0.35. A seismic survey confirms the location of the top and bottom boundaries and images various features within the Pengjiakuang gold mineralization belt. The gold-bearing shovel slipped belt dips to the south at an angle of 50–55° at the surface and 15–20° at depth. The seismic profile is interpreted in terms of a structural band on the seismic section characterized by a three-layered model. The upper layer is represented by weakly discontinuous reflections that represent the overlying conglomerates. A zone of stronger reflections representing the interlayer slip fault (gold-bearing mineralized zone) is imaged within the middle of the section, while the strongest reflections are in the lower part of the section and represent metamorphic rocks at depth. At the same time, the seismic reflection survey confirms the existence of a granite body at depth, indicating that ore-forming fluids may be related to the granite. A CSAMT survey showed that the gold-bearing mineralized zone is a conductive layer and contains a low-resistivity anomaly ranging from 2 Ωm to 200 Ωm.

Notes: The elastic properties and anisotropy of shales are strongly influenced by the degree of alignment of the grain scale texture. In general, an orientation distribution function (ODF) can be used to describe this alignment, which, in practice, can be characterized by two Legendre coefficients. We discuss various statistical ODFs that define the alignment by spreading from a mean value; in particular, the Gaussian, Fisher and Bingham distributions. We compare the statistical models with an ODF resulting from pure vertical compaction (no shear strain) of a sediment. The compaction ODF may be used to estimate how the elastic properties and anisotropy evolve due to burial of clayey sediments.Our study shows that the three statistical ODFs produce almost identical correspondence between the two Legendre coefficients as a function of the spreading parameter, so that the spreading parameter of one ODF can be converted to the spreading parameter of another ODF. In most cases it is then sufficient to apply the spreading parameter for the ODF instead of the two Legendre coefficients. The effect of compaction on the ODF gives a slightly different correspondence between the two Legendre coefficients from that for the other models. In principle, this opens up the possibility of distinguishing anisotropy effects due to compaction from those due to other processes.We also study reflection amplitudes versus angle of incidence (AVA) for all wave modes, where shales having various ODFs overlie an isotropic medium. The AVA responses are modelled using both exact and approximation formulae, and their intercepts and gradients are compared. The modelling shows that the S-wave velocity is sensitive to any perturbation in the spreading parameter, while the P-wave velocity becomes increasingly sensitive to a perturbation of a less ordered system. Similar observations are found for the AVA of the P-P and P-SV waves. Modelling indicates that a combined use of the amplitude versus offset of P-P and P-SV reflected waves may reveal certain grain scale alignment properties of shale-like rocks.

Notes: Although it is believed that natural fracture sets predominantly have near-vertical orientation, oblique stresses and some other mechanisms may tilt fractures away from the vertical. Here, we examine an effective medium produced by a single system of obliquely dipping rotationally invariant fractures embedded in a transversely isotropic with a vertical symmetry axis (VTI) background rock. This model is monoclinic with a vertical symmetry plane that coincides with the dip plane of the fractures.Multicomponent seismic data acquired over such a medium possess several distinct features that make it possible to estimate the fracture orientation. For example, the vertically propagating fast shear wave (and the fast converted PS-wave) is typically polarized in the direction of the fracture strike. The normal-moveout (NMO) ellipses of horizontal reflection events are co-orientated with the dip and strike directions of the fractures, which provides an independent estimate of the fracture azimuth. However, the polarization vector of the slow shear wave at vertical incidence does not lie in the horizontal plane – an unusual phenomenon that can be used to evaluate fracture dip. Also, for oblique fractures the shear-wave splitting coefficient at vertical incidence becomes dependent on fracture infill (saturation).A complete medium-characterization procedure includes estimating the fracture compliances and orientation (dip and azimuth), as well as the Thomsen parameters of the VTI background. We demonstrate that both the fracture and background parameters can be obtained from multicomponent wide-azimuth data using the vertical velocities and NMO ellipses of PP-waves and two split SS-waves (or the traveltimes of PS-waves) reflected from horizontal interfaces. Numerical tests corroborate the accuracy and stability of the inversion algorithm based on the exact expressions for the vertical and NMO velocities.

