Optimal transport for mitigating cycle skipping in full-waveform inversion: A graph-space transform approach

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. R515-R540 ◽  
Author(s):  
Ludovic Métivier ◽  
Aude Allain ◽  
Romain Brossier ◽  
Quentin Mérigot ◽  
Edouard Oudet ◽  
...  
Keyword(s):  
Seismic Data ◽  
Optimal Transport ◽  
Waveform Inversion ◽  
P Wave ◽  
Imaging Method ◽  
Convexity Property ◽  
Full Waveform Inversion ◽  
Low Frequencies ◽  
Transport Distance ◽  
Full Waveform

Optimal transport distance has been recently promoted as a tool to measure the discrepancy between observed and seismic data within the full-waveform-inversion strategy. This high-resolution seismic imaging method, based on a data-fitting procedure, suffers from the nonconvexity of the standard least-squares discrepancy measure, an issue commonly referred to as cycle skipping. The convexity of the optimal transport distance with respect to time shifts makes it a good candidate to provide a more convex misfit function. However, the optimal transport distance is defined only for the comparison of positive functions, while seismic data are oscillatory. A review of the different attempts proposed in the literature to overcome this difficulty is proposed. Their limitations are illustrated: Basically, the proposed strategies are either not applicable to real data, or they lose the convexity property of optimal transport. On this basis, we introduce a novel strategy based on the interpretation of the seismic data in the graph space. Each individual trace is considered, after discretization, as a set of Dirac points in a 2D space, where the amplitude becomes a geometric attribute of the data. This ensures the positivity of the data, while preserving the geometry of the signal. The differentiability of the misfit function is obtained by approximating the Dirac distributions through 2D Gaussian functions. The interest of this approach is illustrated numerically by computing misfit-function maps in schematic examples before moving to more realistic synthetic full-waveform exercises, including the Marmousi model. The better convexity of the graph-based optimal transport distance is shown. On the Marmousi model, starting from a 1D linearly increasing initial model, with data without low frequencies (no energy less than 3 Hz), a meaningful estimation of the P-wave velocity model is recovered, outperforming previously proposed optimal-transport-based misfit functions.

scholarly journals Full waveform inversion of short-offset, band-limited seismic data inthe Alboran basin (SE Iberia)

2019 ◽  
Author(s):  
Clàudia Gras ◽  
Valentí Sallarès ◽  
Daniel Dagnino ◽  
C. Estela Jiménez ◽  
Adrià Meléndez ◽  
...  
Keyword(s):  
Travel Time ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Velocity Model ◽  
P Wave ◽  
Full Waveform Inversion ◽  
Time Inversion ◽  
Full Waveform ◽  
Travel Time Tomography ◽  
Band Limited

Abstract. We present a high-resolution P-wave velocity model of the sedimentary cover and the uppermost basement until ~ 3 km depth obtained by full-waveform inversion of multichannel seismic data acquired with a 6 km-long streamer in the Alboran Sea (SE Iberia). The inherent non-linearity of the method, especially for short-offset, band-limited seismic data as this one, is circumvented by applying a data processing/modeling sequence consisting of three steps: (1) data re-datuming by back-propagation of the recorded seismograms to the seafloor; (2) joint refraction and reflection travel-time tomography combining the original and the re-datumed shot gathers; and (3) FWI of the original shot gathers using the model obtained by travel-time tomography as initial reference. The final velocity model shows a number of geological structures that cannot be identified in the travel-time tomography models or easily interpreted from seismic reflection images alone. A sharp strong velocity contrast accurately defines the geometry of the top of the basement. Several low-velocity zones that may correspond to the abrupt velocity change across steeply dipping normal faults are observed at the flanks of the basin. A 200–300 m thick, high-velocity layer embedded within lower velocity sediment may correspond to evaporites deposited during the Messinian crisis. The results confirm that the combination of data re-datuming and joint refraction and reflection travel-time inversion provides reference models that are accurate enough to apply full-waveform inversion to relatively short offset streamer data in deep water settings starting at field-data standard low frequency content of 6 Hz.

scholarly journals Semiglobal viscoacoustic full-waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R271-R293 ◽  
Author(s):  
Nuno V. da Silva ◽  
Gang Yao ◽  
Michael Warner
Keyword(s):  
Physical Properties ◽  
Wave Velocity ◽  
Seismic Data ◽  
Waveform Inversion ◽  
P Wave ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Intrinsic Attenuation ◽  
Full Waveform ◽  
P Wave Velocity

