We have developed and implemented a robust and practical scheme for anisotropic 3D acoustic full-waveform inversion (FWI). We demonstrate this scheme on a field data set, applying it to a 4C ocean-bottom survey over the Tommeliten Alpha field in the North Sea. This shallow-water data set provides good azimuthal coverage to offsets of 7 km, with reduced coverage to a maximum offset of about 11 km. The reservoir lies at the crest of a high-velocity antiformal chalk section, overlain by about 3000 m of clastics within which a low-velocity gas cloud produces a seismic obscured area. We inverted only the hydrophone data, and we retained free-surface multiples and ghosts within the field data. We invert in six narrow frequency bands, in the range 3 to 6.5 Hz. At each iteration, we selected only a subset of sources, using a different subset at each iteration; this strategy is more efficient than inverting all the data every iteration. Our starting velocity model was obtained using standard PSDM model bui...

https://library.seg.org/doi/pdf/10.1190/geo2012-0338.1

Anisotropic 3D full-waveform inversion

We used a novel iterative estimation scheme for separation of blended seismic data from simultaneous sources. The scheme is based on an augmented estimation problem that can be solved by iteratively constraining the deblended data using shaping regularization in the seislet domain. We formulated the forward modeling operator in the common-receiver domain, in which two sources were assumed to be blended using a random time-shift dithering approach. The nonlinear shaping-regularization framework offered some freedom in designing a shaping operator to constrain the model in an underdetermined inverse problem. We designed the backward operator and the shaping operator for the shaping-regularization framework. The backward operator can be optimally chosen as half of the identity operator in the two-source case, and the shaping operator can be chosen as coherency-promoting operator. The high performance deblending effect of the iterative framework was tested on three numerically blended synthetic data s...

Iterative deblending of simultaneous-source seismic data using seislet-domain shaping regularization

Full waveform inversion (FWI) aims to reconstruct high-resolution subsurface models from the full wavefield, which includes diving waves, post-critical reflections and short-spread reflections. Most successful applications of FWI are driven by the information carried by diving waves and post-critical reflections to build the long-to-intermediate wavelengths of the velocity structure. Alternative approaches, referred to as reflection waveform inversion (RWI), have been recently revisited to retrieve these long-to-intermediate wavelengths from short-spread reflections by using some prior knowledge of the reflectivity and a scale separation between the velocity macromodel and the reflectivity. This study presents a unified formalism of FWI, named as Joint FWI, whose aim is to efficiently combine the diving and reflected waves for velocity model building. The two key ingredients of Joint FWI are, on the data side, the explicit separation between the short-spread reflections and the wide-angle arrivals and, on the model side, the scale separation between the velocity macromodel and the short-scale impedance model. The velocity model and the impedance model are updated in an alternate way by Joint FWI and waveform inversion of the reflection data (least-squares migration), respectively. Starting from a crude velocity model, Joint FWI is applied to the streamer seismic data computed in the synthetic Valhall model. While the conventional FWI is stuck into a local minimum due to cycle skipping, Joint FWI succeeds in building a reliable velocity macromodel. Compared with RWI, the use of diving waves in Joint FWI improves the reconstruction of shallow velocities, which translates into an improved imaging at deeper depths. The smooth velocity model built by Joint FWI can be subsequently used as a reliable initial model for conventional FWI to increase the high-wavenumber content of the velocity model.

/pdf/full-waveform-inversion-of-diving-reflected-waves-for-2hdc6cmlmd.pdf

Full waveform inversion of diving & reflected waves for velocity model building with impedance inversion based on scale separation

/pdf/acoustic-and-elastic-waveform-inversion-using-a-modified-37mbrx3khq.pdf

Acoustic- and elastic-waveform inversion using a modified total-variation regularization scheme

The gradient of standard full-waveform inversion (FWI) attempts to map the residuals in the data to perturbations in the model. Such perturbations may include smooth background updates from the transmission components and high wavenumber updates from the reflection components. However, if we fix the reflection components using imaging, the gradient of what is referred to as reflected-waveform inversion (RWI) admits mainly transmission background-type updates. The drawback of existing RWI methods is that they lack an optimal image capable of producing reflections within the convex region of the optimization. Because the influence of velocity on the data was given mainly by its background (propagator) and perturbed (reflectivity) components, we have optimized both components simultaneously using a modified objective function. Specifically, we used an objective function that combined the data generated from a source using the background velocity, and that by the perturbed velocity through Born modeli...

