Joint wave-equation traveltime inversion of diving/direct and reflected waves for the P- and S-wave velocity macromodel building

Full waveform inversion (FWI) suffers from the local minima problem and requires a sufficiently accurate starting model to converge to the correct solution. Wave-equation traveltime inversion (WETI) is an effective tool to retrieve the long-wavelength components of the velocity model. We develop a joint diving/direct and reflected wave WETI (JDRWETI) method to build the P- and S-wave velocity macromodels. We estimate the traveltime shifts of seismic events (diving/direct waves, PP and PS reflections) through the dynamic warping scheme and construct a misfit function using both the time shifts of diving/direct and reflected waves. We derive the adjoint wave equations and the gradients with respect to the background models based on the joint misfit function. We apply the kernel decomposition scheme to extract the kernel of the diving/direct wave and the tomography kernels of PP and PS reflections. For an explosive source, the kernels of diving/direct wave and PP reflections and the kernel of PS reflections are used to compute the P- and S-wave gradients of the background models, respectively. We implement JDRWETI by a two-stage inversion workflow: first invert the P- and S-wave velocity models using the P-wave gradients and then improve the S-wave velocity model using the S-wave gradients. Numerical tests on synthetic and field datasets reveal that the JDRWETI method successfully recovers the long-wavelength components of P- and S-wave velocity models, which can be used for an initial model for the subsequent elastic FWI. Moreover, the proposed JDRWETI method prevails over the existing reflection WETI method and the cascaded diving/direct and reflected wave WETI method, especially when large velocity errors are present in the shallow part of the starting models. The JDRWETI method with the two-stage inversion workflow can give rise to reasonable inversion results even for the model with different P- and S-wave velocity structures.

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Inversion of seismic refraction and reflection data for building long-wavelength velocity models

Geophysics ◽

10.1190/geo2014-0174.1 ◽

2015 ◽

Vol 80 (2) ◽

pp. R81-R93 ◽

Cited By ~ 22

Author(s):

Haiyang Wang ◽

Satish C. Singh ◽

Francois Audebert ◽

Henri Calandra

Keyword(s):

Wave Equation ◽

Short Wavelength ◽

Velocity Model ◽

Density Model ◽

Data Set ◽

Reflected Waves ◽

Long Wavelength ◽

Velocity Models ◽

Computation Efficiency ◽

Refracted Waves

Long-wavelength velocity model building is a nonlinear process. It has traditionally been achieved without appealing to wave-equation-based approaches for combined refracted and reflected waves. We developed a cascaded wave-equation tomography method in the data domain, taking advantage of the information contained in the reflected and refracted waves. The objective function was the traveltime residual that maximized the crosscorrelation function between real and synthetic data. To alleviate the nonlinearity of the inversion problem, refracted waves were initially used to provide vertical constraints on the velocity model, and reflected waves were then included to provide lateral constraints. The use of reflected waves required scale separation. We separated the long- and short-wavelength subsurface structures into velocity and density models, respectively. The velocity model update was restricted to long wavelengths during the wave-equation tomography, whereas the density model was used to absorb all the short-wavelength impedance contrasts. To improve the computation efficiency, the density model was converted into the zero-offset traveltime domain, where it was invariant to changes of the long-wavelength velocity model. After the wave-equation tomography has derived an optimized long-wavelength velocity model, full-waveform inversion was used to invert all the data to retrieve the short-wavelength velocity structures. We developed our method in two synthetic tests and then applied it to a marine field data set. We evaluated the results of the use of refracted and reflected waves, which was critical for accurately building the long-wavelength velocity model. We showed that our wave-equation tomography strategy was robust for the real data application.

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Elastic reflection traveltime inversion with decoupled wave equation

Geophysics ◽

10.1190/geo2017-0631.1 ◽

2018 ◽

Vol 83 (5) ◽

pp. R463-R474 ◽

Cited By ~ 6

Author(s):

Guanchao Wang ◽

Shangxu Wang ◽

Jianyong Song ◽

Chunhui Dong ◽

Mingqiang Zhang

Keyword(s):

