Residual moveout analysis of prestack depth migrated common image point gathers is used for velocity model building in areas of complex geology. Where the velocity varies smoothly, the model is commonly built from stacking velocity analysis of the residual curvature on the gathers after conversion back to time. Where the velocity varies more rapidly, the model must be built instead by projecting the residual depth errors back over individually traced raypaths in a full tomographic inversion in depth. In this paper we show results of the latter method applied to a Gulf Coast data set. The 3D field example was run in a highly automated fashion. The depth errors (residual moveout) were first picked in batch mode throughout a sparsely sampled volume of common image point gathers and then minimized through a global inversion of all picks at all depths simultaneously. The inverse problem was constrained with preconditioning to solve for the smoothest part of the velocity field first. This automated approach improves turnaround by minimizing human intervention.
Over the last decade, conventional full waveform inversion (FWI) has been widely applied to real seismic data for both production and research purposes. The underlying theory has been well established and produces high resolution subsurface models by minimizing the misfit between the seismic data and simulated seismograms obtained by solving the wave equation exactly. However, in practice, it is still a challenging inversion method for updating the model parameters. A local optimization scheme is used to solve the minimization problem and it does not prevent convergence towards local minima because of the nonlinearity and ill-posedness of the problem. For example, FWI may converge to a local minimum because of the lack of low frequencies in the recorded data or an inaccurate starting model. We propose a novel approach to time domain full waveform inversion with the reconstructed wavefield method (RFWI). RFWI relaxes the constraint that the forward modeled data exactly solve the wave equation as in conventional FWI, and instead uses an 2 approximate solution. RFWI estimates earth models and jointly reconstructs the forward wavefield by minimizing an objective function that includes penalties for both the data misfit and wave equation error. By extending the search space, RFWI offers potential benefits of avoiding cycle skipping and overcoming some of the problems with local minima. This paper first presents the theory and implementation of time domain RFWI. It also discusses the differences and similarities between conventional FWI and RFWI. The benefits of RFWI over conventional FWI are demonstrated using a 2D synthetic example. Finally, the applicability of RFWI on field data is illustrated on a 2D streamer data set from offshore Congo and a 3D ocean bottom seismic data set from the Gulf of Mexico.
The goal of full-waveform inversion (WFI) is to derive high-fidelity Earth models for seismic imaging from the full waveforms of the acquired seismic data. The attractiveness of WFI lies mainly in its limited number of approximations, at least in a theoretical sense, in contrast to other model determination techniques such as semblance or ray-based tomography. Despite this, various methodologies must be utilized to make the technique viable with today's computing technology and restrictions of seismic acquisition. These are collectively referred to as “waveform-inversion strategies” and in this article we discuss mainly regularization and preconditioning strategies. As the wavefields need to be accurately modeled to represent the kinematics of all the waves during WFI iterations, the inclusion of anisotropy often helps to improve the WFI results. In the first section of this article, we introduce forward modeling and its adjoint based on acoustic-wave equations in vertical transversely isotropic (VTI) media. We discuss a multiparameter acoustic VTI inversion for P-wave velocity and the anisotropy parameter epsilon. Furthermore, we include well logs as constraints to help stabilize the inversion and provide us with more reliable velocity updates. In the next section, we include attenuation and dispersion effects to better simulate wave propagation through real Earth materials. We present a viscoacoustic WFI for updating both the velocity model and the quality factor (Q) in a recursive mode. We illustrate these approaches on applications to real 3D data.
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