/pdf/simultaneous-inversion-of-the-background-velocity-and-the-4dsi17guis.pdf

Simultaneous inversion of the background velocity and the perturbation in full-waveform inversion

The waveform inversion problem is inherently ill-posed. Traditionally, regularization schemes are used to address this issue. For waveform inversion, where the model is expected to have many details reflecting the physical properties of the Earth, regularization and data fitting can work in opposite directions: the former smoothing and the latter adding details to the model. We propose constraining estimated velocity fields by reparameterizing the model. This technique, also called model-space preconditioning, is based on directional Laplacian filters: It preserves most of the details of the velocity model while smoothing the solution along known geological dips. Preconditioning also yields faster convergence at early iterations. The Laplacian filters have the property to smooth or kill local planar events according to a local dip field. By construction, these filters can be inverted and used in a preconditioned waveform inversion strategy to yield geologically meaningful models. We illustrate with 2D syn...

Constrained full-waveform inversion by model reparameterization

For some acquisition geometries, the cost of Full Waveform Inversion (FWI) can be considerably reduced by inverting simultaneously encoded shots. Encoded‐shot strategies have the undesirable effect of leaving crosstalk noise in the final result. For FWI, changing the coding sequence periodically mitigates this effect. Another alternative is to use preconditioning, whereby the gradient is smoothed at every iteration along predefined directions. Preconditioning steers the solution towards accurate models while attenuating crosstalk artefacts. It also increases convergence speed and robustness to noise present in the data.

Attenuating crosstalk noise with simultaneous source full waveform inversion

One of the main challenge of full waveform inversion (FWI) is its computing cost because each iteration is equivalent to one reverse time migration. To increase the performance of FWI, few shots can be randomly selected at each iteration. The shot location can be changed after every iteration, or kept constant for few iterations before being changed. This random decimation method helps decreasing the memory footprint of FWI because much fewer shots are needed at any time during the inversion. In addition, FWI can be sped-up effectively while preserving the ability to recover the model. Using a synthetic 2-D dataset, the memory footprint is divided by a factor twenty while the computation costs is decreased by a factor four.

Fast Full Waveform Inversion With Random Shot Decimation

One of the main challenges for full-waveform inversion (FWI) is taking into account both anisotropy and elasticity. Here, we perform elastic FWI for a synthetic 2D VTI (transversely isotropic with a vertical symmetry axis) model based on the geologic section at Valhall field in the North Sea. Multicomponent surface data are generated by a finite-difference code. We apply FWI in the time domain using a multiscale approach with three frequency bands. An approximate inverse Hessian matrix, computed using the L-BFGS-B algorithm, is employed to scale the gradients of the objective function and improve the convergence. In the absence of significant diving-wave energy in the deeper part of the section, the model is updated primarily with reflection data. An oblique displacement source, which excites sufficiently intensive shear waves in the conventional offset range, helps provide more accurate updates in the Shear-wave vertical velocity, especially in the shallow layers. We test three model parameteriza...

Elastic full-waveform inversion for VTI media: A synthetic parameterization study

Reverse time migration backscattered events are produced by the cross-correlation between waves reflected from sharp interfaces (e.g., salt bodies). These events, along with head waves and diving waves, produce the so-called reverse time migration artefacts, which are visible as low wavenumber energy on migrated images. Commonly, these events are seen as a drawback for the reverse time migration method
because they obstruct the image of the geologic structure, which is the real objective for the process. In this paper, we perform numeric and theoretical analysis to understand the reverse time migration backscattering energy in conventional and extended images. We show that the reverse time migration backscattering contains a measure of the synchronization and focusing information between the source and receiver wavefields. We show that this synchronization and focusing information is sensitive
to velocity errors; this implies that a correct velocity model produces reverse time migration backscattering with maximum energy. Therefore, before filtering the reverse time migration backscattered energy, we should try to obtain a model that maximizes it.

/pdf/understanding-the-reverse-time-migration-backscattering-33ygfqcjgj.pdf

Esteban Díaz

Papers

Constrained full-waveform inversion by model reparameterization

Attenuating crosstalk noise with simultaneous source full waveform inversion

Fast Full Waveform Inversion With Random Shot Decimation

Elastic full-waveform inversion for VTI media: A synthetic parameterization study

Understanding the reverse time migration backscattering: noise or signal?