ALBERT

Notes: Pseudo-velocity-logs are tentative determinations of subsurface velocity variations with depth, using both information of seismic amplitude and reflection curvature.A rigorous theoretical method would consist in〈list xml:id="l1" style="custom"〉a) deconvolving the seismic traces to remove the filtering effects of the ground and of the recording equipmentb) demultiplying the deconvolved traces by a complete desynthesization with convergence criteriac) computing the velocities.While this method works with synthetic examples, it is not generally applicable to field cases, one of the reasons being the poor reliability of desynthesization in the presence of noise.The present method is a compromise between a rigorous and a practical process: the complete desynthesization is not performed; deconvolution and demultiplication are done by more classical techniques using real amplitudes; absolute velocities are determined to fit both the reflection coefficients and the rms velocities. It leads to pseudovelocity-logs, accurate enough to show lithologic variations, smoothed enough to preserve the signal/noise ratio.Examples are shown of Flexichoc profiles recorded in 2500 m (8000–9000 feet) deep areas of the Mediterranean Sea. Pseudo-velocity-logs show 1000 m (3000 feet) of a velocity-increasing-with-depth Plio-pleistocene marl formation, overlying Miocene evaporites. Intercalations of high and low-velocity layers in the evaporites seem to indicate vertical facies variations.The Pseudo-velocity-log, associated with other lithologic determination processes, should become a geological tool for deep offshore exploration.

Notes: Dynamic predictive deconvolution makes use of an entire seismic trace including all primary and multiple reflections to yield an approximation to the subsurface structure. We consider plane-wave motion at normal incidence in an horizontally layered system sandwiched between the air and the basement rock. Energy degradation effects are neglected so that the layered system represents a lossless system in which energy is lost only by net transmission downward into the basement or net reflection upward into the air; there is no internal loss of energy by absorption within the layers. The layered system is frequency selective in that the energy from a surface input is divided between that energy which is accepted over time by net transmission downward into the basement and the remaining energy that is rejected over time by net reflection upward into the air. Thus the energy from a downgoing unit spike at the surface as input is divided between the wave transmitted by the layered system into the basement and the wave reflected by the layered system into the air. This reflected wave is the observed seismic trace resulting from the unit spike input. From surface measurements we can compute both the input energy spectrum, which by assumption is unity, and the reflection energy spectrum, which is the energy spectrum of the trace. But, by the conservation of energy, the input energy spectrum is equal to the sum of the reflection energy spectrum and the transmission energy spectrum. Thus we can compute the transmission energy spectrum as the difference of the input energy spectrum and the reflection energy spectrum. Furthermore, we know that the layered system acts as a pure feedback system in producing the transmitted wave, from which it follows that the transmitted wave is minimum-delay. Hence from the computed energy spectrum of the transmitted wave we can compute the prediction-error operator that contracts the transmitted wave to a spike. We also know that the layered system acts as a system with both a feedback component and a feed-forward component in producing the reflected wave, that is, the observed seismic trace. Moreover, this feedback component is identical to the pure feedback system that produces the transmitted wave. Thus, we can deconvolve the observed seismic trace by the prediction-error operator computed above; the result of the deconvolution is the wave-form due to the feedforward component alone. Now the feedforward component represents the wanted dynamic structure of the layered system whereas the feedback component represents the unwanted reverberatory effects of the layered system. Because this deconvolution process yields the wanted dynamic structure and destroys the unwanted reverberatory effects, we call the process dynamic predictive deconvolution. The resulting feedforward waveform in itself represents an approximation to the subsurface structure; a further decomposition yields the reflection coefficients of the interfaces separating the layers. In this work we do not make the assumption as is commonly done that the surface as a perfect reflector; that is, we do not assume that the surface reflection coefficient has magnitude unity.

Notes: The theory of geoelectric sounding exploration is based on Stefanescu's kernel. In order to study the analytic properties of the kernel, necessary and sufficient conditions on it's poles and zeroes are developed. A distinction is made between “physical” and “perfect” models.It is shown that a physical model may be determined from either the set of poles or the set of zeroes of the raised kernel function at the top of the model. These roots may be of desired multiplicities.For determining a perfect model, both sets of poles and zeroes are required and they all have to be simple ones.

