Least-squares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure and take into account essentially any physics of seismic wave propagation that can be modelled. 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 capable of correcting substantially erroneous initial estimates of velocity at long scales. Migration velocity analysis is based on prestack depth migration, which is in turn based on linearized acoustic modelling (Born or single-scattering approximation). Two major variants of prestack depth migration, using binning of surface data and Claerbout's survey-sinking concept respectively, are in widespread use. Each type of prestack migration produces an image volume depending on redundant parameters and supplies a condition on the image volume, which expresses consistency between data and velocity model and is hence a basis for velocity analysis. The survey-sinking (depth-oriented) approach to prestack migration is less subject to kinematic artefacts than is the binning-based (surface-oriented) approach. Because kinematic artefacts strongly violate the consistency or semblance conditions, this observation suggests that velocity analysis based on depth-oriented prestack migration may be more appropriate in kinematically complex areas. Appropriate choice of objective (differential semblance) turns either form of migration velocity analysis into an optimization problem, for which Newton-like methods exhibit little tendency to stagnate at nonglobal minima. The extended modelling concept links migration velocity analysis to the apparently unrelated waveform inversion approach to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized waveform inversion problem. Extended modelling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests a new approach to nonlinear waveform inversion, which may combine the global convergence of velocity analysis with the physical fidelity of model-based data fitting.

http://www.trip.caam.rice.edu/reports/2007/geoprosp0207.pdf

Migration velocity analysis and waveform inversion

Reverse time migration (RTM) requires that fields computed in forward time be accessed in reverse order. Such out-of-order access, to recursively computed fields, requires that some part of the recursion history be stored (checkpointed), with the remainder computed by repeating parts of the forward computation. Optimal checkpointing algorithms choose checkpoints in such a way that the total storage is minimized for a prescribed level of excess computation, or vice versa. Optimal checkpointing dramatically reduces the storage required by RTM, compared to that needed for nonoptimal implementations, at the price of a small increase in computation. This paper describes optimal checkpointing in a form which applies both to RTM and other applications of the adjoint state method, such as construction of velocity updates from prestack wave equation migration.

/pdf/reverse-time-migration-with-optimal-checkpointing-3efj1bawmz.pdf

Reverse time migration with optimal checkpointing

We described an implementation of differential semblance velocity analysis based on shot-profile migration, and illustrated its ability to estimate complex, strongly refracting velocity fields. The differential semblance approach to velocity analysis uses waveform data directly: it does not require any sort of traveltime picking. The objective function minimized by the differential semblance algorithm can measure either focusing of the image in offset or flatness of the image in (scattering) angle. We showed that the offset variant of differential semblance yields somewhat more reliable migration velocity estimates than does the scattering angle variant, and we explain why this is so. We observed that inconsistency with the underlying model (Born scattering about a transparent background) can lead to degraded velocity estimates from differential semblance, and we showed 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.

Automatic velocity analysis via shot profile migration

Invited review paper: Fault creep caused by subduction of rough seafloor relief

Summary Full waveform inversion has been successful in building high resolution velocity models for shallow layers. To be successful, it requires refracted waves or low frequencies in the reflection/refraction data. We revisit full waveform inversion theory in hopes of relaxing the dependence on low frequency reflections. We implement an approach allowing the updating of long wavelength components of the velocity model affecting the reflected arrivals even with absence of low frequency in the input data. Our tactic is based on a non-linear iterative relaxation approach where short and long wavelength components of the velocity model are updated alternatively. We study theoretically the associated Frechet derivatives and gradients and discussed how and why such a strategy improves the resolution that we can expect from full waveform inversion. The kernel of our approach is very similar to the algorithm of migration based travel time tomography proposed by Chavent et al. (1994). Finally we present a preliminary 2D application to a 2D Gulf of Mexico conventional streamer dataset.

Inversion on Reflected Seismic Wave

The subduction of topographic features has been linked both to earthquake generation and the segmentation of faults. Seismic imaging reveals a seamount subducted to 40-km depth below Sumatra that is associated with an aseismic zone, suggesting that at this location, the seamount reduces coupling of the slab and overriding plate.

/pdf/aseismic-zone-and-earthquake-segmentation-associated-with-a-2ifdead2u4.pdf

Aseismic zone and earthquake segmentation associated with a deep subducted seamount in Sumatra

In recent years, wave-equation migration has greatly enhanced imaging in complex velocity models. However, velocity model building is still dependent on ray-theory approximations. We propose a full wave-equation methodology for velocity model building based on the nonlinear inversion of a semblance criterion with respect to the velocity field. A newly described type of migration, called the modulated-shot migration, is used to obtain the necessary gathers, which are indexed in surface angle. The semblance of these gathers, after spatial averaging, is used as the cost function. This methodology is shown to successfully image the Marmousi model and the subsalt part of the Sigsbee model, especially in terms of focusing, which is as good as with the true model, but also in terms of depthing which is enhanced compared with the initial model. Realistic constraints are used in terms of minimum frequency, maximum offset, and crudeness of the starting model. A key point in the success of this methodology is the mu...

Velocity model building by semblance maximization of modulated-shot gathers

Summary Variable-depth streamer acquisition is becoming a key technique for providing wide bandwidth seismic data Varying the receiver depth creates wide receiver ghost diversity and produces a spectacular increase in the frequency bandwidth However, compared to conventional data, this variable-depth streamer data implies a major challenge in processing: how to deal with various receiver ghosts The ghosts have to be preserved up to the deghosting step Here we present the implication for the following de-multiple methods: Shallow-Water Demultiple, Tau-P deconvolution and Surface-related multiples elimination in deep and shallow water environments

Multiple Attenuation For Variable-depth Streamer Data: From Deep to Shallow Water

Velocity model building by semblance maximization of modulated‐shot gathers

The invention relates to a method of processing seismic data acquired by means of a sensor having at least three geophone components, characterized in that estimators are determined which are combinations of these components making it possible to isolate the various data depending on whether they correspond to propagation with reflection or with conversion. The estimators find application in particular for determining a sensor reconstruction according to which the operators to be applied to the various components of the sensor are determined in such a way as to minimize the deviation between reference data and data obtained by applying the estimators to the sensor reconstruction, the operators thus determined being applied to the data acquired.

Bruno Gratacos

Papers

Aseismic zone and earthquake segmentation associated with a deep subducted seamount in Sumatra

Velocity model building by semblance maximization of modulated-shot gathers

Multiple Attenuation For Variable-depth Streamer Data: From Deep to Shallow Water

Velocity model building by semblance maximization of modulated‐shot gathers

Method of processing seismic data acquired by means of multicomponent sensors