Wave‐equation traveltime inversion

Geophysics ◽  
1991 ◽  
Vol 56 (5) ◽  
pp. 645-653 ◽  
Author(s):  
Y. Luo ◽  
G. T. Schuster
Keyword(s):  
Wave Equation ◽  
Ray Tracing ◽  
High Frequency ◽  
Velocity Model ◽  
Head Wave ◽  
Inversion Method ◽  
Diffraction Reflection ◽  
Traveltime Inversion ◽  
Wave Inversion ◽  
Full Wave

This paper presents a new traveltime inversion method based on the wave equation. In this new method, designated as wave‐equation traveltime inversion (WT), seismograms are computed by any full‐wave forward modeling method (we use a finite‐difference method). The velocity model is perturbed until the traveltimes from the synthetic seismograms are best fitted to the observed traveltimes in a least squares sense. A gradient optimization method is used and the formula for the Frechét derivative (perturbation of traveltimes with respect to velocity) is derived directly from the wave equation. No traveltime picking or ray tracing is necessary, and there are no high frequency assumptions about the data. Body wave, diffraction, reflection and head wave traveltimes can be incorporated into the inversion. In the high‐frequency limit, WT inversion reduces to ray‐based traveltime tomography. It can also be shown that WT inversion is approximately equivalent to full‐wave inversion when the starting velocity model is “close” to the actual model. Numerical simulations show that WT inversion succeeds for models with up to 80 percent velocity contrasts compared to the failure of full‐wave inversion for some models with no more than 10 percent velocity contrast. We also show that the WT method succeeds in inverting a layered velocity model where a shooting ray‐tracing method fails to compute the correct first arrival times. The disadvantage of the WT method is that it appears to provide less model resolution compared to full‐wave inversion, but this problem can be remedied by a hybrid traveltime + full‐wave inversion method (Luo and Schuster, 1989).

scholarly journals Wave-equation traveltime inversion with multifrequency bands: Synthetic and land data examples

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. B305-B315 ◽  
Author(s):  
Han Yu ◽  
Sherif M. Hanafy ◽  
Gerard T. Schuster
Keyword(s):  
Wave Equation ◽  
Velocity Model ◽  
Inversion Method ◽  
Data Sets ◽  
Traveltime Inversion ◽  
Numerical Tests ◽  
Classical Wave ◽  
Classical Wave Equation ◽  
Zero Offset ◽  
Starting Model

We have developed a wave-equation traveltime inversion method with multifrequency bands to invert for the shallow or intermediate subsurface velocity distribution. Similar to the classical wave-equation traveltime inversion, this method searches for the velocity model that minimizes the squared sum of the traveltime residuals using source wavelets with progressively higher peak frequencies. Wave-equation traveltime inversion can partially avoid the cycle-skipping problem by recovering the low-wavenumber parts of the velocity model. However, we also use the frequency information hidden in the traveltimes to obtain a more highly resolved tomogram. Therefore, we use different frequency bands when calculating the Fréchet derivatives so that tomograms with better resolution can be reconstructed. Results are validated by the zero-offset gathers from the raw data associated with moderate geometric irregularities. The improved wave-equation traveltime method is robust and merely needs a rough estimate of the starting model. Numerical tests on the synthetic and field data sets validate the above claims.

Acoustic wave‐equation traveltime and waveform inversion of crosshole seismic data

Geophysics ◽  
1995 ◽  
Vol 60 (3) ◽  
pp. 765-773 ◽  
Author(s):  
Changxi Zhou ◽  
Wenying Cai ◽  
Yi Luo ◽  
Gerard T. Schuster ◽  
Sia Hassanzadeh
Keyword(s):  
Wave Equation ◽  
Velocity Profile ◽  
Seismic Data ◽  
Structural Information ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Quality Data ◽  
Inversion Method ◽  
Wave Inversion ◽  
Full Wave

A hybrid wave‐equation traveltime and waveform inversion method is presented that reconstructs the interwell velocity distribution from crosshole seismic data. This inversion method, designated as WTW, retains the advantages of both full wave inversion and traveltime inversion; i.e., it is characterized by reasonably fast convergence which is somewhat independent of the initial model, and it can resolve detailed features of the velocity model. In principle, no traveltime picking is required and the computational cost of the WTW method is about the same as that for full wave inversion. We apply the WTW method to synthetic data and field crosshole data collected by Exxon at their Friendswood, Texas, test site. Results show that the WTW tomograms are much richer in structural information relative to the traveltime tomograms. Subtle structural features in the WTW Friendswood tomogram are resolved to a spatial resolution of about 1.5 m, yet are smeared or completely absent in the traveltime tomogram. This suggests that it might be better to obtain high quality (distinct reflections) crosshole data at intermediate frequencies, compared to intermediate quality data (good quality first arrivals, but the reflections are buried in noise) at high frequencies. Comparison of the reconstructed velocity profile with a log in the source well shows very good agreement within the 0–200 m interval. The 200–300 m interval shows acceptable agreement in the velocity fluctuations, but the tomogram’s velocity profile differs from the sonic log velocities by a DC shift. This highlights both the promise and the difficulty with the WTW method; it can reconstruct both the and high wavenumber parts of the model, but it can have difficulty recovering the very low wavenumber parts of the model.

