Conventional semblance velocity analysis is equivalent to modeling prestack seismic data with events that have hyperbolic moveout but no amplitude variation with offset (AVO). As a result of its assumption that amplitude is independent of offset, this method might be expected to perform poorly for events with strong AVO—especially for events with polarity reversals at large offset, such as reflections from tops of some class 1 and class 2 sands. We find that substantial amplitude variation and even phase change with offset do not compromise the conventional semblance measure greatly. Polarity reversal, however, causes conventional semblance to fail. The semblance method can be extended to take into account data with events that have amplitude variation, expressed by AVO intercept and gradient (i.e., the Shuey approximation). However, because of the extra degrees of freedom introduced in AVO‐sensitive semblance, resolution of the estimated velocities is decreased. This is because the data can be modeled acceptably with a range of combined erroneous velocity and AVO behavior. To address this problem, in addition to using the Shuey equation to describe the amplitude variation, we constrain the AVO parameters (intercept and gradient) to be related linearly within each semblance window. With this constraint we can preserve velocity resolution and improve the quality of velocity analysis in the presence of amplitude and even polarity variation with offset. Results from numerical tests suggest that the modified semblance is accurate in the presence of polarity reversals. Tests also indicate, however, that in the presence of noise, the signal peak in conventional semblance has better standout than does that in the modified semblance measures.

The method of complex basis functions proposed by Rescigno and Reinhardt is applied to the calculation of the amplitude in a model problem which can be treated analytically. It is found for an important class of potentials, including some of infinite range and also the square well, that the method does not provide a converging sequence of approximations. However, in some cases, approximations of relatively low order might be close to the correct result. The method is also applied to 8-wave e-H elastic scattering above the ionization threshold, and spurious "convergence" to the wrong result is found.A procedure which might overcome the difficulties of the method is proposed.

The presence of wavelet stretch due to imaging presents serious difficulty in AVO or inversion analysis, especially for 3-term wide-angle analysis. Wavelet stretch significantly alters the gradient and wide-angle coefficient and reduces resolution of stacks. In this paper we present a method for correcting wavelet stretch that is exact for any v(z) (layered) medium. It does not depend on an underlying AVO/AVA approximation and is therefore applicable for 2-or 3-term AVA analysis. The required input is an extracted wavelet from any known reflection angle. The resulting correction operator is stationary over the time coordinate of the angle domain and is robustly implemented by a Weiner-Levinson method. This filter corrects angle gathers for wavelet stretch, producing improved resolution in subsequent angle stacks or gradient computations. Wavelet stretch correction is essential for linear inversion for density.

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We imaged the Marmousi dataset using an efficient Kirchhoff prestack depth migration algorithm combined with a layer-stripping velocity analysis technique. The method relies on repeated common-offset test migrations to build a velocity model systematically from the top down. Results of these common-offset depth migrations are sorted into common image-point displays. By observing residual moveout as a function of offset in these displays, we determine veloeities and boundary locations for each layer. The assumed model is 'blocky' with constant layer velocities. Application of this method to the Marmousi data produced a good quality image except in the central region with its large-velocity-contrast fault blocks. Our data treatment for the EAEG workshop consisted of wavelet processing, followed by our layer-stripping depth migration/model building, and residual processing. Some additional improvement has been obtained by reprocessing after the workshop. Although a blocky model with constant-velocity layers is a highly idealized model, our success in applying it to this complex synthetic dataset makes us more comfortable in using this method to image datasets from the real world. lNTRODUCTION Our procedure for building velocity models for depth migration uses common-offset depth migration combined with a top-down layer-stripping velocity analysis technique. The technique utilizes a stabie and Jast (12 minutes epu time for the Marmousi prestack dataset on a CRAY X-MP) Kirchhoff depth migration algorithm, which allows many trial veloeities to be tested.We processed the Marmousi dataset in three main steps: (1) pre-processing to remove the seismie wavelet, (2) iterative depth migration and layer-stripping velocity analysis, and (3) postmigration processing inc1uding a residual moveout correction. The second step, namely, iterative construction of the migration velo city model, comprised the bulk of the effort, and will also receive most of the discussion in this report.Our velocity-depth models consist of constantvelocity layers with arbitrarily dipping boundaries. We construct such a model systematically, one layer at a time, from the top down. With the model determined to any given layer, common-offset test migrations are run for various (constant) veloeities below that layer. The common-offset results are sorted into common image-point gathers, which help determine the velocity and location of the next layer.This velo city analysis is quite sensitive. It is usabie whenever the image-point gathers are sufficiently coherent to display event moveout over an adequate range of offsets. However, poor data quality or structural complexity can cause the method to break down at sufficiently great depths.For the Marmousi dataset, near the east and west ends of the line, our systematic layer-stripping method was usabie (and yielded accurate veloci-139