Full-waveform inversion deals with estimating physical properties of the earth’s subsurface by matching simulated to recorded seismic data. Intrinsic attenuation in the medium leads to the dispersion of propagating waves and the absorption of energy — media with this type of rheology are not perfectly elastic. Accounting for that effect is necessary to simulate wave propagation in realistic geologic media, leading to the need to estimate intrinsic attenuation from the seismic data. That increases the complexity of the constitutive laws leading to additional issues related to the ill-posed nature of the inverse problem. In particular, the joint estimation of several physical properties increases the null space of the parameter space, leading to a larger domain of ambiguity and increasing the number of different models that can equally well explain the data. We have evaluated a method for the joint inversion of velocity and intrinsic attenuation using semiglobal inversion; this combines quantum particle-swarm optimization for the estimation of the intrinsic attenuation with nested gradient-descent iterations for the estimation of the P-wave velocity. This approach takes advantage of the fact that some physical properties, and in particular the intrinsic attenuation, can be represented using a reduced basis, substantially decreasing the dimension of the search space. We determine the feasibility of the method and its robustness to ambiguity with 2D synthetic examples. The 3D inversion of a field data set for a geologic medium with transversely isotropic anisotropy in velocity indicates the feasibility of the method for inverting large-scale real seismic data and improving the data fitting. The principal benefits of the semiglobal multiparameter inversion are the recovery of the intrinsic attenuation from the data and the recovery of the true undispersed infinite-frequency P-wave velocity, while mitigating ambiguity between the estimated parameters.

scholarly journals Increasing the robustness and applicability of full-waveform inversion: An optimal transport distance strategy

2016 ◽  
Vol 35 (12) ◽  
pp. 1060-1067 ◽  
Author(s):  
L. Métivier ◽  
R. Brossier ◽  
Q. Mérigot ◽  
E. Oudet ◽  
J. Virieux
Keyword(s):  
Optimal Transport ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Transport Distance ◽  
Full Waveform

Seismic characterization of submarine gas-hydrate deposits in the Western Black Sea by acoustic full-waveform inversion of ocean-bottom seismic data

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. B311-B324 ◽  
Author(s):  
Laura Gassner ◽  
Tobias Gerach ◽  
Thomas Hertweck ◽  
Thomas Bohlen
Keyword(s):  
Wave Velocity ◽  
Black Sea ◽  
Gas Hydrate ◽  
Seismic Data ◽  
Field Data ◽  
Waveform Inversion ◽  
P Wave ◽  
Full Waveform Inversion ◽  
Ocean Bottom ◽  
Full Waveform

Evidence for gas-hydrate occurrence in the Western Black Sea is found from seismic measurements revealing bottom-simulating reflectors (BSRs) of varying distinctness. From an ocean-bottom seismic data set, low-resolution traveltime-tomography models of P-wave velocity [Formula: see text] are constructed. They serve as input for acoustic full-waveform inversion (FWI), which we apply to derive high-resolution parameter models aiding the interpretation of the seismic data for potential hydrate and gas deposits. Synthetic tests indicate the applicability of the FWI approach to robustly reconstruct [Formula: see text] models with a typical hydrate and gas signature. Models of S-wave velocity [Formula: see text] containing a hydrate signature can only be reconstructed when the parameter distribution of [Formula: see text] is already well-known. When we add noise to the modeled data to simulate field-data conditions, it prevents the reconstruction of [Formula: see text] completely, justifying the application of an acoustic approach. We invert for [Formula: see text] models from field data of two parallel profiles of 14 km length with a distance of 1 km. Results indicate a characteristic velocity trend for hydrate and gas occurrence at BSR depth in the first of the analyzed profiles. We find no indications for gas accumulations below the BSR on the second profile and only weak indications for hydrate. These differences in the [Formula: see text] signature are consistent with the reflectivity behavior of the migrated seismic streamer data of both profiles in which a zone of high-reflectivity amplitudes is coincident with the potential gas zone derived from the FWI result. Calculating saturation estimates for the potential hydrate and gas zones yields values of up to 30% and 1.2%, respectively.

Relaxing the initial model constraint for crustal-scale full-waveform inversion with graph-space optimal transport misfit function

2020 ◽  
Author(s):  
Andrzej Górszczyk ◽  
Ludovic Métivier ◽  
Romain Brossier
Keyword(s):  
Seismic Data ◽  
Optimal Transport ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Wide Angle ◽  
Initial Model ◽  
Full Waveform ◽  
Long Offset ◽  
Obs Data

