Target-oriented wave-equation inversion

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. A35-A38 ◽  
Author(s):  
Alejandro A. Valenciano ◽  
Biondo Biondi ◽  
Antoine Guitton
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Seismic Data ◽  
Hessian Matrix ◽  
Velocity Model ◽  
Complex Model ◽  
Inverse Filtering ◽  
Band Limited ◽  
Filtering Problem ◽  
Number Of Iterations

A target-oriented strategy can be applied to estimate a wave-equation least-squares inverse (LSI) image. By explicitly computing the wave-equation Hessian, the LSI image is obtained as the solution of a nonstationary least-squares inverse filtering problem. The rows of the Hessian are the nonstationary filters containing information about the acquisition geometry, the velocity model, and the band-limited characteristics of the seismic data. By exploiting the sparsity and the structure of the Hessian matrix, a large number of iterations, necessary to achieve convergence, can be computed cheaply. The results on a structurally complex model show the improvements of the LSI image versus the migrated image.

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.

scholarly journals Full waveform inversion of short-offset, band-limited seismic data inthe Alboran basin (SE Iberia)

2019 ◽  
Author(s):  
Clàudia Gras ◽  
Valentí Sallarès ◽  
Daniel Dagnino ◽  
C. Estela Jiménez ◽  
Adrià Meléndez ◽  
...  
Keyword(s):  
Travel Time ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Velocity Model ◽  
P Wave ◽  
Full Waveform Inversion ◽  
Time Inversion ◽  
Full Waveform ◽  
Travel Time Tomography ◽  
Band Limited

Abstract. We present a high-resolution P-wave velocity model of the sedimentary cover and the uppermost basement until ~ 3 km depth obtained by full-waveform inversion of multichannel seismic data acquired with a 6 km-long streamer in the Alboran Sea (SE Iberia). The inherent non-linearity of the method, especially for short-offset, band-limited seismic data as this one, is circumvented by applying a data processing/modeling sequence consisting of three steps: (1) data re-datuming by back-propagation of the recorded seismograms to the seafloor; (2) joint refraction and reflection travel-time tomography combining the original and the re-datumed shot gathers; and (3) FWI of the original shot gathers using the model obtained by travel-time tomography as initial reference. The final velocity model shows a number of geological structures that cannot be identified in the travel-time tomography models or easily interpreted from seismic reflection images alone. A sharp strong velocity contrast accurately defines the geometry of the top of the basement. Several low-velocity zones that may correspond to the abrupt velocity change across steeply dipping normal faults are observed at the flanks of the basin. A 200–300 m thick, high-velocity layer embedded within lower velocity sediment may correspond to evaporites deposited during the Messinian crisis. The results confirm that the combination of data re-datuming and joint refraction and reflection travel-time inversion provides reference models that are accurate enough to apply full-waveform inversion to relatively short offset streamer data in deep water settings starting at field-data standard low frequency content of 6 Hz.

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.

Case Study: Improving the quality of the seismic reflection image for a Fujian mineral exploration data set with offset-domain common-image gathers

Geophysics ◽  
2021 ◽  
pp. 1-45
Author(s):  
Guofeng Liu ◽  
Xiaohong Meng ◽  
Johanes Gedo Sea
Keyword(s):  
Wave Equation ◽  
Image Quality ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Mineral Exploration ◽  
Velocity Model ◽  
Image Point ◽  
Single Shot ◽  
Data Set ◽  
Depth Migration

Seismic reflection is a proven and effective method commonly used during the exploration of deep mineral deposits in Fujian, China. In seismic data processing, rugged depth migration based on wave-equation migration can play a key role in handling surface fluctuations and complex underground structures. Because wave-equation migration in the shot domain cannot output offset-domain common-image gathers in a straightforward way, the use of traditional tools for updating the velocity model and improving image quality can be quite challenging. To overcome this problem, we employed the attribute migration method. This worked by sorting the migrated stack results for every single-shot gather into the offset gathers. The value of the offset that corresponded to each image point was obtained from the ratio of the original migration results to the offset-modulated shot-data migration results. A Gaussian function was proposed to map every image point to a certain range of offsets. This helped improve the signal-to-noise ratio, which was especially important in handing low quality seismic data obtained during mineral exploration. Residual velocity analysis was applied to these gathers to update the velocity model and improve image quality. The offset-domain common-image gathers were also used directly for real mineral exploration seismic data with rugged depth migration. After several iterations of migration and updating the velocity, the proposed procedure achieved an image quality better than the one obtained with the initial velocity model. The results can help with the interpretation of thrust faults and deep deposit exploration.

