A Fast 3-D Free-surface Topography Method for Acoustic Full-waveform Inversion

Huiskes, Mark J.; Plessix, RE; Mulder, W.A.

doi:10.3997/2214-4609.201601664

Cited by 2 publications

(4 citation statements)

References 6 publications

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“…Applying this extension along the coordinate directions introduces an additional numerical error, although the zero-pressure condition at the free surface is always respected. The mechanics of the field extension procedure are described in Huiskes et al (2016). The extension scheme depends on α, the relative distance, in terms of grid cell size h, of the first interior grid point to the free surface.…”

Section: Methodsmentioning

confidence: 99%

“…We present a method to handle 3-D free-surface topography for acoustic FWI by directly modelling the effect of the topography with a finite-difference scheme for the first-order wave equation introduced earlier (Huiskes et al, 2016;Mulder and Huiskes, 2017). …”

Section: Introductionmentioning

confidence: 99%

“…We refer to Huiskes et al (2016) for a more detailed overview of methods for simulating seismic waves interacting with free-surface topography.…”

Section: Introductionmentioning

confidence: 99%

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Acoustic VTI Full-waveform Inversion with 3-D Free-surface Topography

2017

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SummaryIn land applications, topography may impact the imaging if not taken into account. With low-frequency and wide-aperture data, the long-to-intermediate wavelength components of the velocity model can be recovered by full-waveform inversion. Standard static corrections to handle the topography do not work satisfactorily on long-offset data. We present a method to handle 3-D free-surface topography for acoustic FWI by directly modelling the effect of the topography with an immersed-boundary finite-difference scheme. The numerical scheme is aimed specifically at first-order wave equations discretized on standard staggered grids, using high-order derivative operators that are modified based on their relative position to the free surface. We extend the approach to VTI media to be able to model velocity anisotropy required in long-offset inversions. We then investigate the topography artefacts seen on real land full-waveform inversions in relatively simple synthetic experiments, allowing us to quantify the effect of elevation variation on the inversion accuracy. The experiments demonstrate that elevation variations in the order of 1/4 wavelength or somewhat smaller can already create artefacts in the inversion results if ignored.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Acoustic VTI Full-waveform Inversion with 3-D Free-surface Topography

2017

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“…The majority of these applications are carried out under finite-difference (FD) approximation, due to the numerical efficiency of this method and its ease of implementation. Standard formulations of this approach are, however, limited on regular grids, which require significant extra effort in terms of design and computational cost in the presence of surface topography or important geological interfaces (Robertsson 1996;Bohlen & Saenger 2006;Fuji et al 2016;Huiskes et al 2016). Finite-element (FE) methods have become popular for regional and global problems, especially spectral-element methods (SEMs), where complex geometry can be handled with accurate numerical calculation of wavefields (Komatitsch & Tromp 1999).…”

Section: Introductionmentioning

confidence: 99%

Bessel smoothing filter for spectral-element mesh

Trinh¹,

Brossier²,

Métivier

et al. 2017

Geophysical Journal International

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Smoothing filters are extremely important tools in seismic imaging and inversion, such as for traveltime tomography, migration and waveform inversion. For efficiency, and as they can be used a number of times during inversion, it is important that these filters can easily incorporate prior information on the geological structure of the investigated medium, through variable coherent lengths and orientation. In this study, we promote the use of the Bessel filter to achieve these purposes. Instead of considering the direct application of the filter, we demonstrate that we can rely on the equation associated with its inverse filter, which amounts to the solution of an elliptic partial differential equation. This enhances the efficiency of the filter application, and also its flexibility. We apply this strategy within a spectral-element-based elastic full waveform inversion framework. Taking advantage of this formulation, we apply the Bessel filter by solving the associated partial differential equation directly on the spectralelement mesh through the standard weak formulation. This avoids cumbersome projection operators between the spectral-element mesh and a regular Cartesian grid, or expensive explicit windowed convolution on the finite-element mesh, which is often used for applying smoothing operators. The associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation. Significant scaling behaviour is obtained when comparing this strategy with the explicit convolution method. The theoretical numerical complexity of this approach increases linearly with the coherent length, whereas a sublinear relationship is observed practically. Numerical illustrations are provided here for schematic examples, and for a more realistic elastic full waveform inversion gradient smoothing on the SEAM II benchmark model. These examples illustrate well the efficiency and flexibility of the approach proposed.

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A Fast 3-D Free-surface Topography Method for Acoustic Full-waveform Inversion

Cited by 2 publications

References 6 publications

Acoustic VTI Full-waveform Inversion with 3-D Free-surface Topography

Acoustic VTI Full-waveform Inversion with 3-D Free-surface Topography

Bessel smoothing filter for spectral-element mesh

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