Notes: The azimuth moveout (AMO) operator in homogeneous transversely isotropic media with a vertical symmetry axis (VTI), as in isotropic media, has an overall skewed saddle shape. However, the AMO operator in anisotropic media is complicated; it includes, among other things, triplications at low angles. Even in weaker anisotropies, with the anisotropy parameter η= 0.1 (10% anisotropy), the AMO operator is considerably different from the isotropic operator, although free of triplications. The structure of the operator in VTI media (positive η) is stretched (has a wider aperture) compared with operators in isotropic media, with the amount of stretch being dependent on the strength of anisotropy. If the medium is both vertically inhomogeneous, i.e. the vertical velocity is a function of depth (v(z)), and anisotropic, which is a common combination in practical problems, the shape of the operator again differs from that for isotropic media. However, the difference in the AMO operator between the homogeneous and the v(z) cases, even for anisotropic media, is small. Stated simply, anisotropy influences the shape and aperture of the AMO operator far more than vertical inhomogeneity does.

Notes: The attenuation of ground-penetrating radar (GPR) energy in the subsurface decreases and shifts the amplitude spectrum of the radar pulse to lower frequencies (absorption) with increasing traveltime and causes also a distortion of wavelet phase (dispersion). The attenuation is often expressed by the quality factor Q. For GPR studies, Q can be estimated from the ratio of the real part to the imaginary part of the dielectric permittivity.We consider a complex power function of frequency for the dielectric permittivity, and show that this dielectric response corresponds to a frequency-independent-Q or simply a constant-Q model. The phase velocity (dispersion relationship) and the absorption coefficient of electromagnetic waves also obey a frequency power law. This approach is easy to use in the frequency domain and the wave propagation can be described by two parameters only, for example Q and the phase velocity at an arbitrary reference frequency. This simplicity makes it practical for any inversion technique. Furthermore, by using the Hilbert transform relating the velocity and the absorption coefficient (which obeys a frequency power law), we find the same dispersion relationship for the phase velocity. Both approaches are valid for a constant value of Q over a restricted frequency-bandwidth, and are applicable in a material that is assumed to have no instantaneous dielectric response.Many GPR profiles acquired in a dry aeolian environment have shown a strong reflectivity inside dunes. Changes in water content are believed to be the origin of this reflectivity. We model the radar reflections from the bottom of a dry aeolian dune using the 1D wavelet modelling method. We discuss the choice of the reference wavelet in this modelling approach. A trial-and-error match of modelled and observed data was performed to estimate the optimum set of parameters characterizing the materials composing the site. Additionally, by combining the complex refractive index method (CRIM) and/or Topp equations for the bulk permittivity (dielectric constant) of moist sandy soils with a frequency power law for the dielectric response, we introduce them into the expression for the reflection coefficient. Using this method, we can estimate the water content and explain its effect on the reflection coefficient and on wavelet modelling.

Notes: The forward computation of the gravitational and magnetic fields due to a 3D body with an arbitrary boundary and continually varying density or magnetization is an important problem in gravitational and magnetic prospecting. In order to solve the inverse problem for the arbitrary components of the gravitational and magnetic anomalies due to an arbitrary 3D body under complex conditions, including an uneven observation surface, the existence of background anomalies and very little or no a priori information, we used a spherical coordinate system to systematically investigate forward methods for such anomalies and developed a series of universal spherical harmonic expansions of gravitational and magnetic fields. For the case of a 3D body with an arbitrary boundary and continually varying magnetization, we have also given the surface integral expressions for the common spherical harmonic coefficients in the expansion of the magnetic field due to the body, and a very precise numerical integral algorithm to calculate them. Thus a simple and effective method of solving the forward problem for magnetic fields due to 3D bodies of this kind has been found, and in this way a foundation is laid for solving the inverse problem of these magnetic fields. In addition, by replacing the parameters and unit vectors in the spherical harmonic expansion of a magnetic field by gravitational parameters and a downward unit vector, we have also derived a forward method for the gravitational field (similar to that for the magnetic case) of a 3D body with an arbitrary boundary and continually varying density.

