Finite‐frequency resolution limits of traveltime tomography for smoothly varying velocity models

SUMMARY Wave-equation-based traveltime tomography has been extensively applied in both global tomography and seismic exploration. Typically, the traveltime Fréchet derivative is obtained using the first-order Born approximation, which is only satisfied for weak velocity perturbations and small phase shifts (i.e. the weak-scattering assumption). Although the small phase-shift restriction can be handled with the Rytov approximation, the weak velocity-perturbation assumption is still a major limitation. The recently developed generalized Rytov approximation (GRA) method can achieve an improved phase accuracy of the forward-scattered wavefield, in the presence of large-scale and strong velocity perturbations. In this paper, we combine GRA with the classical finite-frequency theory and propose a GRA-based traveltime sensitivity kernel (GRA-TSK), which overcomes the weak-scattering limitation of the conventional finite-frequency methods. Numerical examples demonstrate that the accumulated time delay of forward-scattered waves caused by large-scale smooth perturbations can be correctly handled by the GRA-TSK, regardless of the magnitude of the velocity perturbations. Then, we apply the new sensitivity kernel to solve the traveltime inverse problem, and we propose a matrix-free Gauss–Newton method that has a faster convergence rate compared with the gradient-based method. Numerical tests show that, compared with the conventional adjoint traveltime tomography, the proposed GRA-based traveltime tomography can obtain a more accurate model with a faster convergence rate, making it more suited for recovering the large-intermediate scale of the velocity model, even for strong-perturbation and complex subsurface structures.

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Crustal and mantle velocity models of southern Tibet from finite frequency tomography

Journal of Geophysical Research Atmospheres ◽

10.1029/2009jb007159 ◽

2011 ◽

Vol 116 (B2) ◽

Cited By ~ 23

Author(s):

Xiaofeng Liang ◽

Yang Shen ◽

Yongshun John Chen ◽

Yong Ren

Keyword(s):

Finite Frequency ◽

Southern Tibet ◽

Velocity Models ◽

Mantle Velocity

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Resolution of slowness and reflectors in crosswell tomography with transmission and reflection traveltimes

Geophysics ◽

10.1190/1.2969777 ◽

2008 ◽

Vol 73 (5) ◽

pp. VE321-VE335 ◽

Cited By ~ 1

Author(s):

Kenneth P. Bube ◽

Robert T. Langan

Keyword(s):

Field Experiments ◽

Oil Field ◽

Data Sets ◽

Traveltime Tomography ◽

Velocity Models ◽

West Texas ◽

Well Spacing ◽

High Level ◽

Transmission And Reflection

We sometimes encounter situations in seismic imaging in which knowing the position of key reflectors between wells would be very useful. In many crosswell data sets, both transmission and reflection traveltimes for selected reflectors can be picked. We investigated the possibility that transmission-plus-reflection crosswell traveltime tomography can determine the position of these reflectors with a high level of accuracy, thereby providing an independent way of verifying (and perhaps improving) the position of these reflectors obtained from crosswell reflection imaging. We studied the effect of combining reflection traveltimes for selected reflectors with transmission traveltimes on the resolution of the interwell slowness field and depth determination of selected reflectors. We found that theoretically, the position of reflectors is determined uniquely from transmission and reflection traveltimes in a linearized continuum formulation ofcrosswell tomography. We also computed diagonal elements of the resolu-tion matrix for two crosswell geometries based on field experiments conducted in a west Texas oil field to see what effect noise has on the accuracy of our determination of reflector depths. These computational results indicate that reflector positions are indeed very well determined for these geometries, with expected errors of [Formula: see text] of the well spacing when noise in traveltimes is [Formula: see text]. Because reflector-position parameters are so well determined, including reflection traveltimes does not degrade the resolution of the slowness field as a result of introducing additional reflector-depth parameters. Actually, the resolution of the slowness field, particularly near reflectors, improves by including reflection traveltimes, in spite of the fact that we must solve for these additional depth parameters. The improvement in slowness resolution should provide velocity models that can yield more accurate reflection images.

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Damped wave-equation-based first-arrival traveltime tomography using the embedded boundary method

Geophysics ◽

10.1190/geo2020-0233.1 ◽

2021 ◽

pp. 1-91

Author(s):

Yunhui Park ◽

Sukjoon Pyun

Keyword(s):

Wave Equation ◽

Real Data ◽

Damped Wave Equation ◽

Traveltime Tomography ◽

Velocity Models ◽

Boundary Method ◽

Embedded Boundary ◽

First Arrival ◽

Irregular Topography ◽

Modeling Algorithm

First-arrival traveltime tomography (FATT) is used to delineate shallow velocity structures to identify static effects in oil exploration as well as to characterize the near surface for geotechnical purposes. Because FATT is generally used for land seismic data processing, it becomes necessary to consider irregular topography especially when performing wave-based tomography. However, the standard Cartesian finite-difference method cannot properly handle irregular topography. Hence, the embedded boundary method (EBM) is incorporated into the frequency-domain damped-wave equation in order to correctly describe irregular topography. The developed modeling algorithm is used to calculate first-arrival traveltimes and to perform FATT. The EBM-based modeling algorithm accurately describes the irregular surfaces of numerical velocity models on a regular mesh by exploiting the mirror image principle. The accuracy of the EBM-based traveltime calculation is validated by using two homogeneous velocity models with dipping and complex surfaces. The validation results demonstrate that the proposed algorithm is unaffected by the staircase approximation. The FATT is then applied to synthetic and real data to demonstrate the applicability of the developed algorithm to velocity models with complex topography. For the real data example, the inverted velocity model is used to apply static corrections. The processing results demonstrate an improvement in the continuity of seismic events, thus confirming the accuracy of the developed FATT method.

