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- Volume 39, Issue 2, 1991
Geophysical Prospecting - Volume 39, Issue 2, 1991
Volume 39, Issue 2, 1991
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τ‐p SEISMIC DATA FOR VISCOELASTIC MEDIA – PART 1: MODELLING1
Authors RUBEN D. MARTINEZ and GEORGE A. McMECHANAbstractViscoelastic modelling reveals that the interaction of compressional‐wave velocity Cp, compressional‐wave quality factor Qp, shear‐wave velocity Cs, shear‐wave quality factor Qs and Poisson's ratio as a function of time intercept τ and ray parameter p, is complicated; however, distinct, potentially diagnostic behaviours are seen for different combinations of viscoelastic parameters.
Synthetic seismograms for three viscoelastic reservoir models show that variations in the Poisson's ratio produce visible differences when compared to the corresponding elastic synthetic seismograms; these differences are attributable to interaction of the elastic parameters with Qp and Qs.
When the P‐wave acoustic impedance contrast is small, viscoelastic effects become more apparent and more useful for interpretation purposes. The corresponding amplitude and net phase spectra reveal significant differences between the elastic and the viscoelastic responses. When P‐wave reflectivities are large, they tend to dominate the total response and to mask the Q reflectivity effects. The attenuation effects are manifested as an amplitude decay that increases with both time and ray parameter.
The sensitivity of the computed seismic responses for various combinations of viscoelastic parameters suggests the opportunity for diagnostic interpretation of τ‐p seismic data. The interpretation of the viscoelastic parameters can permit a better understanding of the rock types and pore fluid distribution existing in the subsurface.
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τ‐p SEISMIC DATA FOR VISCOELASTIC MEDIA ‐ PART 2: LINEARIZED INVERSION1
Authors RUBEN D. MARTINEZ and GEORGE A. McMECHANAbstractAn approach to extraction of viscoelastic parameters from seismic data is implemented and succesfully tested. Viscoelastic inversion is performed using adaptive damping factors to control the sensitivity of the viscoelastic parameters in relation to the τ‐p seismic data. A priori information is incorporated through the damping factors as standard deviations of the data and of the viscoelastic model parameters. The stability of the inversion process is controlled by the variation of the damping factors as a function of the residual errors and parameter updates at each iteration.
Tests on synthetic and real data show that P‐ and S‐wave quality factors, Qp and Qs, in addition to P‐ and S‐wave velocities and density Cp, Cs and p, can be extracted from τ‐p seismic information. Singular value decomposition analysis demonstrates that estimated Qp and Qs values are more affected by the presence of data inaccuracies and noise than are those of Cp and p. Cs and Qs are not uniquely recovered due to the limited contribution of P‐S converted waves.
Knowledge of the viscoelastic parameters is of particular importance in accurately describing petrophysical properties of rocks and pore fluids existing in the subsurface; this is demonstrated with real data from the Gulf of Mexico.
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SEQUENTIAL WIENER DECONVOLUTION TO IMPROVE SEISMIC RESOLUTION1
Authors R.‐G. FERBER and H. KOITKAAbstractTwo different techniques for performing time‐variable Wiener deconvolution are compared using stacked seismic data. The conventional technique involves the empirical division of the data into a number of gates and the determination of time‐invariant deconvolution filters for each gate. In the second technique, the deconvolution filter is recomputed after each time increment from a fixed‐length data gate sliding along the trace. This scheme has the advantage that no a priori segmentation of the data is needed.
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GEOMETRIC CORRECTIONS IN ATTENUATION MEASUREMENTS1
More LessAbstractSeismic wave attenuation in porous rocks consists of intrinsic or anelastic attenuation (the lost energy is converted into heat due to interaction between the waves and the rocks) and the extrinsic or geometric attenuation (the energy is lost due to beam spreading, transmission loss and scattering). The first is of great importance because it can give additional information on the petrophysical properties of rocks (permeability, degree of saturation, type of saturant, etc.). The most difficult problem in attenuation measurements is estimating or eliminating extrinsic attenuation, so that the intrinsic attenuation can be obtained. To date, in laboratory attenuation measurements using wave propagation, several methods have been used. The difficulties vary with the method. The coupling effect and the geometric divergence or beam spreading are the major problems.
Papadakis’ diffraction corrections have been used extensively by Winkler and Plona in their modified pulse‐echo high‐pressure attenuation measurements. These corrections are computed for homogeneous liquid media and their failure to fit data for solid material implies that these corrections must be used with caution, especially for high Q values.
Three new methods for laboratory ultrasonic attenuation measurements are presented. The first is the ‘ultrasonic lens’ method for attenuation measurements at atmospheric pressure, in which an ultrasonic lens placed between transmitter and sample transforms the initially oblique incident beam into normal incidence so that the geometric divergence is eliminated. The second method is the ‘panoramic receiver’, in which the beam spreading can be eliminated by integrating the ultrasonic energy over a large area. The third method is called 'self‐spectral ratio’ and is applicable for all pressure conditions. Attenuation is estimated by comparing two signals recorded on the same rock but with two slightly different thicknesses under the same pressure conditions. Hence the extrinsic attenuation for both thicknesses is approximately the same. A comparison between the self‐spectral ratio method and that of Winkler and Plona demonstrates a very good agreement for a broad band of frequencies. Hence the Winkler‐Plona technique and Papadakis’ diffraction corrections can be accepted as reliable in any future work.