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

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.

Traveltime information-based wave-equation inversion

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC27-WCC36 ◽  
Author(s):  
Yu Zhang ◽  
Daoliu Wang
Keyword(s):  
Wave Equation ◽  
Conventional Method ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Velocity Model ◽  
Data Fitting ◽  
Inversion Method ◽  
New Wave ◽  
Seismic Record

We propose a new wave-equation inversion method that mainly depends on the traveltime information of the recorded seismic data. Unlike the conventional method, we first apply a [Formula: see text] transform to the seismic data to form the delayed-shot seismic record, back propagate the transformed data, and then invert the velocity model by maximizing the wavefield energy around the shooting time at the source locations. Data fitting is not enforced during the inversion, so the optimized velocity model is obtained by best focusing the source energy after a back propagation. Therefore, inversion accuracy depends only on the traveltime information embedded in the seismic data. This method may overcome some practical issues of waveform inversion; in particular, it relaxes the dependency of the seismic data amplitudes and the source wavelet.

Two robust imaging methodologies for challenging environments: Wave-equation dispersion inversion of surface waves and guided waves and supervirtual interferometry + tomography for far-offset refractions

2018 ◽  
Vol 6 (4) ◽  
pp. SM27-SM37 ◽  
Author(s):  
Jing Li ◽  
Kai Lu ◽  
Sherif Hanafy ◽  
Gerard Schuster
Keyword(s):  
Wave Equation ◽  
Velocity Distribution ◽  
Surface Waves ◽  
Guided Waves ◽  
Velocity Model ◽  
Dispersion Curves ◽  
P Wave ◽  
Head Wave ◽  
Near Surface ◽  
Velocity Models

Two robust imaging technologies are reviewed that provide subsurface geologic information in challenging environments. The first one is wave-equation dispersion (WD) inversion of surface waves and guided waves (GW) for the shear-velocity (S-wave) and compressional-velocity (P-wave) models, respectively. The other method is traveltime inversion for the velocity model, in which supervirtual refraction interferometry (SVI) is used to enhance the signal-to-noise ratio of far-offset refractions. We have determined the benefits and liabilities of both methods with synthetic seismograms and field data. The benefits of WD are that (1) there is no layered-medium assumption, as there is in conventional inversion of dispersion curves. This means that 2D or 3D velocity models can be accurately estimated from data recorded by seismic surveys over rugged topography, and (2) WD mostly avoids getting stuck in local minima. The liability is that WD for surface waves is almost as expensive as full-waveform inversion (FWI) and, for Rayleigh waves, only recovers the S-velocity distribution to a depth no deeper than approximately 1/2 to 1/3 wavelength of the lowest-frequency surface wave. The limitation for GW is that, for now, it can estimate the P-velocity model by inverting the dispersion curves from GW propagating in near-surface low-velocity zones. Also, WD often requires user intervention to pick reliable dispersion curves. For SVI, the offset of usable refractions can be more than doubled, so that traveltime tomography can be used to estimate a much deeper model of the P-velocity distribution. This can provide a more effective starting velocity model for FWI. The liability is that SVI assumes head-wave first arrivals, not those from strong diving waves.

Frequency‐domain acoustic‐wave modeling and inversion of crosshole data: Part II—Inversion method, synthetic experiments and real‐data results

Geophysics ◽  
1995 ◽  
Vol 60 (3) ◽  
pp. 796-809 ◽  
Author(s):  
Zhong‐Min Song ◽  
Paul R. Williamson ◽  
R. Gerhard Pratt
Keyword(s):  
Frequency Domain ◽  
Real Data ◽  
Forward Modeling ◽  
Two Dimensions ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Data Set ◽  
Wave Inversion ◽  
Full Wave ◽  
And Inversion