Wave Equation ◽

Wave Velocity ◽

Waveform Inversion ◽

P Wave ◽

Model Parameters ◽

Local Minima ◽

S Wave ◽

Traveltime Inversion ◽

Velocity Models ◽

Elastic Reflection

Elastic full-waveform inversion (FWI) updates high-resolution model parameters by minimizing the residuals of multicomponent seismic records between the field and model data. FWI suffers from the potential to converge to local minima and more serious nonlinearity than acoustic FWI mainly due to the absence of low frequencies in seismograms and the extended model domain (P- and S-velocities). Reflection waveform inversion can relax the nonlinearity by relying on the tomographic components, which can be used to update the low-wavenumber components of the model. Hence, we have developed an elastic reflection traveltime inversion (ERTI) approach to update the low-wavenumber component of the velocity models for the P- and S-waves. In our ERTI algorithm, we took the P- and S-wave impedance perturbations as elastic reflectivity to generate reflections and a weighted crosscorrelation as the misfit function. Moreover, considering the higher wavenumbers (lower velocity value) of the S-wave velocity compared with the P-wave case, optimizing the low-wavenumber components for the S-wave velocity is even more crucial in preventing the elastic FWI from converging to local minima. We have evaluated an equivalent decoupled velocity-stress wave equation to ERTI to reduce the coupling effects of different wave modes and to improve the inversion result of ERTI, especially for the S-wave velocity. The subsequent application on the Sigsbee2A model demonstrates that our ERTI method with the decoupled wave equation can efficiently update the low-wavenumber parts of the model and improve the precision of the S-wave velocity.

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PS Energy Imaging Condition for Microseismic Data - Part 1: Theory and Applications in 3D Isotropic Media

Geophysics ◽

10.1190/geo2020-0476.1 ◽

2020 ◽

pp. 1-79

Author(s):

Can Oren ◽

Jeffrey Shragge

Keyword(s):

Wave Velocity ◽

Model Building ◽

Velocity Model ◽

Microseismic Monitoring ◽

Elastic Model ◽

S Wave ◽

Imaging Condition ◽

Velocity Models ◽

Monitoring Programs ◽

Imaging Conditions

Accurately estimating event locations is of significant importance in microseismic investigations because this information greatly contributes to the overall success of hydraulic fracturing monitoring programs. Full-wavefield time-reverse imaging (TRI) using one or more wave-equation imaging conditions offers an effective methodology for locating surface-recorded microseismic events. To be most beneficial in microseismic monitoring programs, though, the TRI procedure requires using accurate subsurface models that account for elastic media effects. We develop a novel microseismic (extended) PS energy imaging condition that explicitly incorporates the stiffness tensor and exhibits heightened sensitivity to isotropic elastic model perturbations compared to existing imaging conditions. Numerical experiments demonstrate the sensitivity of microseismic TRI results to perturbations in P- and S-wave velocity models. Zero-lag and extended microseismic source images computed at selected subsurface locations yields useful information about 3D P- and S-wave velocity model accuracy. Thus, we assert that these image volumes potentially can serve as the input into microseismic elastic velocity model building algorithms.

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Full-traveltime inversion

Geophysics ◽

10.1190/geo2015-0353.1 ◽

2016 ◽

Vol 81 (5) ◽

pp. R261-R274 ◽

Cited By ~ 67

Author(s):

Yi Luo ◽

Yue Ma ◽

Yan Wu ◽

Hongwei Liu ◽

Lei Cao

Keyword(s):

Wave Equation ◽

Seismic Data ◽

Low Frequency ◽

Velocity Model ◽

New Wave ◽

Severe Problem ◽

Reflected Waves ◽

Traveltime Inversion ◽

Velocity Models ◽

Kinematic Information

Many previously published wave-equation-based methods, which attempt to automatically invert traveltime or kinematic information in seismic data or migrated gathers for smooth velocities, suffer a common and severe problem — the inversions are involuntarily and unconsciously hijacked by amplitude information. To overcome this problem, we have developed a new wave-equation-based traveltime inversion methodology, referred to as full-traveltime (i.e., fully dependent on traveltime) inversion (FTI), to automatically estimate a kinematically accurate velocity model from seismic data. The key idea of FTI is to make the inversion fully dependent on traveltime information, and thus prevent amplitude interference during inversion. Under the assumption that velocity perturbations cause only traveltime changes, we have derived the FTI method in the data and image domains, which are applicable to transmitted arrivals and reflected waves, respectively. FTI does not require an accurate initial velocity model or low-frequency seismic data. Synthetic and field data tests demonstrate that FTI produces satisfactory inversion results, even when using constant velocity models as initials.

