Kirchhoff migration is the most popular method of three‐dimensional prestack depth migration because of its flexibility and efficiency. Its effectiveness can become limited, however, when complex velocity structure causes multipathing of seismic energy. An alternative is Gaussian beam migration, which is an extension of Kirchhoff migration that overcomes many of the problems caused by multipathing. Unlike first‐arrival and most‐energetic‐arrival methods, which retain only one traveltime, this alternative method retains most arrivals by the superposition of Gaussian beams. This paper presents a prestack Gaussian beam migration method that operates on common‐offset gathers. The method is efficient because the computation of beam superposition isolates summations that do not depend on the seismic data and evaluates these integrals by considering their saddle points. Gaussian beam migration of the two‐dimensional Marmousi test data set demonstrates the method’s effectiveness for structural imaging in a case w...

Prestack Gaussian‐beam depth migration

Building high-resolution models of several physical properties of the subsurface by multiparameter full waveform inversion (FWI) of multicomponent data will be a challenge for seismic imaging for the next decade. The physical properties, which govern propagation of seismic waves in visco-elastic media, are the velocities of the P- and S-waves, density, attenuation, and anisotropic parameters. Updating each property is challenging because several parameters of a different nature can have a coupled effect on the seismic response for a particular propagation regime (from transmission to reflection). This is generally referred to as trade-off or crosstalk between parameters. Moreover, different parameter classes can have different orders of magnitude or physical units and footprints of different strength in the wavefield, which can make the inversion poorly conditioned if it is not properly scaled.

A guided tour of multiparameter full-waveform inversion with multicomponent data: From theory to practice

Over the past 10 years, ray-based postmigration grid tomography has become the standard model-building tool for seismic depth imaging. While the basics of the method have remained unchanged since the late 1990s, the problems it solves have changed dramatically. This evolution has been driven by exploration demands and enabled by computer power. There are three main areas of change. First, standard model resolution has increased from a few thousand meters to a few hundred meters. This order of magnitude improvement may be attributed to both high-quality, complex residual-moveout data picked as densely as 25 m to 50 m vertically and horizontally, and to a strategy of working down from long-wavelength to short-wavelength solutions. Second, more and more seismic data sets are being acquired along multiple azimuths, for improved illumination and multiple suppression. High-resolution velocity tomography must solve for all azimuths simultaneously, to prevent short-wavelength velocity heterogeneity from being mistaken for azimuthal anisotropy. Third, there has been a shift from predominantly isotropic to predominantly anisotropic models, both VTI and TTI. With four-component data, anisotropic grid tomography can be used to build models that tie PZ and PS images in depth.

A decade of tomography

3D angle gathers from reverse time migrationXu et al.RTM 3D angle gathers

The hybrid cellular automaton (HCA) algorithm is a methodology developed to simulate the process of structural adaptation in bones. This methodology incorporates a distributed control loop within a structure in which ideally localized sensor cells activate local processes of the formation and resorption of material. With a proper control strategy, this process drives the overall structure to an optimal configuration. The controllers developed in this investigation include two-position, proportional, integral and derivative strategies. The HCA algorithm combines elements of the cellular automaton (CA) paradigm with finite element analysis (FEA). This methodology has proved to be computationally efficient to solve topology optimization problems. The resulting optimal structures are free of numerical instabilities such as the checkerboarding effect. This investigation presents the main features of the HCA algorithm and the influence of different parameters applied during the iterative optimization process. DOI: 10.1115/1.2336251

Topology Optimization Using a Hybrid Cellular Automaton Method With Local Control Rules

Full waveform inversion (FWI) delivers high-resolution quantitative images and is a promising technique to obtain macroscale physical property model of the subsurface. In most geophysical applications, prior information, such as that collected in wells, is available and should be used to increase the image reliability. For this, we propose to introduce three terms in the definition of the FWI misfit function: the data misfit itself, the first-order Tikhonov regularization term acting as a smoothing operator, and a prior model norm term. This last term is the way to smoothly introduce prior information into the FWI workflow. On a selected target of the Marmousi synthetic example, significant improvement was obtained when using the prior model term for noise-free and noisy synthetic data. The prior model term may significantly reduce the inversion sensi tivity to incorrect initial conditions. The limited range of spatial wavenumber sampling by the acquisition may be compensated with the prior model information, for multiple-free and multiplecontaminated data. Prior and initial models play different roles in the inversion scheme. The starting model is used for wave propagation and therefore drives the data-misfit gradient, whereas the prior model is never explicitly used for solving the wave equation and only drives the optimization step as an additional constraint to minimize the total objective function. Thus, the prior model is not required to follow kinematic properties as precisely as the initial model, except in zones of poor illumination. In addition, we investigate the influence of a simple dynamic decreasing weighting of the prior model term. Once the cycle-skipping problem has been solved, the impact of the prior model term is gradually reduced within the misfit function to be driven by seismic-data only.