<p>Investigations of the deep lithosphere aiming at the reconstruction of the geological models remain one of the key sources of the knowledge about the processes shaping the outer shell of our planet. Among different methods, the active seismic Ocean-Bottom Seismometer (OBS) experiments conducted in wide-angle configuration are routinely employed to better understand these processes. Indeed, long-offset seismic data, combined with computationally efficient travetime tomographic methods, have a great potential to constrain the macro-scale subsurface velocity models at large depths. </p><p>On the other hand, decades of development of acquisition systems, more and more efficient algorithms and high-performance computing resources make it now feasible to move beyond the regional raytracing-based traveltime tomography. In particular, the waveform inversion methods, such as Full-Waveform Inversion (FWI), are able to exhaustively exploit the rich information collected along the long-offset diving and refraction wavepaths, additionally enriched with the wide-angle reflection arrivals. So far however, only a few attempts have been conducted in the academic community to combine wide-angle seismic data with FWI for high-resolution crustal-scale velocity model reconstruction. This is partially due to the non-convexity of FWI misfit function, which increases with the complexity of the geological setting reflected by the seismograms. </p><p>In its classical form FWI is a nonlinear least-squares problem, which is solved through the local optimization techniques. This imposes the strong constraint on the accuracy of the starting FWI model. To avoid cycle-skipping problem the initial model must predict synthetic data within the maximum error of half-period time-shift with respect to the observed data. The criterion is difficult to fulfil when facing the crustal-scale FWI, because the long-offset acquisition translates to the long time of wavefront propagation and therefore accumulation of the traveltime error along the wavepath simulated in the initial model. This in turns increases the possibility of the cycle-skipping taking into account large number of propagated wavelengths.</p><p>Searching to mitigate this difficulty, here we investigate FWI with a Graph-Space Optimal Transport (GSOT) misfit function. Comparing to the classical least-squares norm, GSOT is convex with respect to the patterns in the waveform which can be shifted in time for more than half-period. Therefore, with proper data selection strategy GSOT misfit-function has potential to reduce the risk of cycle-skipping. We demonstrate the robustness of this novel approach using 2D wide-angle OBS data-set generated in a GO_3D_OBS synthetic model of subduction zone (30 km x 175 km). We show that using GSOT cost-function combined with the multiscale FWI strategy, we reconstruct in details the highly complex geological structure starting from a simple 1D velocity model. We believe that further developments of OT-based misfit functions can significantly reduce the constraints on the starting model accuracy and reduce the overall risk of cycle-skipping during FWI of wide-angle OBS data.</p>

scholarly journals On cycle-skipping and misfit functions modification for full-wave inversion: comparison of five recent approaches

Geophysics ◽  
2021 ◽  
pp. 1-85
Author(s):  
Arnaud Pladys ◽  
Romain Brossier ◽  
Yubing Li ◽  
Ludovic Métivier
Keyword(s):  
Least Squares ◽  
Field Data ◽  
Optimal Transport ◽  
Waveform Inversion ◽  
Imaging Method ◽  
Full Waveform Inversion ◽  
Wave Inversion ◽  
Full Waveform ◽  
Full Wave ◽  
Definition Of

Full waveform inversion, a high-resolution seismic imaging method, is known to require sufficiently accurate initial models to converge toward meaningful estimations of the subsurface mechanical properties. This limitation is due to the non-convexity of the least-squares distance with respect to kinematic mismatch. We propose a comparison of five misfit functions promoted recently to mitigate this issue: adaptive waveform inversion, instantaneous envelope, normalized integration, and two methods based on optimal transport. We explain which principles these methods are based on and illustrate how they are designed to better handle kinematic mismatch than a least-squares misfit function. By doing so, we can exhibit specific limitations of these methods in canonical cases. We further assess the interest of these five approaches for application to field data based on a synthetic Marmousi case study. We illustrate how adaptive waveform inversion and the two methods based on optimal transport possess interesting properties, making them appealing strategies applicable to field data. Another outcome is the definition of generic tools to compare misfit functions for full-waveform inversion.

Elastic full waveform inversion of multicomponent ocean-bottom cable seismic data: Application to Alba Field, U. K. North Sea

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. R109-R119 ◽  
Author(s):  
Timothy J. Sears ◽  
Penny J. Barton ◽  
Satish C. Singh
Keyword(s):  
Wave Velocity ◽  
Seismic Data ◽  
Waveform Inversion ◽  
P Wave ◽  
Full Waveform Inversion ◽  
Ocean Bottom ◽  
S Wave ◽  
Wave Data ◽  
Data Inversion ◽  
Full Waveform

Elastic full waveform inversion of multichannel seismic data represents a data-driven form of analysis leading to direct quantification of the subsurface elastic parameters in the depth domain. Previous studies have focused on marine streamer data using acoustic or elastic inversion schemes for the inversion of P-wave data. In this paper, P- and S-wave velocities are inverted for using wide-angle multicomponent ocean-bottom cable (OBC) seismic data. Inversion is undertaken using a two-dimensional elastic algorithm operating in the time domain, which allows accurate modeling and inversion of the full elastic wavefield, including P- and mode-converted PS-waves and their respective amplitude variation with offset (AVO) responses. Results are presented from the application of this technique to an OBC seismic data set from the Alba Field, North Sea. After building an initial velocity model and extracting a seismic wavelet, the data are inverted instages. In the first stage, the intermediate wavelength P-wave velocity structure is recovered from the wide-angle data and then the short-scale detail from near-offset data using P-wave data on the [Formula: see text] (vertical geophone) component. In the second stage, intermediate wavelengths of S-wave velocity are inverted for, which exploits the information captured in the P-wave’s elastic AVO response. In the third stage, the earlier models are built on to invert mode-converted PS-wave events on the [Formula: see text] (horizontal geophone) component for S-wave velocity, targeting first shallow and then deeper structure. Inversion of [Formula: see text] alone has been able to delineate the Alba Field in P- and S-wave velocity, with the main field and outlier sands visible on the 2D results. Inversion of PS-wave data has demonstrated the potential of using converted waves to resolve shorter wavelength detail. Even at the low frequencies [Formula: see text] inverted here, improved spatial resolution was obtained by inverting S-wave data compared with P-wave data inversion results.

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