Ray illumination compensation for adjoint-state first-arrival traveltime tomography

Geophysics ◽  
2021 ◽  
pp. 1-43
Author(s):  
Jiangtao Hu ◽  
Jianliang Qian ◽  
Junxing Cao ◽  
Xingjian Wang ◽  
Huazhong Wang ◽  
...  
Keyword(s):  
Velocity Model ◽  
State Equation ◽  
Surface Velocity ◽  
Illumination Compensation ◽  
Traveltime Tomography ◽  
Velocity Models ◽  
Source Point ◽  
Gradient Direction ◽  
Adjoint State ◽  
First Arrival

First-arrival traveltime tomography is an essential method for obtaining near-surface velocity models. The adjoint-state first-arrival traveltime tomography is appealing due to its straightforward implementation, low computational cost, and low memory consumption. Because solving the point-source isotropic eikonal equation by either ray tracers or eikonal solvers intrinsically corresponds to emanating discrete rays from the source point, the resulting traveltime gradient is singular at the source point, and we denote such a singular pattern the imprint of ray illumination. Because the adjoint-state equation propagates traveltime residuals back to the source point according to the negative traveltime gradient, the resulting adjoint state will inherit such an imprint of ray illumination, leading to singular gradient descent directions when updating the velocity model in the adjoint-state traveltime tomography. To mitigate this imprint, we propose to solve the adjoint-state equation twice but with different boundary conditions: one being taken to be regular data residuals, and the other taken to be ones uniformly, so that we are able to use the latter adjoint state to normalize the regular one and we further use the normalized quantity to serve as the gradient direction to update the velocity model; we call this process the ray-illumination compensation. To overcome the issue of limited aperture, we propose a spatially varying regularization method to stabilize the new gradient direction. A synthetic example demonstrates that the proposed method is able to mitigate the imprint of ray illumination, remove the footprint effect near source points, and provide uniform velocity updates along ray paths. A complex example extracted from the Marmousi2 model and a migration example illustrate that the new method accurately recovers the velocity model, and an offset-dependent inversion strategy can further improve the quality of recovered velocity models.

Joint refraction traveltime tomography and migration for multilayer near-surface imaging

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. U31-U43
Author(s):  
Yihao Wang ◽  
Jie Zhang
Keyword(s):  
High Velocity ◽  
Velocity Structure ◽  
Joint Inversion ◽  
Velocity Model ◽  
Surface Velocity ◽  
Inversion Method ◽  
Near Surface ◽  
Traveltime Tomography ◽  
First Arrival ◽  
Migration Method

In near-surface velocity structure estimation, first-arrival traveltime tomography tends to produce a smooth velocity model. If the shallow structures include a weathering layer over high-velocity bedrock, first-arrival traveltime tomography may fail to recover the sharp interface. However, with the same traveltime data, refraction traveltime migration proves to be an effective tool for accurately mapping the refractor. The approach downward continues the refraction traveltime curves and produces an image (position) of the refractor for a given overburden velocity model. We first assess the validity of the refraction traveltime migration method and analyze its uncertainties with a simple model. We then develop a multilayer refraction traveltime migration method and apply the migration image to constrain traveltime tomographic inversion by imposing discontinuities at the refraction interfaces in model regularization. In each subsequent iteration, the shape of the migrated refractors and the velocity model are simultaneously updated. The synthetic tests indicate that the joint inversion method performs better than the conventional first-arrival traveltime tomography method with Tikhonov regularization and the delay-time method in reconstructing near-surface models with high-velocity contrasts. In application to field data, this method produces a more accurately resolved velocity model, which improves the quality of common midpoint stacking by making long-wavelength static corrections.

Waveform tomography of field vibroseis data using an approximate 2D geometry leads to improved velocity models

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. R33-R43 ◽  
Author(s):  
Brendan R. Smithyman ◽  
Ronald M. Clowes
Keyword(s):  
Waveform Inversion ◽  
Velocity Model ◽  
Surface Velocity ◽  
Time Shift ◽  
Full Waveform Inversion ◽  
Near Surface ◽  
Traveltime Tomography ◽  
Full Waveform ◽  
First Arrival ◽  
Waveform Tomography

Waveform tomography, a combination of traveltime tomography (or inversion) and waveform inversion, is applied to vibroseis first-arrival data to generate an interpretable model of P-wave velocity for a site in the Nechako Basin, south-central British Columbia, Canada. We use constrained 3D traveltime inversion followed by 2D full-waveform inversion to process long-offset (14.4 km) first-arrival refraction waveforms, resulting in a velocity model of significantly higher detail than a conventional refraction-statics model generated for a processing workflow. The crooked-line acquisition of the data set makes 2D full-waveform inversion difficult. Thus, a procedure that improves the tractability of waveform tomography processing of vibroseis data recorded on crooked roads is developed to generate a near-surface ([Formula: see text]) velocity model for the study area. The data waveforms are first static corrected using a time shift determined by 3D raytracing, which accounts for the crossline offsets produced by the crooked-line acquisition. The velocity model generated from waveform tomography exhibits substantial improvement when compared with a conventional refraction-statics model. It also shows improved resolution of sharp discontinuities and low-velocity regions when compared to the model from traveltime tomography alone, especially in regions where the geometry errors are moderate. Interpretation of the near-surface velocity model indicates possible subbasins in the Nechako Basin and delineates the Eocene volcanic rocks of the study area. This approach limits the ability of the full-waveform inversion to fit some propagation modes; however, the tractability of the inversion in the near-surface region is improved. This new development is especially useful in studies that do not warrant 3D seismic acquisition and processing.