Notes: 2.5D modelling approximates 3D wave propagation in the dip-direction of a 2D geological model. Attention is restricted to raypaths for waves propagating in a plane. In this way, fast inversion or migration can be performed. For velocity analysis, this reduction of the problem is particularly useful.We review 2.5D modelling for Born volume scattering and Born–Helmholtz surface scattering. The amplitudes are corrected for 3D wave propagation, taking into account both in-plane and out-of-plane geometrical spreading. We also derive some new inversion/migration results. An AVA-compensated migration routine is presented that is simplified compared with earlier results. This formula can be used to create common-image gathers for use in velocity analysis by studying the residual moveout. We also give a migration formula for the energy-flux-normalized plane-wave reflection coefficient that models large contrast in the medium parameters not treated by the Born and the Born–Helmholtz equation results. All results are derived using the generalized Radon transform (GRT) directly in the natural coordinate system characterized by scattering angle and migration dip. Consequently, no Jacobians are needed in their calculation.Inversion and migration in an orthorhombic medium or a transversely isotropic (TI) medium with tilted symmetry axis are the lowest symmetries for practical purposes (symmetry axis is in the plane). We give an analysis, using derived methods, of the parameters for these two types of media used in velocity analysis, inversion and migration. The kinematics of the two media involve the same parameters, hence there is no distinction when carrying out velocity analysis. The in-plane scattering coefficient, used in the inversion and migration, also depends on the same parameters for both media. The out-of-plane geometrical spreading, necessary for amplitude-preserving computations, for the TI medium is dependent on the same parameters that govern in-plane kinematics. For orthorhombic media, information on additional parameters is required that is not needed for in-plane kinematics and the scattering coefficients.Resolution analysis of the scattering coefficient suggests that direct inversion by GRT yields unreliable parameter estimates. A more practical approach to inversion is amplitude-preserving migration followed by AVA analysis.SYMBOLS AND NOTATIONA list of symbols and notation is given in Appendix D.

Notes: Errors in acoustic logs have a significant influence on the assessment of formations, the description of oil deposits and modelling using synthetic seismograms. The elimination of these errors is a problem that many researchers have been trying to solve for many years. We derive theoretical formulae for calculating the radial depth of investigation of acoustic logging, and analyse the relationship between the error in acoustic interval transit time and the altered zone thickness. We explain in detail how mud affects the acoustic interval transit time. We also describe the variation of altered zone thickness with time and a method for calculating the altered zone thickness. Finally, we present a set of new methods that can be directly applied to correct the disturbing influence on acoustic curves. Our results are obtained based on the fact that acoustic velocities in the altered zone show a small lateral variation. Examples are given of analysing the acoustic log data, which are collected from a BS well at three different times. This paper is significant both for selection of the acoustic logging device with proper transmitter-to-receiver distance (spacing) and improvement of the device.

Notes: A strategy for multiple removal consists of estimating a model of the multiples and then adaptively subtracting this model from the data by estimating shaping filters. A possible and efficient way of computing these filters is by minimizing the difference or misfit between the input data and the filtered multiples in a least-squares sense. Therefore, the signal is assumed to have minimum energy and to be orthogonal to the noise. Some problems arise when these conditions are not met. For instance, for strong primaries with weak multiples, we might fit the multiple model to the signal (primaries) and not to the noise (multiples). Consequently, when the signal does not exhibit minimum energy, we propose using the L1-norm, as opposed to the L2-norm, for the filter estimation step. This choice comes from the well-known fact that the L1-norm is robust to ‘large’ amplitude differences when measuring data misfit. The L1-norm is approximated by a hybrid L1/L2-norm minimized with an iteratively reweighted least-squares (IRLS) method. The hybrid norm is obtained by applying a simple weight to the data residual. This technique is an excellent approximation to the L1-norm. We illustrate our method with synthetic and field data where internal multiples are attenuated. We show that the L1-norm leads to much improved attenuation of the multiples when the minimum energy assumption is violated. In particular, the multiple model is fitted to the multiples in the data only, while preserving the primaries.

Notes: We characterize the seismic response of Lake Vostok, an Antarctic subglacial lake located at nearly 4 km depth below the ice sheet. This study is relevant for the determination of the location and morphology of subglacial lakes. The characterization requires the design of a methodology based on rock physics and numerical modelling of wave propagation. The methodology involves rock-physics models of the shallow layer (firn), the ice sheet and the lake sediments, numerical simulation of synthetic seismograms, ray tracing, τ–p transforms, and AVA analysis, based on the theoretical reflection coefficients. The modelled reflection seismograms show a set of straight events (refractions through the firn and top-ice layer) and the two reflection events associated with the top and bottom of the lake. Theoretical AVA analysis of these reflections indicates that, at near offsets, the PP-wave anomaly is negative for the ice/water interface and constant for the water/sediment interface. This behaviour is shown by AVA analysis of the synthetic data set. This study shows that subglacial lakes can be identified by using seismic methods. Moreover, the methodology provides a tool for designing suitable seismic surveys.

