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- Volume 40, Issue 1, 1992
Geophysical Prospecting - Volume 40, Issue 1, 1992
Volume 40, Issue 1, 1992
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TOMOGRAPHIC INVERSION OF NORMALIZED DATA: DOUBLE‐TRACE TOMOGRAPHY ALGORITHMS1
Authors MICHAEL DOBROKA, LOTHAR DRESEN, CHRISTOPH GELBKE and HORST RÜTERAbstractTomography is widely used in geophysics as a technique for imaging geological structures by means of data that are line integrals of physical characteristics. In some transmission measurements, due to various kinds of normalization, the measured data are related to two (the current and the reference) raypaths and can be expressed as a function of differences between line integrals. This is the case, for example, in seismo‐acoustic emission measurements, when (since the exact start time is unknown) only the differences between traveltimes (differences between line integrals of the slowness) can be determined. Similarly the use of normalized Fourier amplitudes results in data dependent upon the difference between line integrals of the absorption coefficient (computed along the actual and the reference raypaths).
In order to invert these data the ordinary tomography algorithms should be modified. Some generalizations are presented for series expansion tomography methods in order to make them applicable to reconstruction problems in which the input data are differences between two line integrals. The conjugate gradient and the simultaneous iterative reconstruction technique (SIRT) methods were adapted and tested. It is shown that the modified tomography algorithms are stable and sufficiently accurate for practical use. In the reconstruction of noise‐free difference data, the conjugate gradient algorithm is found to be faster and more accurate while, in the case of noisy difference data, the modified SIRT algorithm is more stable and insensitive to noise.
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PSEUDOREFLECTION PROFILING METHOD: AN EFFICIENT COMPLEMENT TO CDP METHOD1
More LessAbstractA method for pseudoreflection profiling (PRP) is presented. By using transmission seismograms, this method produces time sections similar to those obtained using the common depth point (CDP) method.
Pseudoreflection profiles are obtained using the following procedure. Equivalent transmission responses at sites on soft deposits are derived by Wiener filter estimation using seismograms acquired on the sites and on the basement rock. These responses are substituted into the Claerbout‐Kunetz equation to obtain the pseudoreflection profiles.
A 3D subsurface model is produced when the PRP method is applied to explosion seismograms. The time sections thus obtained are consistent with those obtained using the CDP method in a neighbouring area. The maximum station interval for obtaining coherent profiles with this method is estimated to be one quarter of the wavelength of the transmitted waves.
This technique should be used in combination with another method such as the CDP method because it has two weak points: the velocity structure cannot be obtained directly and undesirable waves cannot be eliminated through processing.
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SEISMOGRAM SYNTHESIS AND RECOMPRESSION OF DISPERSIVE IN‐SEAM SEISMIC MULTIMODE DATA USING A NORMAL‐MODE SUPERPOSITION APPROACH
More LessAbstractIn spite of a geometrical rotation into radial and transverse parts, two‐ or three‐component in‐seam seismic data used for underground fault detection often suffer from the problem of overmoding ‘noise’. Special recompression filters are required to remove this multimode dispersion so that conventional reflection seismic data processing methods, e.g. CMP stacking techniques, can be applied afterwards.
A normal‐mode superposition approach is used to design such multimode recompression filters. Based on the determination of the Green's function in the far‐field, the normal‐mode superposition approach is usually used for the computation of synthetic single‐ and multi‐mode (transmission) seismograms for vertically layered media. From the filter theory's point of view these Green's functions can be considered as dispersion filters which are convolved with a source wavelet to produce the synthetic seismograms. Thus, the design of multimode recompression filters can be reduced to a determination of the inverse of the Green's function. Two methods are introduced to derive these inverse filters. The first operates in the frequency domain and is based on the amplitude and phase spectrum of the Green's function. The second starts with the Green's function in the time domain and calculates two‐sided recursive filters.
To test the performance of the normal‐mode superposition approach for in‐seam seismic problems, it is first compared and applied to synthetic finite‐difference seismograms of the Love‐type which include a complete solution of the wave equation. It becomes obvious that in the case of one and two superposing normal modes, the synthetic Love seam‐wave seismograms based on the normal‐mode superposition approach agree exactly with the finite‐difference data if the travel distance exceeds two dominant wavelengths. Similarly, the application of the one‐ and two‐mode recompression filters to the finite‐difference data results in an almost perfect reconstruction of the source wavelet already two dominant wavelengths away from the source.
Subsequently, based on the dispersion analysis of an in‐seam seismic transmission survey, the normal‐mode superposition approach is used both to compute one‐ and multi‐mode synthetic seismograms and to apply one‐ and multimode recompression filters to the field data. The comparison of the one‐ and two‐mode synthetic seismograms with the in‐seam seismic transmission data reveals that arrival times, duration and shape of the wavegroups and their relative excitation strengths could well be modelled by the normal‐mode superposition approach. The one‐mode recompressions of the transmission seismograms result in non‐dispersive wavelets whose temporal resolution and signal‐to‐noise ratio could clearly be improved. The simultaneous two‐mode recompressions of the underground transmission data show that, probably due to band‐limitation, the dispersion characteristics of the single modes could not be evaluated sufficiently accurately from the field data in the high‐frequency range. Additional techniques which overcome the problem of band‐limitation by modelling all of the enclosed single‐mode dispersion characteristics up to the Nyquist frequency will be mandatory for future multimode applications.
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PARAMETRIZATION OF GRT INVERSION FOR ACOUSTIC AND P–P SCATTERING1
Authors L. T. IKELLE, P. W. KITCHENSIDE and P. S. SCHULTZAbstractThe generalized Radon transform (GRT) inversion contains an explicit relationship between seismic amplitude variations, the reflection angle and the physical parameters which can be used to describe the earth efficiently for inversion purposes. Using this relationship, we have derived parametrizations for acoustic and P–P scattering so that the variations in seismic amplitude with reflection angle for each parameter are sufficiently independent. These parametrizations show that small offset and large offset amplitudes are related to different physical parameters. In the case of acoustic scattering, the small‐offset amplitudes are related to impedance variations while large‐offset amplitudes are related to velocity variations. A similar result has been established for P–P scattering.
The Born approximation (which is used to derive the GRT inversion) does not correctly predict the amplitude due to velocity variations at large offsets, and thus the inversion of velocity is not as satisfactory as the inversion of impedance.
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RESISTIVITY OF ROCK‐SALT IN ASSE (GERMANY) AND PETROPHYSICAL ASPECTS1
Authors U. YARAMANCI and D. FLACHIn the Asse salt‐mine (Germany), where extensive research is carried out on various aspects of nuclear waste disposal in rock‐salt formations, the resistivity of a future construction site for a test seal at a depth of 945 m has been investigated. Measurements have been conducted, using various types of the four‐point electrode configuration, on a network of 180 electrodes permanently installed in boreholes. A fully computer‐controlled measurement system has been built consisting of a resistivity meter, a switchbox for electrodes and a computer with special control software. The system has interactive and programmable automatic working modes with an extensive capability for documentation and processing including the immediate evaluation of apparent resistivities and is suitable for long‐term continuous observations.
The average resistivity at the site which consists of almost homogeneous Stassfurt rock‐salt, is approximately 0.6 × 106Ωm with little variation. There is a small anomaly due to a conductive inclusion, probably a local anhydrite band. There is no indication of anisotropy so far and no significant change with time. The specific amount of water in the effective pores and its change can be estimated from the observed resistivities using the extended form of Archie's equation with pore saturation included. In this case data for the specific internal surface from samples are available and the order of permeability may be estimated using the formation factor derived from resistivities.
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