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.

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.

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).

A reality check on full-wave inversion applied to land seismic data for near-surface modeling

2022 ◽  
Vol 41 (1) ◽  
pp. 40-46
Author(s):  
Öz Yilmaz ◽  
Kai Gao ◽  
Milos Delic ◽  
Jianghai Xia ◽  
Lianjie Huang ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Seismic Data ◽  
Surface Modeling ◽  
P Wave ◽  
Borehole Data ◽  
Near Surface ◽  
Traveltime Tomography ◽  
Wave Inversion ◽  
Full Wave ◽  
Elastic Inversion

We evaluate the performance of traveltime tomography and full-wave inversion (FWI) for near-surface modeling using the data from a shallow seismic field experiment. Eight boreholes up to 20-m depth have been drilled along the seismic line traverse to verify the accuracy of the P-wave velocity-depth model estimated by seismic inversion. The velocity-depth model of the soil column estimated by traveltime tomography is in good agreement with the borehole data. We used the traveltime tomography model as an initial model and performed FWI. Full-wave acoustic and elastic inversions, however, have failed to converge to a velocity-depth model that desirably should be a high-resolution version of the model estimated by traveltime tomography. Moreover, there are significant discrepancies between the estimated models and the borehole data. It is understandable why full-wave acoustic inversion would fail — land seismic data inherently are elastic wavefields. The question is: Why does full-wave elastic inversion also fail? The strategy to prevent full-wave elastic inversion of vertical-component geophone data trapped in a local minimum that results in a physically implausible near-surface model may be cascaded inversion. Specifically, we perform traveltime tomography to estimate a P-wave velocity-depth model for the near-surface and Rayleigh-wave inversion to estimate an S-wave velocity-depth model for the near-surface, then use the resulting pairs of models as the initial models for the subsequent full-wave elastic inversion. Nonetheless, as demonstrated by the field data example here, the elastic-wave inversion yields a near-surface solution that still is not in agreement with the borehole data. Here, we investigate the limitations of FWI applied to land seismic data for near-surface modeling.

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.

Comparison of source-independent methods of elastic waveform inversion

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. R91-R100 ◽  
Author(s):  
Kun Xu ◽  
Stewart A. Greenhalgh ◽  
MiaoYue Wang
Keyword(s):  
Elastic Wave ◽  
Frequency Domain ◽  
Numerical Experiments ◽  
Random Noise ◽  
Waveform Inversion ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Practical Procedure ◽  
Wave Inversion ◽  
Full Waveform

In this paper, we investigate several source-independent methods of nonlinear full-waveform inversion of multicomponent elastic-wave data. This includes iterative estimation of source signature (IES), standard trace normalization (STN), and average trace normalization (ATN) inversion methods. All are based on the finite-element method in the frequency domain. One synthetic elastic crosshole model is used to compare the recovered images with all these methods as well as the known source signature (KSS) inversion method. The numerical experiments show that the IES method is superior to both STN and ATN methods in two-component, elastic-wave inversion in the frequency domain when the source signature is unknown. The STN and ATN methods have limitations associated with near-zero amplitudes (or polarity reversals) in traces from one of the components, which destroy the energy balance in the normalized traces and cause a loss of frequency information. But the ATN method is somewhat superior to the STN method in suppressing random noise and improving stability, as the developed formulas and the numerical experiments show. We suggest the IES method as a practical procedure for multicomponent seismic inversion.

scholarly journals Direct micro-seismic event location and characterization from passive seismic data using convolutional neural networks

Geophysics ◽  
2021 ◽  
pp. 1-77
Author(s):  
Hanchen Wang ◽  
Tariq Alkhalifah
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Convolutional Neural Networks ◽  
Event Detection ◽  
Seismic Data ◽  
High Performance ◽  
Input Data ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Seismic Events