Notes: The Galerkin method of solving integral equations is well suited to the solution of the integral equations describing the transient response of a sphere embedded in a layered medium, which is excited by a large co-axial loop.The transient response is calculated by transforming the steady state solutions obtained in the frequency domain.The analysis shows that the scattering matrix is extremely diagonally dominant and the maximum number of modes required to obtain convergence does not rapidly increase with frequency. The number of modes required is about eight. This type of scattering matrix can be taken to be an expression of the principle of elementary superposition. This principle is reflected in the decay curves. These show that the early part of the decay curves asymptotically approach the decay curves to be expected for a layered structure without the sphere. The slope of the latter stages of the decay curve gives a decay constant that is the same as was obtained for spheres in free space excited by planar or dipolar sources.The point of departure in time of these curves from the layered ground curves is delayed either by placing the sphere at a greater depth or by placing a more conductive overburden above the sphere.

Notes: The hydrocarbon-brine contact produces a flat reflection, unconformable with the lithologic reflections from the trap boundaries, and over a limited area bounded by structural contours. When it can be reliably detected and mapped, the flat spot can provide (i) a reasonably unambiguous indication and areal extent of a reservoir and (ii) an estimate of reservoir thickness.The gas-brine contact in thick reservoirs in offshore elastic sections is the easiest target. An example of gas mapping is presented in the paper. Other reservoirs represent a continuum of increasingly elusive targets.Increasing the range of applicability of flat spot exploration will require (i) increases in signal/noise and multiple ratio, increases in the three dimensional depth point density (or grid density), increased resolution and static and dynamic correction accuracy, and (ii) processing and interpretation aimed directly at flat spot mapping.Low relief structural and stratigraphic traps should provide the most attractive targets. The approach should be at least theoretically feasible, though not necessarily cost effective, for most major reservoirs with a well-behaved hydrocarbon brine contact.

Notes: The estimation of residual static corrections is investigated as a linear system. For 1200% coverage shot one way offset weighting functions—or in other words, estimation error operators—are computed. Assuming zero time shift determination errors and zero RNMO it is seen that large residual corrections will distort the effectivity of the estimation.With an iterative procedure which includes the repeated averaging according to depth point, shot point, and geophone point the effectivity of the method becomes more favourable. This can be learnt from the evaluation of estimation error operators computed by recursive formulae.In practice, due to the time shift determination errors, the routine does not give improved results in the desired level. Errors can be reduced with a more reliable time shift determination routine.For detecting and suppressing the unfavourable effect of time shift errors still remaining in the data a self-adaptive method was developed. In this non linear routine the data are evaluated at all three averaging processes according to limit values and weighting factors computed from the data itself.Field examples processed in different ways are presented.

Notes: The spectral representation of gravity and magnetic fields shows that the mathematical expressions describing these fields are the result of convolution of factors which depend on the geometry of the causative body, the physical properties of the body and the type of field being observed. If a field is known, it is possible to remove or alter these factors to map other fields or physical parameters which are linearly related to the observed field. The transformations possible are: continuation, reduction to the pole, converting between gravity and magnetic fields, converting between components of measurement, calculation of derivatives, and mapping magnetization and density distribution, relief on interfaces, and vertical thicknesses of layers.

Notes: The hidden layer problem in seismic refraction work has been studied for three velocity configurations – the intermediate layer having (a) lower, (b) intermediate and (c) higher velocity than the underlying and overlying beds. It has been shown that conventional methods fail to locate the presence of the intermediate layer for the cases (a) and (c) and lead to errors in calculating the depth to the bedrock. For the case (b), it is possible to interpret the first arrival travel time analytically as an alternative to Green's graphical approach. It has been suggested that the hidden layer may be detected in all the three cases if converted S waves are also recorded in the seismogram.

Notes: The depth of causative bodies may be derived from the power spectrum of their magnetic anomalies. After a short review of the theoretical basis of the method, several examples of its application to synthetic cases are shown. Disturbing effects due to improper choice of the sampling interval and to anomalies only partially contained in the examined segment of the profile are studied.The spectral method is then applied to real cases; the tapering of the anomalies, the application of non-linear filters and the effects of anomaly superpositions are investigated.In conclusion, an appraisal of the method and of its possible practical impact has been given.