No abstract

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Waveform (output least squares) inversion of seismic reflection data can reconstruct remarkably detailed models of subsurface structure, and take into account essentially any physics of seismic wave propagation that can be modeled. However the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long-scale velocity structure. Migration velocity analysis, on the other hand, is based on the Born approximation but is capable of correcting substantially erroneous initial velocities. Appropriate choice of objective (differential semblance) turns migration velocity analysis into an optimization problem, for which Newton-like methods exhibit little tendency to stagnate at nonglobal minima. The extended modeling concept links these two apparently unrelated approaches to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized (single scattering, Born) waveform inversion problem. Extended modeling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests that this new approach to nonlinear waveform inversion may combine the global convergence of velocity analysis with the physical fidelity of least squares.

Differential semblance optimization (DSO) is an approach to inversion of reflection seismograms which avoids the severe convergence difficulties associated with nonlinear least‐squares inversion. The method exploits both moveout and amplitude characteristics of reflections. We have implemented a version appropriate to plane‐wave (p‐tau) seismograms and layered constant‐density acoustic earth models. Theoretical and numerical analyses of this version of DSO indicate that stable and reasonably accurate estimates of both velocity trend and reflectivity can be derived. To test DSO further, we applied it to a marine data set from the Gulf of Mexico, where the method produced results which compare favorably to well‐log information. The method can be extended to incorporate laterally heterogeneous velocity models.

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No abstract

We analyze the kinematic properties of offset-domain Common Image Gathers (CIGs) and Angle-Domain CIGs (ADCIGs) computed by wavefield-continuation migration. Our results are valid regardless of whether the CIGs were obtained by using the correct migration velocity. They thus can be used as a theoretical basis for developing Migration Velocity Analysis (MVA) methods that exploit the velocity information contained in ADCIGs.We demonstrate that in an ADCIG cube the image point lies on the normal to the apparent reflector dip, passing through the point where the source ray intersects the receiver ray. Starting from this geometric result, we derive an analytical expression for the expected movements of the image points in ADCIGs as functions of the traveltime perturbation caused by velocity errors. By applying this analytical result and assuming stationary raypaths, we then derive two expressions for the Residual Moveout (RMO) function in ADCIGs. We verify our theoretical results and test the accuracy of the proposed RMO functions by analyzing the migration results of a synthetic data set with a wide range of reflector dips.Our kinematic analysis leads also to the development of a new method for computing ADCIGs when significant geological dips cause strong artifacts in the ADCIGs computed by conventional methods. The proposed method is based on the computation of offsetdomain CIGs along the vertical-offset axis (VOCIGs) and on the "optimal" combination of these new CIGs with conventional CIGs. We demonstrate the need for and the advantages of the proposed method on a real data set acquired in the North Sea.

Shot profile migration provides a convenient framework for implementation of a differential semblance algorithm for estimation of complex, strongly refracting velocity fields. The objective function minimized in this algorithm may measure either focussing of the image in offset or flatness of the image in (scattering) angle. Velocity estimation based on this measure of data-model consistency uses waveform data directly: it does not require any sort of traveltime picking. We show that the offset variant of differential semblance yields somewhat more reliable migration velocity estimates than does the scattering angle variant, and explain why this is so. We observe that inconsistency with the underlying model (Born scattering about a transparent background) may lead to degraded velocity estimates from differential semblance, and show how to augment the objective function with stack power to enhance ultimate accuracy. A 2D marine survey over a target obscured by the lensing effects of a gas chimney provides an opportunity for direct comparison of differential semblance with reflection tomography. The differential semblance estimate yields a more data-consistent model (flatter angle gathers) than does reflection tomography in this application, resulting in a more interpretable image below the gas cloud.