Notes: A walkaround VSP is a novel acquisition geometry comprising multiple sources azimuthally distributed around a fixed multi-component receiver at approximately the same offset. Such a configuration allows the robust measurement of fracture-induced anisotropy by the analysis of certain seismic attributes with respect to azimuth.

Notes: We investigate the interactions between the elastic parameters, VP, VS and density, estimated by non-linear inversion of AVA data, and the petrophysical parameters, depth (pressure), porosity, clay content and fluid saturation, of an actual gas-bearing reservoir. In particular, we study how the ambiguous solutions derived from the non-uniqueness of the seismic inversion affect the estimates of relevant rock properties. It results that the physically admissible values of the rock properties greatly reduce the range of possible seismic solutions and this range contains the actual values given by the well. By means of a statistical inversion, we analyse how approximate a priori knowledge of the petrophysical properties and of their relationships with the seismic parameters can be of help in reducing the ambiguity of the inversion solutions and eventually in estimating the petrophysical properties of the specific target reservoir. This statistical inversion allows the determination of the most likely values of the sought rock properties along with their uncertainty ranges. The results show that the porosity is the best-resolved rock property, with its most likely value closely approaching the actual value found by the well, even when we insert somewhat erroneous a priori information. The hydrocarbon saturation is the second best-resolved parameter, but its most likely value does not match the well data. The depth of the target interface is the least-resolved parameter and its most likely value is strongly dependent on a priori information. Although no general conclusions can be drawn from the results of this exercise, we envisage that the proposed AVA–petrophysical inversion and its possible extensions may be of use in reservoir characterization.

Notes: The main objective of the AVO inversion is to obtain posterior distributions for P-wave velocity, S-wave velocity and density from specified prior distributions, seismic data and well-log data. The inversion problem also involves estimation of a seismic wavelet and the seismic-noise level. The noise model is represented by a zero mean Gaussian distribution specified by a covariance matrix. A method for joint AVO inversion, wavelet estimation and estimation of the noise level is developed in a Bayesian framework. The stochastic model includes uncertainty of both the elastic parameters, the wavelet, and the seismic and well-log data. The posterior distribution is explored by Markov-chain Monte-Carlo simulation using the Gibbs' sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The use of a coloured seismic-noise model resulted in about 10% lower uncertainties for the P-wave velocity, S-wave velocity and density compared with a white-noise model. The uncertainty of the estimated wavelet is low. In the Heidrun example, the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results.

Notes: We use a poroelastic modelling algorithm to compute numerical experiments on wave propagation in a rock sample with partial saturation using realistic fluid distribution patterns from tomography scans. Frequencies are in the range 10 to 500 kHz. The rock is a homogeneous isotropic sandstone partially filled with gas and water, which are defined by their characteristic values of viscosity, compressibility and density. We assume no mixing and that the two different pore-fills occupy different macroscopic regions. The von Kármán self-similar correlation function is used, employing different fractal parameters to model uniform and patchy fluid distributions, respectively, where effective saturation is varied in steps from full gas to full water saturation.Without resorting to additional matrix–fluid interaction mechanisms, we are able to reproduce the main features of the variation in wave velocity and attenuation with effective saturation and frequency, as those of published laboratory experiments. Furthermore, the behaviour of the attenuation peaks versus water saturation and frequency is similar to that of White's model. The conversion of primary P-wave energy into dissipating slow waves at the heterogeneities is shown to be the main mechanism for attenuating the primary wavefield. Fluid/gas patches are shown to affect attenuation more than equivalent patches in the permeability or solid-grain properties.

Notes: 3D Kirchhoff migration (KM) smears a trace's time sample along a quasi-ellipsoid in the model space. This is a costly and sometimes noisy process as reflection energy is smeared far away from the actual reflector position, introducing far-field migration artefacts. As a reduced form of 3D KM, 3D wavepath migration (WM) smears a picked reflection arrival to a small Fresnel zone portion centred about the specular reflection point, leading to fewer migration artefacts and reduced computation time. Both the traveltime and the angle of incidence are required by WM for locating the specular reflection point. Our results with 3D prestack synthetic data show that WM generates fewer migration artefacts and can sometimes define complex structure better than KM. Our results with 3D prestack field data show that WM can mostly suppress migration artefacts and can sometimes resolve reflection interfaces better than KM. The CPU comparison shows that, for both the synthetic and field data examples, WM can be more than an order of magnitude faster than KM. The limitation with 3D WM is that the angle of incidence calculation is sensitive to the recording geometry and the signal-to-noise (S/N) ratio, which can lead to blurred images.