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Elastic reflection waveform inversion based on the decomposition of sensitivity kernels

Geophysics ◽

10.1190/geo2018-0220.1 ◽

2019 ◽

Vol 84 (2) ◽

pp. R235-R250 ◽

Cited By ~ 1

Author(s):

Zhiming Ren ◽

Zhenchun Li ◽

Bingluo Gu

Keyword(s):

Wave Velocity ◽

Waveform Inversion ◽

Velocity Model ◽

P Wave ◽

Background Model ◽

Reverse Time ◽

S Wave ◽

Velocity Models ◽

Time Migration ◽

Starting Model

Full-waveform inversion (FWI) has the potential to obtain an accurate velocity model. Nevertheless, it depends strongly on the low-frequency data and the initial model. When the starting model is far from the real model, FWI tends to converge to a local minimum. Based on a scale separation of the model (into the background model and reflectivity model), reflection waveform inversion (RWI) can separate out the tomography term in the conventional FWI kernel and invert for the long-wavelength components of the velocity model by smearing the reflected wave residuals along the transmission (or “rabbit-ear”) paths. We have developed a new elastic RWI method to build the P- and S-wave velocity macromodels. Our method exploits a traveltime-based misfit function to highlight the contribution of tomography terms in the sensitivity kernels and a sensitivity kernel decomposition scheme based on the P- and S-wave separation to suppress the high-wavenumber artifacts caused by the crosstalk of different wave modes. Numerical examples reveal that the gradients of the background models become sufficiently smooth owing to the decomposition of sensitivity kernels and the traveltime-based misfit function. We implement our elastic RWI in an alternating way. At each loop, the reflectivity model is generated by elastic least-squares reverse time migration, and then the background model is updated using the separated traveltime kernels. Our RWI method has been successfully applied in synthetic and real reflection seismic data. Inversion results demonstrate that the proposed method can retrieve preferable low-wavenumber components of the P- and S-wave velocity models, which are reliable to serve as a starting model for conventional elastic FWI. Also, our method with a two-stage inversion workflow, first updating the P-wave velocity using the PP kernels and then updating the S-wave velocity using the PS kernels, is feasible and robust even when P- and S-wave velocities have different structures.

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Time-reverse imaging with limited S-wave velocity model information

Geophysics ◽

10.1190/geo2010-0303.1 ◽

2011 ◽

Vol 76 (5) ◽

pp. MA33-MA40 ◽

Cited By ~ 3

Author(s):

Brian Steiner ◽

Erik H. Saenger ◽

Stefan M. Schmalholz

Keyword(s):

Energy Density ◽

Wave Velocity ◽

Wave Energy ◽

Velocity Model ◽

Body Waves ◽

P Wave ◽

S Wave ◽

Velocity Models ◽

Wave Energy Density ◽

Wavefield Extrapolation

Time-reverse imaging is a wave propagation algorithm for locating sources. Signals recorded by synchronized receivers are reversed in time and propagated back to the source location by elastic wavefield extrapolation. Elastic wavefield extrapolation requires a P-wave as well as an S-wave velocity model. The velocity models available from standard reflection seismic methods are usually restricted to only P-waves. In this study, we use synthetically produced time signals to investigate the accuracy of seismic source localization by means of time-reverse imaging with the correct P-wave and a perturbed S-wave velocity model. The studies reveal that perturbed S-wave velocity models strongly influence the intensity and position of the focus. Imaging the results with the individual maximum energy density for both body wave types instead of mixed modes allows individual analysis of the two body waves. P-wave energy density images render stable focuses in case of a correct P-wave and incorrect S-wave velocity model. Thus, P-wave energy density seems to be a more suitable imaging condition in case of a high degree of uncertainty in the S-wave velocity model.

