Parsimonious slope tomography based on eikonal solvers and the adjoint-state method

Abstract

Velocity macromodel building is an essential step of the seismic imaging workflow. Indeed, obtaining acceptable results through migration or full waveform inversion is highly dependent on the kinematic accuracy of the background/initial velocity model. Two decades ago, stereotomography was proposed as an alternative to reflection traveltime tomography, the first relying on semi-automatic picking of locally coherent events associated with small reflection or diffraction segments tied to scatterers in depth by a pair of rays, while the latter on interpretive picking of laterally continuous reflections. The flexibility of stereotomography paved the way for many developments that have shown the efficiency of the method whilst emphasizing on the complementary information carried out by traveltimes and slopes of locally coherent events. A recent formulation recast stereotomography under a matrix-free formulation based on eikonal solvers and the adjoint-state method. In the latter, like in the previous works, the scatterer positions and the velocity field are updated jointly to tackle the ill-famed velocityposition coupling in reflection tomography. Following on from this adjoint-state formulation, we propose a new parsimonious formulation of slope tomography that offers the chance to restrain the problem to minimizing the residuals of a single data class being a slope, in search of a sole parameter class being the subsurface velocity field. This parsimonious formulation results from a variable projection, which is implemented by enforcing a consistency between the scatterer coordinates and the velocity macromodel through migration of kinematic attributes. We explain why the resulting reduced-parametrization inversion is more suitable for tomographic problems than the most common joint inversion strategy. We benchmark our method against the complex Marmousi model along with a validation through time domain full waveform inversion and then present the results of a field data case study.

Mitigating the ill-posedness of first-arrival traveltime tomography using slopes: application to the eastern Nankai Trough (Japan) OBS data set

“…In fact, most state of the art scattering-based or reflection-based tomographic methods rely on a differential information as a needed complement to traveltimes. Stereotomography (Billette & Lambaré 1998;Lambaré 2008;Tavakoli F. et al 2017b;Sambolian et al 2019;Tavakoli F. et al 2019), a slope tomography method based on locally coherent events utilizes slopes in order to constrain and define the scattering position associated with reflections or diffractions (Fig. 2a).…”

Seismic Exploration of the Deep Structure and Seismogenic Faults in the Ligurian Sea by Joint Multi Channel and Ocean Bottom Seismic Acquisitions: Preliminary Results of the SEFASILS Cruise

“…After a careful binning of the MCS data using shot and receiver navigation files, the postcruise processing sequence, applied to both reflection profiles using CGG's Geovation ® software (version 6401) includes (1) field data transcription, (2) 2.5 Hz low-cut filter, (3) spherical divergence compensation, (4) noise attenuation in f-x domain, (5) trace editing, (6) cable and source corrections, (7) resampling from 2 to 4 ms, (8) first pass velocity picking, (9) multiple attenuation with 2D-SRME method (two passes) followed by Radon demultiple, (10) second pass velocity picking, (11) deconvolution, (12) third pass velocity picking, and (13) pre-stack Kirchhoff time migration. Prestack depth migration is also performed using a Ray+Born imaging technique [16], Common Image Gather analysis [17], as well as slope tomography being tested to build suitable velocity models for migration [18].…”

GO_3D_OBS: the multi-parameter benchmark geomodel for seismic imaging method assessment and next-generation 3D survey design (version 1.0)

“…In the context of this study, by seismic imaging we understand the broad range of procedures for estimating the earth's rock parameters from seismic data -including travel time tomography, migration-based velocity analysis, raybased and reverse-time pre-stack depth migration, and full waveform inversion. Among them, velocity reconstruction methods including first-arrival travel time tomography (FAT) (Zelt and Barton, 1998), reflection tomography (Bishop et al, 1985;Farra and Madariaga, 1988), joint refraction and reflection tomography (Korenaga et al, 2000;Meléndez et al, 2015), slope tomography (Billette et al, 1998;Lambaré, 2008;Tavakoli F. et al, 2017Tavakoli F. et al, , 2019Sambolian et al, 2019), wavefront tomography (Bauer et al, 2017), finite-frequency travel time tomography (Mercerat and Nolet, 2013;Zelt and Chen, 2016), wave equation tomography (Luo and Schuster, 1991;Tong et al, 2014), and full waveform inversion (FWI) (Tarantola, 1984;Mora, 1988;Pratt et al, 1996) shall be examined against large-scale numerical problems and complex synthetic datasets generated in an ultra-long-offset configuration. Combining these methods with the up-to-date seismic acquisition techniques available nowadays should allow for regional-scale seismic imaging of continental margins at subwavelength spatial resolution (typically few hundred metres) (Morgan et al, 2013).…”

“…from complementary OBS data) and the deep reflection are recorded with an acceptable signal-to-noise ratio. Higher-resolution velocity models can also be built from streamer data by FWI (Shipp and Singh, 2002;Qin and Singh, 2017) if the information carried out by diving waves is made usable after the re-datuming of the data on the seabed (Gras et al, 2019). As an alternative to classical FWI, a velocity model can be built by reflection waveform inversion (RWI), a reformulation of FWI where the reflectivity estimated by least-squares RTM is used as a secondary buried source to update the velocities along the reflection paths connecting the reflectors to the sources and receivers (Xu et al, 2012;Brossier et al, 2015;Zhou et al, 2015;Wu and Alkhalifah, 2015).…”