Resolution in seismic trace inversion by parameter estimation

Riel, P. van; Berkhout, A. J.

doi:10.1190/1.1442012

Cited by 34 publications

(12 citation statements)

References 7 publications

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“…Algorithms that fall into this class use the 1D convolution model ͑Oldenburg et al., 1983;van Riel and Berkhout, 1985;Lancaster and Whitcombe, 2000͒. Hence, these algorithms do not account for the lateral resolution aspects of the migration process.…”

Section: ͑10͒mentioning

confidence: 99%

“…Current industry practice is to estimate attributes such as acoustic impedance from the migrated real data by a seismic inversion process known as constrained sparse-spike inversion ͑see Veeken and Da Silva, 2004͒. Basically, a simulated seismic trace is created with the help of the 1D convolution model and matched to one trace of the migrated real data by varying the position and strength of a number of spikes ͑Oldenburg et al, 1983;van Riel and Berkhout, 1985͒. We refer to the final result of a seismic inversion process as a 1D inversion image.…”

Section: Introductionmentioning

confidence: 99%

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Simulating migrated and inverted seismic data by filtering a geologic model

et al. 2008

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The simulation of migrated and inverted data is hampered by the high computational cost of generating 3D synthetic data, followed by processes of migration and inversion. For example, simulating the migrated seismic signature of subtle stratigraphic traps demands the expensive exercise of 3D forward modeling, followed by 3D migration of the synthetic seismograms. This computational cost can be overcome using a strategy for simulating migrated and inverted data by filtering a geologic model with 3D spatial-resolution and angle filters, respectively. A key property of the approach is this: The geologic model that describes a target zone is decoupled from the macrovelocity model used to compute the filters. The process enables a target-oriented approach, by which a geologically detailed earth model describing a reservoir is adjusted without having to recalculate the filters. Because a spatial-resolution filter combines the results of the modeling and migration operators, the simulated images can be compared directly to a real migration image. We decompose the spatial-resolution filter into two parts and show that applying one of those parts produces output directly comparable to 1D inverted real data. Two-dimensional synthetic examples that include seismic uncertainties demonstrate the usefulness of the approach. Results from a real data example show that horizontal smearing, which is not simulated by the 1D convolution model result, is essential to understand the seismic expression of the deformation related to sulfate dissolution and karst collapse.

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Section: ͑10͒mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simulating migrated and inverted seismic data by filtering a geologic model

et al. 2008

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“…However, the industry practice is that most algorithms are working on a trace by trace basis (Oldenburg et al, 1988;van Riel and Berkhout, 1985), meaning that only the Band limitation filter is (partly) removed. Consequently, the derived impedance values from pre-stack depth migrated seismic cannot straight forwardly be compared to impedance values (density times velocity) directly computed from the synthetic Geological Depth Model.…”

Section: Introductionmentioning

confidence: 99%

Simulating high resolution inversion: Decomposing the resolution function

Toxopeus

Thorbecke

Wapenaar

et al. 2004

SEG Technical Program Expanded Abstracts 2004

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SummaryIn order to correctly compare an impedance section obtained from industry practice inversion algorithms to the impedance of a synthetic geological model (velocity times density), the synthetic impedance values have to be filtered by an Angle filter. This is concluded after decomposing the resolution function into an Angle and Band limiting filter. The low computational costs of the method make it possible that an interpreter can iteratively use the method to minimize the mismatch between a real and a synthetic impedance section.

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“…In this case, the noise is assumed to be filtered white noise and the discrete filter coefficients are estimated in addition to the reflection coefficients. Another method used to improve the least-squares procedure is singular value decomposition (SVD; Levy and Clowes 1980, Shim and Cho 1981, Van Riel 1982, Tufts and Kumaresan 1982, Van Riel and Berkhout 1983, Lines and Treitel 1984. Two methods may be used to stabilize the least-squares procedure (Lawson and Hanson 1974).…”

mentioning

confidence: 99%

“…Two methods may be used to stabilize the least-squares procedure (Lawson and Hanson 1974). One is the SVD cut-off method which has been discussed by Shim and Cho (1981) and Van Riel (1982). The inverse of the singular values may be replaced by zeros when they are less than some threshold.…”

mentioning

confidence: 99%

Identification of seismic reflections using singular value decomposition

Ursin¹,

Zheng

1984

SEG Technical Program Expanded Abstracts 1984

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TIflE,rnl, FREDUENCYl hZ 1 FIG. 2. Pulse estimated from the reflectivity function and the stacked trace at CDP 278.bound to depend upon bandwidth, time gate, pulse length, signal-to-noise ratio, and a priori information. We have not been able to establish a theoretical resolution limit, and we leave this as an open question.Real data example Figure 1 shows a part of a stacked, unprocessed seismic section. The sampling interval is 4 ms. A reflection coeffi-FIG. 3. Stacked traces and their estimates. Reflectivity function obtained from the well at CDP 278 is included for comparison.Cient series obtained from well data at CDP 278 is also displayed. The sampling interval of the reflection coefficient series iS 2.0 ms. We focus our attention on the area between 2082 and 2222 ms two-way traveltime. Reflection coefficients in this interval together with the stacked trace for CDP 278 are used to estimate the pulse displayed in Figure 2. AS can be seen from its "tail," the estimated pulse is distorted by multiple reflections and/or edge effects. These effects cannot be expected to be spatially invariant. Hence the estimated pulse will only be suited for inversion of traces close to the well.The results displayed in Figure 3 are obtained using the estimated pulse and with zero starting values for r and c. For LS estimation, the trace had to be resampled to 8.0 ms sampling interval. The event at approximately 2100 ms twoway traveltime is resolved, but the rest of the trace is corrupted by spurious events with alternating polarity. Maximum-likelihood estimation was performed with 4.0 ms sampling interval and NC equal to five. The result of ML estimation appears to be a smoothed version of the reflection coefficient series obtained from the well log. The event at approximately 2100 ms two-way time is nicely resolved, but the negative peak at approximately 2150 ms is not properly recovered. The polarity changes from 2150 to 2220 ms vary consistently along the traces. Conclusions Synthetic and real data examples demonstrated that the maximum-likelihood method gives better resolution andimproved numerical stability when compared to the leastsquares method. When least-squares estimation is applied, the sampling rate must be chosen approximately equal to the Nyquist rate of the trace. Maximum-likelihood estimation yields resolution that is superior to the resolution provided by least-squares estimation. The ML method also appears to be numerically more stable. In real data applications, inversion is distorted by multiple reflections and also by edge effects when only a limited part of the seismic trace is considered. ReferencesAstrom, J. K., 1981, Maximum likelihood and prediction error methods, in Trends and progress in system identification: P. Eykhoff, ed., Pergamon Press. Ekstrom, M. P., 1973, A spectral characterization of the ill-conditioning in numerical deconvolution: IEEE Trans. on Audio and Electroacoustics, AU-S. @zdemir, H., 1982, Seismic impulse response estimation by the maximum-likelihood and the least-squares metho...

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Resolution in seismic trace inversion by parameter estimation

Cited by 34 publications

References 7 publications

Simulating migrated and inverted seismic data by filtering a geologic model

Simulating migrated and inverted seismic data by filtering a geologic model

Simulating high resolution inversion: Decomposing the resolution function

Identification of seismic reflections using singular value decomposition

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