https://users.isterre.fr/brossier/Asnaashari_2013_GEO.pdf

Regularized seismic full waveform inversion with prior model information

Full-waveform inversion is an appealing technique for time-lapse imaging, especially when prior model information is included into the inversion workflow. Once the baseline reconstruction is achieved, several strategies can be used to assess the physical parameter changes, such as parallel difference (two separate inversions of baseline and monitor data sets), sequential difference (inversion of the monitor data set starting from the recovered baseline model) and double-difference (inversion of the difference data starting from the recovered baseline model) strategies. Using syntheticMarmousi data sets, we investigate which strategy should be adopted to obtain more robust and more accurate time-lapse velocity changes in noise-free and noisy environments. This synthetic application demonstrates that the double-difference strategy provides the more robust time-lapse result. In addition, we propose a target-oriented time-lapse
imaging using regularized full-waveform inversion including a prior model and model weighting, if the prior information exists on the location of expected variations. This scheme applies strong prior model constraints outside of the expected areas of timelapse changes and relatively less prior constraints in the time-lapse target zones. In application of this process to the Marmousi model data set, the local resolution
analysis performed with spike tests shows that the target-oriented inversion prevents the occurrence of artefacts outside the target areas, which could contaminate and compromise the reconstruction of the effective time-lapse changes, especially when using the sequential difference strategy. In a strongly noisy case, the target-oriented prior model weighting ensures the same behaviour for both time-lapse strategies, the double-difference and the sequential difference strategies and leads to a more robust reconstruction of the weak time-lapse changes. The double-difference strategy can deliver more accurate time-lapse variation since it can focus to invert the difference data. However, the double-difference strategy requires a preprocessing step on data sets such as time-lapse binning to have a similar source/receiver location between two surveys, while the sequential difference needs less this requirement. If we have prior information about the area of changes, the target-oriented sequential difference strategy can be an alternative and can provide the same robust result as the doubledifference strategy.

Time‐lapse seismic imaging using regularized full‐waveform inversion with a prior model: which strategy?

We compare various forms of single-arrival Kirchhoff prestack depth migration to a full-waveform, finite-difference migration image, using synthetic seismic data generated from the structurally complex 2-D Marmousi velocity model. First-arrival-traveltime Kirchhoff migration produces severe artifacts and image contamination in regions of the depth model where significant reflection energy propagates as late or multiple arrivals in the total reflection wavefield. Kirchhoff migrations using maximum-energy-arrival traveltime trajectories significantly improve the image in the complex zone of the Marmousi model, but are not as coherent as the finite-difference migration image. By carefully incorporating continuous phase estimates with the associated maximum-energy arrival traveltimes, we obtain single-arrival Kirchhoff images that are similar in quality to the finite-difference migration image. Furthermore, maximum-energy Green9s function traveltime and phase values calculated within the seismic frequency band give a Kirchhoff image that is (1) far superior to a first-arrival-based image, (2) much better than the analogous high-frequency paraxial-ray Green9s function image, and (3) closely matched in quality to the full-waveform finite-difference migration image.

/pdf/imaging-complex-geologic-structure-with-single-arrival-2xz81pk3mh.pdf

Imaging complex geologic structure with single-arrival Kirchhoff prestack depth migration

3D Finite-offset Tomographic Inversion of CRP-scan Data, With Or Without Anisotropy.

Long-wavelength velocity model building is a nonlinear process It has traditionally been achieved without appealing to wave-equation-based approaches for combined refracted and reflected waves We developed a cascaded wave-equation tomography method in the data domain, taking advantage of the information contained in the reflected and refracted waves The objective function was the traveltime residual that maximized the crosscorrelation function between real and synthetic data To alleviate the nonlinearity of the inversion problem, refracted waves were initially used to provide vertical constraints on the velocity model, and reflected waves were then included to provide lateral constraints The use of reflected waves required scale separation We separated the long- and short-wavelength subsurface structures into velocity and density models, respectively The velocity model update was restricted to long wavelengths during the wave-equation tomography, whereas the density model was used to absorb

Inversion of seismic refraction and reflection data for building long-wavelength velocity models

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