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LAYERED PERMEABLE SYSTEMS1
More LessAbstractPermeability is a second rank tensor relating flow rate to pressure gradient in a porous medium. If the permeability is a constant times the identity tensor the permeable medium is isotropic; otherwise it is anisotropic. A formalism is presented for the simple calculation of the permeability tensor of a heterogeneous layered system composed of interleaved thin layers of several permeable constituent porous media in the static limit. Corresponding to any cumulative thickness H of a constituent is an element consisting of scalar H and a matrix which is H times a hybrid matrix function of permeability. The calculation of the properties of a medium equivalent to the combination of permeable constituents may then be accomplished by simple addition of the corresponding scalar/matrix elements. Subtraction of an element removes a permeable constituent, providing the means to decompose a permeable medium into many possible sets of permeable constituents, all of which have the same flow properties. A set of layers of a constituent medium in the heterogeneous layered system with permeability of the order of 1/h as h→ 0, where h is that constituent's concentration, acts as a set of infinitely thin channels and is a model for a set of parallel cracks or fractures. Conversely, a set of layers of a given constituent with permeability of the order of h as h→ 0 acts as a set of parallel flow barriers and models a set of parallel, relatively impermeable, interfaces, such as shale stringers or some faults. Both sets of channels and sets of barriers are defined explicitly by scalar/matrix elements for which the scalar and three of the four sub‐matrices vanish. Further, non‐parallel sets of channels or barriers can be ‘added’ and 'subtracted’ from a background homogeneous anisotropic medium commutatively and associatively, but not non‐parallel sets of channels and barriers reflecting the physical reality that fractures that penetrate barriers will give a different flow behaviour from barriers that block channels. This analysis of layered media, and the representations of the phenomena that can occur as the thickness of a constituent is allowed to approach zero, are applicable directly to layered heat conductors, layered electrostatic conductors and layered dielectrics.
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ELASTIC PARAMETER ESTIMATION BY COHERENCY OPTIMIZATION1
Authors MOSHE RESHEF, EVGENY LANDA and TAMAR RAVIDAbstractWe present a method for estimating P‐ and S‐velocities within defined layers (macromodel), using only kinematic properties (i.e. traveltimes) of the wavefield. The method does not require identification of mixed‐mode events on prestack or post‐stack data. After obtaining a Vp‐depth model by coherency inversion, S‐velocities are determined by coherency optimization along computed traveltime curves for mixed‐mode events on prestack data. Since the method does not involve any dynamic wavefield computations, a simple ray‐tracing algorithm is used to solve the forward problem. The simplicity of the scheme, together with the ability to apply it locally, makes it highly suitable for interactive use. Results of this method may be used to detect Poisson's ratio anomalies within or between layers and may serve as an initial model for more complicated elastic inversion algorithms.
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INTEGRATED INTERPRETATION, 3D MAP MIGRATION AND VSP MODELLING PROJECT, NORTHERN U.K. SOUTHERN GAS BASIN1
By J. M. REILLYAbstractDepth conversion in the northern part of the U.K. Southern Gas Basin is complicated by the presence of Zechstein (Permian) salt swells and diapirs. In addition, the post‐Zechstein (post‐Permian) section displays large lateral velocity variations. The primary agents which control the velocity of this stratigraphic section are: (1) depth of burial, (2) lithological variation within individual formations, and (3) the effects of subsequent tectonic inversion. An integrated approach which combines well velocity, seismic velocity and seismic interpretation is required for accurate depth estimation.
In 1988 Mobil and partners drilled an exploratory well in the northern part of the U.K. Southern Gas Basin. This well was located near the crest of a Zechstein salt diapir. Over 2000 m of Zechstein was encountered in the well. The Permian Rotliegendes objective was penetrated at a depth of over 3700 m.
The initial delineation of the objective structure was based on the results of 3D map migration of the seismic time interpretation. Spatially‐variant interval velocity functions were used to depth convert through five of the six mapped horizons. Both well and model‐based seismic interval velocity analysis information was used to construct these functions.
A moving‐source well seismic survey was conducted. The survey was run in two critical directions. In conjunction with presurvey modelling, it was possible to confirm immediately the structural configuration as mapped to a distance of 7 km from the well. Post‐survey 3D map migration and modelling was employed to further refine the structural interpretation. Although the question of stratigraphic anisotropy was considered in the evaluation of the long offset modelling, no evidence was found in the field data to support a significant effect.
Finally, comparisons were made of: curved‐ray versus straight‐ray migration/modelling, midpoint‐depth velocity versus (depth‐dependant instantaneous velocity functions, and Hubral‐ versus Fermat‐based map depth migration algorithms. Significant differences in the results were observed for structural dips exceeding 15o and/or offsets exceeding 6 km. Map depth migration algorithms which employed both curved rays and spatially‐variant instantaneous velocity functions were found to best approximate the ‘true’ geological velocity field in the study area.
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INTEGRATED EXPLORATION FOR LOW‐TEMPERATURE GEOTHERMAL RESOURCES IN THE HONEY LAKE BASIN, CALIFORNIA1
More LessAbstractAn integrated exploration study is presented to locate low‐temperature geothermal reservoirs in the Honey Lake area of northern California. Regional studies to locate the geothermal resources included gravity, infra‐red, water‐temperature, and water‐quality analyses. Five anomalies were mapped from resistivity surveys. Additional study of three anomalies by temperature‐gradient and seismic methods was undertaken to define structure and potential of the geothermal resource. The gravity data show a graben structure in the area. Seismic reflection data indicate faults associated with surface‐resistivity and temperature‐gradient data. The data support the interpretation that the shallow reservoirs are replenished along the fault zones by deeply circulating heated meteoric waters.
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