Stereotomography in triangulated models

Yang, Kai; Shao, Weidong; Xing, Fei; Xiong, Kai

doi:10.1093/gji/ggy165

“…The inverse problem is implemented by building explicitly the sensitivity matrix and the resulting sparse tomographic system is solved with a linear conjugate-gradient method during each iteration of the velocity model update, this update being either performed in a linear or nonlinear way. Since the original formulation (Billette 1998), different variants emerged; for example, 3-D extension (Chalard et al 2000), post-stack formulation (Lavaud et al 2004), application in borehole settings (Gosselet et al 2005), adaptation for anisotropic media (Nag et al 2006;Barbosa et al 2008), accounting for converted primary waves (Alerini et al 2007) or wide-aperture data (Prieux et al 2013), triangulated model parametrization (Yang et al 2018), handling complex topography (Jin & Zhang 2018). All of the aforementioned variants follow the same framework of the classical formulation using ray tracing as a forward solver and explicitly building the sensitivity matrix for the inversion.…”

Section: Introductionmentioning

confidence: 99%

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

Sambolian

¹

,

Operto

²

,

Ribodetti

³

et al. 2019

Geophysical Journal International

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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.

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“…The inverse problem is implemented by building explicitly the sensitivity matrix and the resulting sparse tomographic system is solved with a linear conjugate-gradient method during each iteration of the velocity model update, this update being either performed in a linear or nonlinear way. Since the original formulation (Billette 1998), different variants emerged; for example, 3-D extension (Chalard et al 2000), post-stack formulation (Lavaud et al 2004), application in borehole settings (Gosselet et al 2005), adaptation for anisotropic media (Nag et al 2006;Barbosa et al 2008), accounting for converted primary waves (Alerini et al 2007) or wide-aperture data (Prieux et al 2013), triangulated model parametrization (Yang et al 2018), handling complex topography (Jin & Zhang 2018). All of the aforementioned variants follow the same framework of the classical formulation using ray tracing as a forward solver and explicitly building the sensitivity matrix for the inversion.…”

Section: Introductionmentioning

confidence: 99%

Parsimonious Slope Tomography Based On Eikonal Solvers and the Adjoint-state Method

Sambolian

¹

,

Operto

²

,

Ribodetti

³

et al. 2018

View full text Add to dashboard Cite

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.

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Response of rigid and flexible buildings in an earthquake

Lapin,

Shokhbarov,

Aldakhov

et al. 2024

BIO Web Conf.

0

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During the earthquake on March 26, 2018 with a source in the Almaty region, the stations of the engineering and seismometric service received instrumental records on buildings with various design solutions. The article discusses instrumental records (accelerograms) recorded on a four-storey frame building and an 11-storey building with a steel frame. Spectral curves were plotted at the registration points on the roof and basement parts of buildings. It was found that the periods of the prevailing fluctuations of the base of the structure are 0.16-0.21 sec for the two indicated buildings. The spectral curves at the basement level have the same shape. Instrumental records are included in the database of accelerograms of KazRDICA JSC.

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Stereotomography in triangulated models

Cited by 6 publications

References 23 publications

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

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

Parsimonious Slope Tomography Based On Eikonal Solvers and the Adjoint-state Method

Response of rigid and flexible buildings in an earthquake

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