Notes: An accurate and efficient 3D finite-difference (FD) forward algorithm for DC resistivity modelling is developed. In general, the most time-consuming part of FD calculation is to solve large sets of linear equations: Ax=b, where A is a large sparse band symmetric matrix. The direct method using complete Choleski decomposition is quite slow and requires much more computer storage. We have introduced a row-indexed sparse storage mode to store the coefficient matrix A and an incomplete Choleski conjugate-gradient (ICCG) method to solve the large linear systems. By taking advantage of the matrix symmetry and sparsity, the ICCG method converges much more quickly and requires much less computer storage. It takes approximately 15 s on a 533 MHz Pentium computer for a grid with 46 020 nodes, which is approximately 700 times faster than the direct method and 2.5 times faster than the symmetric successive over-relaxation (SSOR) conjugate-gradient method. Compared with 3D finite-element resistivity modelling with the improved ICCG solver, our algorithm is more efficient in terms of number of iterations and computer time. In addition, we solve for the secondary potential in 3D DC resistivity modelling by a simple manipulation of the FD equations. Two numerical examples of a two-layered model and a vertical contact show that the method can achieve much higher accuracy than solving for the total potential directly with the same grid nodes. In addition, a 3D cubic body is simulated, for which the dipole–dipole apparent resistivities agree well with the results obtained with the finite-element and integral-equation methods. In conclusion, the combination of several techniques provides a rapid and accurate 3D FD forward modelling method which is fundamental to 3D resistivity inversion.

Notes: We present results from the resolution and sensitivity analysis of 1D DC resistivity and IP sounding data using a non-linear inversion. The inversion scheme uses a theoretically correct Metropolis–Gibbs' sampling technique and an approximate method using numerous models sampled by a global optimization algorithm called very fast simulated annealing (VFSA). VFSA has recently been found to be computationally efficient in several geophysical parameter estimation problems. Unlike conventional simulated annealing (SA), in VFSA the perturbations are generated from the model parameters according to a Cauchy-like distribution whose shape changes with each iteration. This results in an algorithm that converges much faster than a standard SA. In the course of finding the optimal solution, VFSA samples several models from the search space. All these models can be used to obtain estimates of uncertainty in the derived solution. This method makes no assumptions about the shape of an a posteriori probability density function in the model space. Here, we carry out a VFSA-based sensitivity analysis with several synthetic and field sounding data sets for resistivity and IP. The resolution capability of the VFSA algorithm as seen from the sensitivity analysis is satisfactory. The interpretation of VES and IP sounding data by VFSA, incorporating resolution, sensitivity and uncertainty of layer parameters, would generally be more useful than the conventional best-fit techniques.

Notes: The nth-order moments of the electromagnetic impulse response are useful for interpreting electromagnetic data. We have derived an analytic expression for the half-order moment of a conductive half-space. By inverting this expression, the measured half-order moment can be used to estimate an apparent conductivity of the ground. The first-order moment can also be used to estimate the half-space conductivity. A sensitivity analysis indicates that for an airborne EM configuration, the half-order moment will be most sensitive to material in the top 26–48 m, while the first-order moment will be sensitive to deeper material (down to depths between 66 and 127 m).

Notes: Spectral factorization is a computational procedure for constructing minimum-phase (stable inverse) filters required for recursive inverse filtering. We present a novel method of spectral factorization. The method iteratively constructs an approximation of the minimum-phase filter with the given autocorrelation by repeated forward and inverse filtering and rearranging of the terms. This procedure is especially efficient in the multidimensional case, where the inverse recursive filtering is enabled by the helix transform.To exemplify a practical application of the proposed method, we consider the problem of smooth two-dimensional data regularization. Splines in tension are smooth interpolation surfaces whose behaviour in unconstrained regions is controlled by the tension parameter. We show that such surfaces can be efficiently constructed with recursive filter preconditioning and we introduce a family of corresponding two-dimensional minimum-phase filters. The filters are created by spectral factorization on a helix.