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Waveform tomography at a groundwater contamination site: Surface reflection data

Geophysics ◽

10.1190/1.2752744 ◽

2007 ◽

Vol 72 (5) ◽

pp. G45-G55 ◽

Cited By ~ 44

Author(s):

Fuchun Gao ◽

Alan Levander ◽

R. Gerhard Pratt ◽

Colin A. Zelt ◽

Gian-Luigi Fradelizio

Keyword(s):

Groundwater Contamination ◽

Nonaqueous Phase Liquids ◽

Seismic Profiles ◽

Lateral Velocity ◽

Data Set ◽

Surface Reflection ◽

Traveltime Tomography ◽

Velocity Models ◽

Reflection Data ◽

Waveform Tomography

We have applied acoustic-waveform tomography to 45 2D seismic profiles to image the 3D geometry of a buried paleochannel at a groundwater-contamination site at Hill Air Force Base in Utah. The paleochannel, which is incised into an alluvium-covered clay aquitard, acts as a trap for dense nonaqueous-phase liquids (DNAPLs) that contaminate the shallowest groundwater system in the study area. The 2D profiles were extracted from a 3D surface reflection data set. First-arrival traveltime tomography provided initial velocity models for the waveform tomography. We inverted for six frequency components in the band [Formula: see text] of the direct and refracted waves to produce 45 2D velocity models. The flanks and bottom of a channel with a maximum depth of about [Formula: see text] were well modeled in most of the 45 parallel 2D slices, which allowed us to construct a 3D image of the channel by combining and interpolating between the 45 image slices. The 3D model of the channel will be useful for siting extraction wells within the site remediation program. The alluvium that fills the channel showed marked vertical and lateral velocity heterogeneity. Traveltime tomography and waveform tomography can be complementary approaches. Used together, they can provide high-resolution images of complicated shallow structures.

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Improved interpretation of SAGEEP 2011 blind refraction data using Frequency-Dependent Traveltime Tomography

10.5194/egusphere-egu21-4214 ◽

2021 ◽

Author(s):

Siegfried Rohdewald

Keyword(s):

Current Velocity ◽

Seismic Refraction ◽

Blind Test ◽

Near Surface ◽

Traveltime Inversion ◽

Traveltime Tomography ◽

Velocity Models ◽

First Arrival ◽

Starting Model ◽

Refraction Data

We demonstrate improved resolution in P-wave velocity tomograms obtained by inversion of the synthetic SAGEEP 2011 refraction traveltime data (Zelt 2010) using Wavepath-Eikonal Traveltime Inversion (WET; Schuster 1993) and Wavelength-Dependent Velocity Smoothing (WDVS; Zelt and Chen 2016). We use a multiscale inversion approach and a Conjugate-Gradient based search method. Our default starting model is a 1D-gradient model obtained directly from the traveltime first arrivals assuming diving waves (Sheehan, 2005). As a second approach, we map the first breaks to assumed refractors and obtain a layered starting model using the Plus-Minus refraction method (Hagedoorn, 1959). We compare tomograms obtained using WDVS to smooth the current velocity model grid before forward modeling traveltimes vs. tomograms obtained without WDVS. Results show that WET images velocity layer boundaries more sharply when engaging WDVS. We determine the optimum WDVS frequency iteratively by trial-and-error. We observe that the lower the used WDVS frequency, the stronger the imaged velocity contrast at the top-of-basement. Using a WDVS frequency that is too low makes WDVS based WET inversion unstable exhibiting increasing RMS error, too high modeled velocity contrast and too shallow imaged top-of-basement. To speed up WDVS, we regard each nth node only when scanning the velocity along straight scan lines radiating from the current velocity grid node. Scanned velocities are weighted with a Cosine-Squared function as described by (Zelt and Chen, 2016). We observe that activating WDVS allows decreasing WET regularization (smoothing and damping) to a higher degree than without WDVS.References:Hagedoorn, J.G., 1959, The Plus-Minus method of interpreting seismic refraction sections, Geophysical Prospecting, Volume 7, 158-182.Rohdewald, S.R.C., 2021, SAGEEP11 data interpretation, https://rayfract.com/tutorials/sageep11_16.pdf.Schuster, G.T., Quintus-Bosz, A., 1993, Wavepath eikonal traveltime inversion: Theory. Geophysics, Volume 58, 1314-1323.Sheehan, J.R., Doll, W.E., Mandell, W., 2005, An evaluation of methods and available software for seismic refraction tomography analysis, JEEG, Volume 10(1), 21-34.Shewchuk, J.R., 1994, An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, http://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf. Zelt, C.A., 2010, Seismic refraction shootout: blind test of methods for obtaining velocity models from first-arrival travel times, http://terra.rice.edu/department/faculty/zelt/sageep2011.Zelt, C.A., Haines, S., Powers, M.H. et al. 2013, Blind Test of Methods for Obtaining 2-D Near-Surface Seismic Velocity Models from First-Arrival Traveltimes, JEEG, Volume 18(3), 183-194. Zelt, C.A., Chen, J., 2016, Frequency-dependent traveltime tomography for near-surface seismic refraction data, Geophys. J. Int., Volume 207, 72-88.

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