In full‐wave inversion of seismic data in complex media it is desirable to use finite differences or finite elements for the forward modeling, but such methods are still prohibitively expensive when implemented in 3-D. Full‐wave 2-D inversion schemes are of limited utility even in 2-D media because they do not model 3-D dynamics correctly. Many seismic experiments effectively assume that the geology varies in two dimensions only but generate 3-D (point source) wavefields; that is, they are “two‐and‐one‐half‐dimensional” (2.5-D), and this configuration can be exploited to model 3-D propagation efficiently in such media. We propose a frequency domain full‐wave inversion algorithm which uses a 2.5-D finite difference forward modeling method. The calculated seismogram can be compared directly with real data, which allows the inversion to be iterated. We use a descents‐related method to minimize a least‐squares measure of the wavefield mismatch at the receivers. The acute nonlinearity caused by phase‐wrapping, which corresponds to time‐domain cycle‐skipping, is avoided by the strategy of either starting the inversion using a low frequency component of the data or constructing a starting model using traveltime tomography. The inversion proceeds by stages at successively higher frequencies across the observed bandwidth. The frequency domain is particularly efficient for crosshole configurations and also allows easy incorporation of attenuation, via complex velocities, in both forward modeling and inversion. This also requires the introduction of complex source amplitudes into the inversion as additional unknowns. Synthetic studies show that the iterative scheme enables us to achieve the theoretical maximum resolution for the velocity reconstruction and that strongly attenuative zones can be recovered with reasonable accuracy. Preliminary results from the application of the method to a real data set are also encouraging.

Generalization of traveltime inversion

Geophysics ◽  
1992 ◽  
Vol 57 (1) ◽  
pp. 9-14 ◽  
Author(s):  
Gérard C. Herman
Keyword(s):  
Time Windows ◽  
Velocity Model ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Error Norm ◽  
Arrival Times ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Use Of Data

A nonlinear inversion method is presented, especially suited for the determination of global velocity models. In a certain sense, it can be considered as a generalization of methods based on traveltimes of reflections, with the requirement of accurately having to determine traveltimes replaced by the (less stringent and less subjective) requirement of having to define time windows around main reflections (or composite reflections) of interest. It is based on an error norm, related to the phase of the wavefield, which is directly computed from wavefield measurements. Therefore, the cumbersome step of interpreting arrivals and measuring arrival times is avoided. The method is applied to the reconstruction of a depth‐dependent global velocity model from a set of plane‐wave responses and is compared to other methods. Despite the fact that the new error norm only makes use of data having a temporal bandwidth of a few Hz, its behavior is very similar to the behavior of the error norm used in traveltime inversion.

scholarly journals Sensitivity Analysis of FWI Applied to OVSP Synthetic Data for Fault Detection and Characterization in Crystalline Rocks

Geosciences ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 442
Author(s):  
Yassine Abdelfettah ◽  
Christophe Barnes
Keyword(s):  
Fault Detection ◽  
Reference Model ◽  
Synthetic Data ◽  
Inversion Method ◽  
Physical Parameters ◽  
Wave Inversion ◽  
Full Wave ◽  
Imaging Results ◽  
Antenna Length ◽  
Sensitivity Studies

We have performed several sensitivity studies to assess the ability of the Full Wave Inversion method to detect, delineate and characterize faults in a crystalline geothermal reservoir from OVSP data. The distant goal is to apply the method to the Soultz-sous-Forêts site (France). Our approach consists of performing synthetic Full Wave 2D Inversion experiments using offset vertical seismic and comparing the estimated fields provided by the inversion, i.e., the estimated underground images, to the initial reference model including the fault target. We first tuned the inversion algorithmic parameters in order to adapt the FWI software, originally dedicated to a sedimentary context, to a crystalline context. In a second step, we studied the sensitivity of the FWI fault imaging results as a function of the acquisition geometry parameters, namely, the number of shots, the intershot distance, the maximum offset and also the antenna length and well deviation. From this study, we suggest rules to design the acquisition geometry in order to improve the fault detection, delineation and characterization. In a third step, we studied the sensitivity of the FWI fault imaging results as a function of the fault or the fault zone characteristics, namely, the fault dip, thickness and the contrast of physical parameters between the fault materials and the surrounding fresh rocks. We have shown that a fault with high dip, between 60 and 90° as thin as 10 m (i.e. lower than a tenth of the seismic wavelength of 120 m for Vp and 70 m for Vs) can be imaged by FWI, even in the presence of additive gaussian noise. In summary, for a crystalline geological context, and dealing with acceptable S/N ratio data, the FWI show a high potential for accurately detecting, delineating and characterizing the fault zones.

Full-traveltime inversion

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. R261-R274 ◽  
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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