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.

Waveform inversion using a back-propagation algorithm and a Huber function norm

Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. R15-R24 ◽  
Author(s):  
Taeyoung Ha ◽  
Wookeen Chung ◽  
Changsoo Shin
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Least Squares Method ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Velocity Model ◽  
Back Propagation Algorithm ◽  
Inversion Algorithm ◽  
Coherent Noise ◽  
Complex Valued

Waveform inversion faces difficulties when applied to real seismic data, including the existence of many kinds of noise. The [Formula: see text]-norm is more robust to noise with outliers than the least-squares method. Nevertheless, the least-squares method is preferred as an objective function in many algorithms because the gradient of the [Formula: see text]-norm has a singularity when the residual becomes zero. We propose a complex-valued Huber function for frequency-domain waveform inversion that combines the [Formula: see text]-norm (for small residuals) with the [Formula: see text]-norm (for large residuals). We also derive a discretized formula for the gradient of the Huber function. Through numerical tests on simple synthetic models and Marmousi data, we find the Huber function is more robust to outliers and coherent noise. We apply our waveform-inversion algorithm to field data taken from the continental shelf under the East Sea in Korea. In this setting, we obtain a velocity model whose synthetic shot profiles are similar to the real seismic data.

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.

scholarly journals Elastic envelope inversion using multicomponent seismic data without low frequency

2014 ◽  
Vol 1 (2) ◽  
pp. 1757-1802
Author(s):  
C. Huang ◽  
L. Dong ◽  
Y. Liu ◽  
B. Chi
Keyword(s):  
Seismic Data ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Low Frequency ◽  
Velocity Model ◽  
Inversion Method ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Full Waveform ◽  
Multicomponent Data

Abstract. Low frequency is a key issue to reduce the nonlinearity of elastic full waveform inversion. Hence, the lack of low frequency in recorded seismic data is one of the most challenging problems in elastic full waveform inversion. Theoretical derivations and numerical analysis are presented in this paper to show that envelope operator can retrieve strong low frequency modulation signal demodulated in multicomponent data, no matter what the frequency bands of the data is. With the benefit of such low frequency information, we use elastic envelope of multicomponent data to construct the objective function and present an elastic envelope inversion method to recover the long-wavelength components of the subsurface model, especially for the S-wave velocity model. Numerical tests using synthetic data for the Marmousi-II model prove the effectiveness of the proposed elastic envelope inversion method, especially when low frequency is missing in multicomponent data and when initial model is far from the true model. The elastic envelope can reduce the nonlinearity of inversion and can provide an excellent starting model.

scholarly journals Seismic inversion by Newtonian machine learning

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. WA185-WA200
Author(s):  
Yuqing Chen ◽  
Gerard T. Schuster
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Wave Equation ◽  
Seismic Data ◽  
Velocity Model ◽  
Seismic Inversion ◽  
Low Rank ◽  
Inversion Method ◽  
Model Parameters ◽  
Latent Space

We present a wave-equation inversion method that inverts skeletonized seismic data for the subsurface velocity model. The skeletonized representation of the seismic traces consists of the low-rank latent-space variables predicted by a well-trained autoencoder neural network. The input to the autoencoder consists of seismic traces, and the implicit function theorem is used to determine the Fréchet derivative, i.e., the perturbation of the skeletonized data with respect to the velocity perturbation. The gradient is computed by migrating the shifted observed traces weighted by the skeletonized data residual, and the final velocity model is the one that best predicts the observed latent-space parameters. We denote this as inversion by Newtonian machine learning (NML) because it inverts for the model parameters by combining the forward and backward modeling of Newtonian wave propagation with the dimensional reduction capability of machine learning. Empirical results suggest that inversion by NML can sometimes mitigate the cycle-skipping problem of conventional full-waveform inversion (FWI). Numerical tests with synthetic and field data demonstrate the success of NML inversion in recovering a low-wavenumber approximation to the subsurface velocity model. The advantage of this method over other skeletonized data methods is that no manual picking of important features is required because the skeletal data are automatically selected by the autoencoder. The disadvantage is that the inverted velocity model has less resolution compared with the FWI result, but it can serve as a good initial model for FWI. Our most significant contribution is that we provide a general framework for using wave-equation inversion to invert skeletal data generated by any type of neural network. In other words, we have combined the deterministic modeling of Newtonian physics and the pattern matching capabilities of machine learning to invert seismic data by NML.

scholarly journals 3D wave-equation dispersion inversion of Rayleigh waves

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R673-R691 ◽  
Author(s):  
Zhaolun Liu ◽  
Jing Li ◽  
Sherif M. Hanafy ◽  
Gerard Schuster
Keyword(s):  
Wave Equation ◽  
Wave Velocity ◽  
Rayleigh Waves ◽  
Waveform Inversion ◽  
Shear Velocity ◽  
Velocity Model ◽  
Azimuth Angle ◽  
Inversion Method ◽  
S Wave ◽  
Starting Model

The 2D wave-equation dispersion (WD) inversion method is extended to 3D wave-equation dispersion inversion of surface waves for the shear-velocity distribution. The objective function of 3D WD is the frequency summation of the squared wavenumber [Formula: see text] differences along each azimuth angle of the fundamental or higher modes of Rayleigh waves in each shot gather. The S-wave velocity model is updated by the weighted zero-lag crosscorrelation between the weighted source-side wavefield and the back-projected receiver-side wavefield for each azimuth angle. A multiscale 3D WD strategy is provided, which starts from the pseudo-1D S-velocity model, which is then used to get the 2D WD tomogram, which in turn is used as the starting model for 3D WD. The synthetic and field data examples demonstrate that 3D WD can accurately reconstruct the 3D S-wave velocity model of a laterally heterogeneous medium and has much less of a tendency to getting stuck in a local minimum compared with full-waveform inversion.