Tomographic velocity model building of the near surface with velocity-inversion interfaces: A test using the Yilmaz model

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. U39-U47 ◽  
Author(s):  
Hui Liu ◽  
Hua-wei Zhou ◽  
Wenge Liu ◽  
Peiming Li ◽  
Zhihui Zou
Keyword(s):  
Model Building ◽  
Velocity Model ◽  
Surface Velocity ◽  
Low Velocity ◽  
Near Surface ◽  
Velocity Inversion ◽  
Velocity Models ◽  
Velocity Model Building ◽  
First Arrival ◽  
The Impact

First-arrival traveltime tomography is a popular approach to building the near-surface velocity models for oil and gas exploration, mining, geoengineering, and environmental studies. However, the presence of velocity-inversion interfaces (VIIs), across which the overlying velocity is higher than the underlying velocity, might corrupt the tomographic solutions. This is because most first-arrival raypaths will not traverse along any VII, such as the top of a low-velocity zone. We have examined the impact of VIIs on first-arrival tomographic velocity model building of the near surface using a synthetic near-surface velocity model. This examination confirms the severe impact of VIIs on first-arrival tomography. When the source-to-receiver offset is greater than the lateral extent of the VIIs, good near-surface velocity models can still be established using a multiscale deformable-layer tomography (DLT), which uses a layer-based model parameterization and a multiscale scheme as regularization. Compared with the results from a commercial grid-based tomography, the DLT delivers much better near-surface statics solutions and less error in the images of deep reflectors.

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.

First-arrival traveltime tomography based on the adjoint-state method

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCB1-WCB10 ◽  
Author(s):  
Cédric Taillandier ◽  
Mark Noble ◽  
Hervé Chauris ◽  
Henri Calandra
Keyword(s):  
Synthetic Data ◽  
Point Of View ◽  
Data Set ◽  
Near Surface ◽  
Traveltime Tomography ◽  
Adjoint State ◽  
Gradient Based ◽  
First Arrival ◽  
State Method ◽  
Adjoint State Method

Classical algorithms used for traveltime tomography are not necessarily well suited for handling very large seismic data sets or for taking advantage of current supercomputers. The classical approach of first-arrival traveltime tomography was revisited with the proposal of a simple gradient-based approach that avoids ray tracing and estimation of the Fréchet derivative matrix. The key point becomes the derivation of the gradient of the misfit function obtained by the adjoint-state technique. The adjoint-state method is very attractive from a numerical point of view because the associated cost is equivalent to the solution of the forward-modeling problem, whatever the size of the input data and the number of unknown velocity parameters. An application on a 2D synthetic data set demonstrated the ability of the algorithm to image near-surface velocities with strong vertical and lateral variations and revealed the potential of the method.

A robust first-arrival picking workflow using convolutional and recurrent neural networks

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. U109-U119
Author(s):  
Pengyu Yuan ◽  
Shirui Wang ◽  
Wenyi Hu ◽  
Xuqing Wu ◽  
Jiefu Chen ◽  
...  
Keyword(s):  
Deep Learning ◽  
Model Building ◽  
Signal To Noise Ratio ◽  
Synthetic Data ◽  
Velocity Model ◽  
Surface Velocity ◽  
Data Sets ◽  
Near Surface ◽  
Segmentation Boundary ◽  
First Arrival

A deep-learning-based workflow is proposed in this paper to solve the first-arrival picking problem for near-surface velocity model building. Traditional methods, such as the short-term average/long-term average method, perform poorly when the signal-to-noise ratio is low or near-surface geologic structures are complex. This challenging task is formulated as a segmentation problem accompanied by a novel postprocessing approach to identify pickings along the segmentation boundary. The workflow includes three parts: a deep U-net for segmentation, a recurrent neural network (RNN) for picking, and a weight adaptation approach to be generalized for new data sets. In particular, we have evaluated the importance of selecting a proper loss function for training the network. Instead of taking an end-to-end approach to solve the picking problem, we emphasize the performance gain obtained by using an RNN to optimize the picking. Finally, we adopt a simple transfer learning scheme and test its robustness via a weight adaptation approach to maintain the picking performance on new data sets. Our tests on synthetic data sets reveal the advantage of our workflow compared with existing deep-learning methods that focus only on segmentation performance. Our tests on field data sets illustrate that a good postprocessing picking step is essential for correcting the segmentation errors and that the overall workflow is efficient in minimizing human interventions for the first-arrival picking task.

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

Geophysics ◽  
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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