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Time-average velocity estimation through surface-wave analysis: Part 1 — S-wave velocity

Geophysics ◽

10.1190/geo2016-0367.1 ◽

2017 ◽

Vol 82 (3) ◽

pp. U49-U59 ◽

Cited By ~ 15

Author(s):

Laura Valentina Socco ◽

Cesare Comina ◽

Farbod Khosro Anjom

Keyword(s):

Wave Velocity ◽

Average Velocity ◽

Field Data ◽

Velocity Model ◽

Velocity Estimation ◽

S Wave ◽

Simple Method ◽

Near Surface ◽

Velocity Models ◽

Time Average

In some areas, the estimation of static corrections for land seismic data is a critical step of the processing workflow. It often requires the execution of additional surveys and data analyses. Surface waves (SWs) in seismic records can be processed to extract local dispersion curves (DCs) that can be used to estimate near-surface S-wave velocity models. Here we focus on the direct estimation of time-average S-wave velocity models from SW DCs without the need to invert the data. Time-average velocity directly provides the value of one-way time, given a datum plan depth. The method requires the knowledge of one 1D S-wave velocity model along the seismic line, together with the relevant DC, to estimate a relationship between SW wavelength and investigation depth on the time-average velocity model. This wavelength/depth relationship is then used to estimate all the other time-average S-wave velocity models along the line directly from the DCs by means of a data transformation. This approach removes the need for extensive data inversion and provides a simple method suitable for industrial workflows. We tested the method on synthetic and field data and found that it is possible to retrieve the time-average velocity models with uncertainties less than 10% in sites with laterally varying velocities. The error on one-way times at various depths of the datum plan retrieved by the time-average velocity models is mostly less than 5 ms for synthetic and field data.

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Computing near-surface velocity models for S-wave static corrections using raypath interferometry

Geophysics ◽

10.1190/geo2017-0340.1 ◽

2018 ◽

Vol 83 (3) ◽

pp. U23-U34

Author(s):

Raul Cova ◽

David Henley ◽

Kristopher A. Innanen

Keyword(s):

Wave Velocity ◽

Velocity Model ◽

P Wave ◽

Surface Velocity ◽

S Wave ◽

Converted Wave ◽

Near Surface ◽

Velocity Models ◽

Consistent Solution ◽

Static Corrections

A near-surface velocity model is one of the typical products generated when computing static corrections, particularly in the processing of PP data. Critically refracted waves are the input usually needed for this process. In addition, for the converted PS mode, S-wave near-surface corrections must be applied at the receiver locations. In this case, however, critically refracted S-waves are difficult to identify when using P-wave energy sources. We use the [Formula: see text]-[Formula: see text] representation of the converted-wave data to capture the intercept-time differences between receiver locations. These [Formula: see text]-differences are then used in the inversion of a near-surface S-wave velocity model. Our processing workflow provides not only a set of raypath-dependent S-wave static corrections, but also a velocity model that is based on those corrections. Our computed near-surface S-wave velocity model can be used for building migration velocity models or to initialize elastic full-waveform inversions. Our tests on synthetic and field data provided superior results to those obtained by using a surface-consistent solution.

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First-arrival traveltime inversion of seismic diving waves observed on undulant surface

Geophysical Journal International ◽

10.1093/gji/ggab025 ◽

2021 ◽

Vol 225 (2) ◽

pp. 1020-1031

Author(s):

Huachen Yang ◽

Jianzhong Zhang ◽

Kai Ren ◽

Changbo Wang

Keyword(s):

Turning Points ◽

Analytical Formula ◽

Velocity Model ◽

Western China ◽

Inversion Method ◽

Mountain Area ◽

Traveltime Inversion ◽

Static Correction ◽

Velocity Models ◽

First Arrival

SUMMARY A non-iterative first-arrival traveltime inversion method (NFTI) is proposed for building smooth velocity models using seismic diving waves observed on irregular surface. The new ray and traveltime equations of diving waves propagating in smooth media with undulant observation surface are deduced. According to the proposed ray and traveltime equations, an analytical formula for determining the location of the diving-wave turning points is then derived. Taking the influence of rough topography on first-arrival traveltimes into account, the new equations for calculating the velocities at turning points are established. Based on these equations, a method is proposed to construct subsurface velocity models from the observation surface downward to the bottom using the first-arrival traveltimes in common offset gathers. Tests on smooth velocity models with rugged topography verify the validity of the established equations, and the superiority of the proposed NFTI. The limitation of the proposed method is shown by an abruptly-varying velocity model example. Finally, the NFTI is applied to solve the static correction problem of the field seismic data acquired in a mountain area in the western China. The results confirm the effectivity of the proposed NFTI.

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