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.

scholarly journals Full-Waveform Inversion for Imaging Faulted Structures: A Case Study from the Japan Trench Forearc Slope

2021 ◽  
Author(s):  
Ehsan Jamali Hondori ◽  
Chen Guo ◽  
Hitoshi Mikada ◽  
Jin-Oh Park
Keyword(s):  
Seismic Data ◽  
Initial Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Control Measures ◽  
Japan Trench ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Time Migration ◽  
Shallow Sediments

AbstractFull-waveform inversion (FWI) of limited-offset marine seismic data is a challenging task due to the lack of refracted energy and diving waves from the shallow sediments, which are fundamentally required to update the long-wavelength background velocity model in a tomographic fashion. When these events are absent, a reliable initial velocity model is necessary to ensure that the observed and simulated waveforms kinematically fit within an error of less than half a wavelength to protect the FWI iterative local optimization scheme from cycle skipping. We use a migration-based velocity analysis (MVA) method, including a combination of the layer-stripping approach and iterations of Kirchhoff prestack depth migration (KPSDM), to build an accurate initial velocity model for the FWI application on 2D seismic data with a maximum offset of 5.8 km. The data are acquired in the Japan Trench subduction zone, and we focus on the area where the shallow sediments overlying a highly reflective basement on top of the Cretaceous erosional unconformity are severely faulted and deformed. Despite the limited offsets available in the seismic data, our carefully designed workflow for data preconditioning, initial model building, and waveform inversion provides a velocity model that could improve the depth images down to almost 3.5 km. We present several quality control measures to assess the reliability of the resulting FWI model, including ray path illuminations, sensitivity kernels, reverse time migration (RTM) images, and KPSDM common image gathers. A direct comparison between the FWI and MVA velocity profiles reveals a sharp boundary at the Cretaceous basement interface, a feature that could not be observed in the MVA velocity model. The normal faults caused by the basal erosion of the upper plate in the study area reach the seafloor with evident subsidence of the shallow strata, implying that the faults are active.

scholarly journals Refraction tomography using a waveform-inversion back-propagation technique

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. R21-R30 ◽  
Author(s):  
Dong-Joo Min ◽  
Changsoo Shin
Keyword(s):  
Wave Equation ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Angular Frequency ◽  
Damping Factor ◽  
Traveltime Tomography ◽  
Refraction Tomography ◽  
First Arrival ◽  
Propagation Technique ◽  
Tomography Method

One of the applications of refraction-traveltime tomography is to provide an initial model for waveform inversion and Kirchhoff prestack migration. For such applications, we need a refraction-traveltime tomography method that is robust for complicated and high-velocity-contrast models. Of the many refraction-traveltime tomography methods available, we believe wave-based algorithms to be best suited for dealing with complicated models. We developed a new wave-based, refraction-tomography algorithm using a damped wave equation and a waveform-inversion back-propagation technique. The imaginary part of a complex angular frequency, which is generally introduced in frequency-domain wave modeling, acts as a damping factor. By choosing an optimal damping factor from the numerical-dispersion relation, we can suppress the wavetrains following the first arrival. The objective function of our algorithm consists of residuals between the respective phases of first arrivals in field data and in forward-modeled data. The model-response, first-arrival phases can be obtained by taking the natural logarithm of damped wavefields at a single frequency low enough to yield unwrapped phases, whereas field-data phases are generated by multiplying picked first-arrival traveltimes by the same angular frequency used to compute model-response phases. To compute the steepest-descent direction, we apply a waveform-inversion back-propagation algorithm based on the symmetry of the Green’s function for the wave equation (i.e., the adjoint state of the wave equation), allowing us to avoid directly computing and saving sensitivities (Fréchet derivatives). From numerical examples of a block-anomaly model and the Marmousi-2 model, we confirm that traveltimes computed from a damped monochromatic wavefield are compatible with those picked from synthetic data, and our refraction-tomography method can provide initial models for Kirchhoff prestack depth migration.

scholarly journals Passive seismic event estimation using multiscattering waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. KS59-KS69 ◽  
Author(s):  
Chao Song ◽  
Zedong Wu ◽  
Tariq Alkhalifah
Keyword(s):  
Seismic Data ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Source Image ◽  
Time Inversion ◽  
Multiple Sources ◽  
Origin Time ◽  
Secondary Sources ◽  
Velocity Models ◽  
Passive Seismic

Passive seismic monitoring has become an effective method to understand underground processes. Time-reversal-based methods are often used to locate passive seismic events directly. However, these kinds of methods are strongly dependent on the accuracy of the velocity model. Full-waveform inversion (FWI) has been used on passive seismic data to invert the velocity model and source image, simultaneously. However, waveform inversion of passive seismic data uses mainly the transmission energy, which results in poor illumination and low resolution. We developed a waveform inversion using multiscattered energy for passive seismic to extract more information from the data than conventional FWI. Using transmission wavepath information from single- and double-scattering, computed from a predicted scatterer field acting as secondary sources, our method provides better illumination of the velocity model than conventional FWI. Using a new objective function, we optimized the source image and velocity model, including multiscattered energy, simultaneously. Because we conducted our method in the frequency domain with a complex source function including spatial and wavelet information, we mitigate the uncertainties of the source wavelet and source origin time. Inversion results from the Marmousi model indicate that by taking advantage of multiscattered energy and starting from a reasonably acceptable frequency (a single source at 3 Hz and multiple sources at 5 Hz), our method yields better inverted velocity models and source images compared with conventional FWI.

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