Notes: Fractured rock is often modelled under the assumption of perfect fluid pressure equalization between the fractures and equant porosity. This is consistent with laboratory estimates of the characteristic squirt-flow frequency. However, these laboratory measurements are carried out on rock samples which do not contain large fractures. We consider coupled fluid motion on two scales: the grain scale which controls behaviour in laboratory experiments and the fracture scale. Our approach reproduces generally accepted results in the low- and high-frequency limits. Even under the assumption of a high squirt-flow frequency, we find that frequency-dependent anisotropy can occur in the seismic frequency band when larger fractures are present. Shear-wave splitting becomes dependent on frequency, with the size of the fractures playing a controlling role in the relationship. Strong anisotropic attenuation can occur in the seismic frequency band. The magnitude of the frequency dependence is influenced strongly by the extent of equant porosity. With these results, it becomes possible in principle to distinguish between fracture- and microcrack-induced anisotropy, or more ambitiously to measure a characteristic fracture length from seismic data.

Notes: We consider a layered heterogeneous viscoelastic transversely isotropic medium with a vertical symmetry axis (a viscoelastic TIV medium) and parameters that depend on depth only. This takes into account intrinsic attenuation, anisotropy and thin layering. The seismic wavefield is decomposed into up- and downgoing waves scaled by the vertical energy flux. This scaling gives important symmetry relationships for both reflection and transmission (R/T) responses. For a stack of homogeneous layers, the exact reflection response can be computed in a numerically stable way by a simple layer-recursive algorithm. We derive exact plane-wave R/T coefficients and several linear and quadratic approximations between two viscoelastic TIV media, as functions of the real-valued horizontal slowness. The approximations are valid for pre- and post-critical values of horizontal slowness provided that the proper complex square roots are used when computing the vertical slowness. Numerical examples demonstrate that the quadratic approximations can be used for large differences in medium parameters, while the linear approximations can be used for small differences. For weak anisotropy it is sufficient to use an isotropic background medium, while for strong anisotropy it is necessary to use a weak TIV or TIV background medium. We also extend the O'Doherty–Anstey formula to the P- and SV-wave transmission responses of a stack of viscoelastic TIV layers, taking into account intrinsic attenuation, anisotropy and thin layering.

Notes: The first-order perturbation theory is used for fast 3D computation of quasi-compressional (qP)-wave traveltimes in arbitrarily anisotropic media. For efficiency we implement the perturbation approach using a finite-difference (FD) eikonal solver. Traveltimes in the unperturbed reference medium are computed with an FD eikonal solver, while perturbed traveltimes are obtained by adding a traveltime correction to the traveltimes of the reference medium. The traveltime correction must be computed along the raypath in the reference medium. Since the raypath is not determined in FD eikonal solvers, we approximate rays by linear segments corresponding to the direction of the phase normal of plane wavefronts in each cell. An isotropic medium as a reference medium works well for weak anisotropy. Using a medium with ellipsoidal anisotropy as a background medium in the perturbation approach allows us to consider stronger anisotropy without losing computational speed. The traveltime computation in media with ellipsoidal anisotropy using an FD eikonal solver is fast and accurate. The relative error is below 0.5% for the models investigated in this study. Numerical examples show that the reference model with ellipsoidal anisotropy allows us to compute the traveltime for models with strong anisotropy with an improved accuracy compared with the isotropic reference medium.

Notes: Measurements of seismic anisotropy in fractured rock are used at present to deduce information about the fracture orientation and the spatial distribution of fracture intensity. Analysis of the data is based upon equivalent-medium theories that describe the elastic response of a rock containing cracks or fractures in the long-wavelength limit. Conventional models assume frequency independence and cannot distinguish between microcracks and macrofractures. The latter, however, control the fluid flow in many subsurface reservoirs. Therefore, the fracture size is essential information for reservoir engineers. In this study we apply a new equivalent-medium theory that models frequency-dependent anisotropy and is sensitive to the length scale of fractures. The model considers velocity dispersion and attenuation due to a squirt-flow mechanism at two different scales: the grain scale (microcracks and equant matrix porosity) and formation-scale fractures. The theory is first tested and calibrated against published laboratory data. Then we present the analysis and modelling of frequency-dependent shear-wave splitting in multicomponent VSP data from a tight gas reservoir. We invert for fracture density and fracture size from the frequency dependence of the time delay between split shear waves. The derived fracture length matches independent observations from borehole data.

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.