The ample size of time-lapse data often requires significant event detection and source location efforts, especially in areas like shale gas exploration regions where a large number of micro-seismic events are often recorded. In many cases, the real-time monitoring and locating of these events are essential to production decisions. Conventional methods face considerable drawbacks. For example, traveltime-based methods require traveltime picking of often noisy data, while migration and waveform inversion methods require expensive wavefield solutions and event detection. Both tasks require some human intervention, and this becomes a big problem when too many sources need to be located, which is common in micro-seismic monitoring. Machine learning has recently been used to identify micro-seismic events or locate their sources once they are identified and picked. We propose to use a novel artificial neural network framework to directly map seismic data, without any event picking or detection, to their potential source locations. We train two convolutional neural networks on labeled synthetic acoustic data containing simulated micro-seismic events to fulfill such requirements. One convolutional neural network, which has a global average pooling layer to reduce the computational cost while maintaining high-performance levels, aims to classify the number of events in the data. The other network predicts the source locations and other source features such as the source peak frequencies and amplitudes. To reduce the size of the input data to the network, we correlate the recorded traces with a central reference trace to allow the network to focus on the curvature of the input data near the zero-lag region. We train the networks to handle single, multi, and no event segments extracted from the data. Tests on a simple vertical varying model and a more realistic Otway field model demonstrate the approach's versatility and potential.

scholarly journals A GPU implementation of the second order adjoint state theory to quantify the uncertainty on FWI results

2018 ◽  
Vol 8 (2) ◽  
Author(s):  
Sergio Alberto Abreo ◽  
Ana Beatríz Ramírez- Silva ◽  
Oscar Mauricio Reyes- Torres
Keyword(s):  
Wave Equation ◽  
Probability Distribution ◽  
Hessian Matrix ◽  
Waveform Inversion ◽  
Computational Cost ◽  
State Theory ◽  
Second Order ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Adjoint State

The second order scattering information provided by the Hessian matrix and its inverse plays an important role in both, parametric inversion and uncertainty quantification. On the one hand, for parameter inversion, the Hessian guides the descent direction such that the cost function minimum is reached with less iterations. On the other hand, it provides a posteriori information of the probability distribution of the parameters obtained after full waveform inversion, as a function of the a priori probability distribution information. Nevertheless, the computational cost of the Hessian matrix represents the main obstacle in the state-of-the-art for practical use of this matrix from synthetic or real data. The second order adjoint state theory provides a strategy to compute the exact Hessian matrix, reducing its computational cost, because every column of the matrix can be obtained by performing two forward and two backward propagations. In this paper, we first describe an approach to compute the exact Hessian matrix for the acoustic wave equation with constant density. We then provide an analysis of the use of the Hessian matrix for uncertainty quantification of the full waveform inversion of the velocity model for a synthetic example, using the 2D acoustic and isotropic wave equation operator in time.

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.

scholarly journals Accelerating numerical wave propagation by wavefield adapted meshes. Part II: full-waveform inversion

2020 ◽  
Vol 221 (3) ◽  
pp. 1591-1604 ◽  
Author(s):  
Solvi Thrastarson ◽  
Martin van Driel ◽  
Lion Krischer ◽  
Christian Boehm ◽  
Michael Afanasiev ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Spectral Element ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Order Of Magnitude ◽  
Numerical Wave ◽  
Expected Complexity

SUMMARY We present a novel full-waveform inversion (FWI) approach which can reduce the computational cost by up to an order of magnitude compared to conventional approaches, provided that variations in medium properties are sufficiently smooth. Our method is based on the usage of wavefield adapted meshes which accelerate the forward and adjoint wavefield simulations. By adapting the mesh to the expected complexity and smoothness of the wavefield, the number of elements needed to discretize the wave equation can be greatly reduced. This leads to spectral-element meshes which are optimally tailored to source locations and medium complexity. We demonstrate a workflow which opens up the possibility to use these meshes in FWI and show the computational advantages of the approach. We provide examples in 2-D and 3-D to illustrate the concept, describe how the new workflow deviates from the standard FWI workflow, and explain the additional steps in detail.

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