scholarly journals Mitigation of defocusing by statics and near-surface velocity errors by interferometric least-squares migration with a reference datum

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. S195-S206 ◽  
Author(s):  
Mrinal Sinha ◽  
Gerard T. Schuster
Keyword(s):  
Least Squares ◽  
Prior Knowledge ◽  
Seismic Data ◽  
Field Data ◽  
Velocity Model ◽  
Well Logs ◽  
Surface Velocity ◽  
Near Surface ◽  
Reference Layer ◽  
Least Squares Migration

Imaging seismic data with an erroneous migration velocity can lead to defocused migration images. To mitigate this problem, we first choose a reference reflector whose topography is well-known from the well logs, for example. Reflections from this reference layer are correlated with the traces associated with reflections from deeper interfaces to get crosscorrelograms. Interferometric least-squares migration (ILSM) is then used to get the migration image that maximizes the crosscorrelation between the observed and the predicted crosscorrelograms. Deeper reference reflectors are used to image deeper parts of the subsurface with a greater accuracy. Results on synthetic and field data show that defocusing caused by velocity errors is largely suppressed by ILSM. We have also determined that ILSM can be used for 4D surveys in which environmental conditions and acquisition parameters are significantly different from one survey to the next. The limitations of ILSM are that it requires prior knowledge of a reference reflector in the subsurface and the velocity model below the reference reflector should be accurate.

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 Ray-tracing traveltime tomography versus wave-equation traveltime inversion for near-surface seismic land data

2017 ◽  
Vol 5 (3) ◽  
pp. SO11-SO19
Author(s):  
Lei Fu ◽  
Sherif M. Hanafy
Keyword(s):  
Wave Equation ◽  
Ray Tracing ◽  
Water Table ◽  
Seismic Data ◽  
Velocity Model ◽  
Water Table Depth ◽  
Seismic Survey ◽  
Near Surface ◽  
Traveltime Tomography ◽  
Initial Starting

Full-waveform inversion of land seismic data tends to get stuck in a local minimum associated with the waveform misfit function. This problem can be partly mitigated by using an initial velocity model that is close to the true velocity model. This initial starting model can be obtained by inverting traveltimes with ray-tracing traveltime tomography (RT) or wave-equation traveltime (WT) inversion. We have found that WT can provide a more accurate tomogram than RT by inverting the first-arrival traveltimes, and empirical tests suggest that RT is more sensitive to the additive noise in the input data than WT. We present two examples of applying WT and RT to land seismic data acquired in western Saudi Arabia. One of the seismic experiments investigated the water-table depth, and the other one attempted to detect the location of a buried fault. The seismic land data were inverted by WT and RT to generate the P-velocity tomograms, from which we can clearly identify the water table depth along the seismic survey line in the first example and the fault location in the second example.

Elastic least-squares reverse time migration in vertical transverse isotropic media

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S539-S553 ◽  
Author(s):  
Jidong Yang ◽  
Hejun Zhu ◽  
George McMechan ◽  
Houzhu Zhang ◽  
Yang Zhao
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Transversely Isotropic ◽  
Image Resolution ◽  
Total Variation Regularization ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Isotropic Media ◽  
Band Limited

Using adjoint-based elastic reverse time migration, it is difficult to produce high-quality reflectivity images due to the limited acquisition apertures, band-limited source time function, and irregular subsurface illumination. Through iteratively computing the Hessian inverse, least-squares migration enables us to reduce the point-spread-function effects and improve the image resolution and amplitude fidelity. By incorporating anisotropy in the 2D elastic wave equation, we have developed an elastic least-squares reverse time migration (LSRTM) method for multicomponent data from the vertically transversely isotropic (VTI) media. Using the perturbed stiffness parameters [Formula: see text] and [Formula: see text] as PP and PS reflectivities, we linearize the elastic VTI wave equation and obtain a Born modeling (demigration) operator. Then, we use the Lagrange multiplier method to derive the corresponding adjoint wave equation and reflectivity kernels. With linearized forward modeling and adjoint migration operators, we solve a linear inverse problem to estimate the subsurface reflectivity models for [Formula: see text] and [Formula: see text]. To reduce the artifacts caused by data over-fitting, we introduce total-variation regularization into the reflectivity inversion, which promotes a sparse solution in terms of the model derivatives. To accelerate the convergence of LSRTM, we use source illumination to approximate the diagonal Hessian and use it as a preconditioner for the misfit gradient. Numerical examples help us determine that our elastic VTI LSRTM method can improve the spatial resolution and amplitude fidelity in comparison to adjoint migration.

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.

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