Tomographic inversion by matrix transformation

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE35-VE38 ◽  
Author(s):  
Jonathan Liu ◽  
Lorie Bear ◽  
Jerry Krebs ◽  
Raffaella Montelli ◽  
Gopal Palacharla
Keyword(s):  
Linear System ◽  
Seismic Velocity ◽  
Synthetic Data ◽  
Velocity Model ◽  
Matrix Transformation ◽  
Uniform Grid ◽  
Complex Structures ◽  
Tomographic Inversion ◽  
Velocity Models ◽  
The Stability

We have developed a new method to build seismic velocity models for complex structures. In our approach, we use a spatially nonuniform parameterization of the velocity model in tomography and a uniform grid representation of the same velocity model in ray tracing to generate the linear system of tomographic equations. Subsequently, a matrix transformation is applied to the system of equations to produce a new linear system of tomographic equations using nonuniform parameterization. In this way, we improved the stability of tomographic inversion without adding computing costs. We tested the effectiveness of our process on a 3D synthetic data example.

High-resolution seismic velocity analysis by sign-based weighted semblance

Geophysics ◽  
2021 ◽  
pp. 1-35
Author(s):  
M. Javad Khoshnavaz
Keyword(s):  
Seismic Velocity ◽  
Resolution Enhancement ◽  
Synthetic Data ◽  
Correlation Coefficients ◽  
Velocity Model ◽  
Seismic Attenuation ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Amplitude Versus Offset ◽  
Amplitude Versus

Building an accurate velocity model plays a vital role in routine seismic imaging workflows. Normal-moveout-based seismic velocity analysis is a popular method to make the velocity models. However, traditional velocity analysis methodologies are not generally capable of handling amplitude variations across moveout curves, specifically polarity reversals caused by amplitude-versus-offset anomalies. I present a normal-moveout-based velocity analysis approach that circumvents this shortcoming by modifying the conventional semblance function to include polarity and amplitude correction terms computed using correlation coefficients of seismic traces in the velocity analysis scanning window with a reference trace. Thus, the proposed workflow is suitable for any class of amplitude-versus-offset effects. The approach is demonstrated to four synthetic data examples of different conditions and a field data consisting a common-midpoint gather. Lateral resolution enhancement using the proposed workflow is evaluated by comparison between the results from the workflow and the results obtained by the application of conventional semblance and three semblance-based velocity analysis algorithms developed to circumvent the challenges associated with amplitude variations across moveout curves, caused by seismic attenuation and class II amplitude-versus-offset anomalies. According to the obtained results, the proposed workflow is superior to all the presented workflows in handling such anomalies.

Fast acoustic velocity tomography of focusing operators

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. R121-R131 ◽  
Author(s):  
Hu Jin ◽  
George A. McMechan
Keyword(s):  
Constant Velocity ◽  
Null Space ◽  
Focal Point ◽  
Grid Point ◽  
Synthetic Data ◽  
Velocity Model ◽  
The Stability ◽  
Starting Model ◽  
Velocity Tomography ◽  
Focus Point

A 2D velocity model was estimated by tomographic imaging of overlapping focusing operators that contain one-way traveltimes, from common-focus points to receivers in an aperture along the earth’s surface. The stability and efficiency of convergence and the quality of the resulting models were improved by a sequence of ideas. We used a hybrid parameterization that has an underlying grid, upon which is superimposed a flexible, pseudolayer model. We first solved for the low-wavenumber parts of the model (approximating it as constant-velocity pseudo layers), then we allowed intermediate wavenumbers (allowing the layers to have linear velocity gradients), and finally did unconstrained iterations to add the highest wavenumber details. Layer boundaries were implicitly defined by focus points that align along virtual marker (reflector) horizons. Each focus point sampled an area bounded by the first and last rays in the data aperture at the surface; this reduced the amount of computation and the size of the effective null space of the solution. Model updates were performed simultaneously for the velocities and the local focus point positions in two steps; local estimates were performed independently by amplitude semblance for each focusing operator within its area of dependence, followed by a tomographic weighting of the local estimates into a global solution for each grid point, subject to the constraints of the parameterization used at that iteration. The system of tomographic equations was solved by simultaneous iterative reconstruction, which is equivalent to a least-squares solution, but it does not involve a matrix inversion. The algorithm was successfully applied to synthetic data for a salt dome model using a constant-velocity starting model; after a total of 25 iterations, the velocity error was [Formula: see text] and the final mean focal point position error was [Formula: see text] wavelength.

Migration moveout analysis and depth focusing

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Claude F. Lafond ◽  
Alan R. Levander
Keyword(s):  
Heterogeneous Media ◽  
A Priori ◽  
Complex Structure ◽  
Tomographic Reconstruction ◽  
Synthetic Data ◽  
Real Data ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Data Set ◽  
Velocity Models

Prestack depth migration still suffers from the problems associated with building appropriate velocity models. The two main after‐migration, before‐stack velocity analysis techniques currently used, depth focusing and residual moveout correction, have found good use in many applications but have also shown their limitations in the case of very complex structures. To address this issue, we have extended the residual moveout analysis technique to the general case of heterogeneous velocity fields and steep dips, while keeping the algorithm robust enough to be of practical use on real data. Our method is not based on analytic expressions for the moveouts and requires no a priori knowledge of the model, but instead uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections. These corrections are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction. While this approach is more general than existing migration velocity analysis implementations, it is also much more computer intensive and is best used locally around a particularly complex structure. We demonstrate the technique using synthetic data from a model with strong velocity gradients and then apply it to a marine data set to improve the positioning of a major fault.

scholarly journals Constraining fault interpretation through tomographic velocity gradients: application to northern Cascadia

Solid Earth ◽  
2012 ◽  
Vol 3 (1) ◽  
pp. 53-61 ◽  
Author(s):  
K. Ramachandran
Keyword(s):  
Three Dimensional ◽  
Velocity Model ◽  
Absolute Velocity ◽  
Tomographic Inversion ◽  
Spatial Gradients ◽  
Velocity Models ◽  
Final Velocity ◽  
Velocity Gradients ◽  
Spatial Velocity ◽  
Perturbation Velocity

Abstract. Spatial gradients of tomographic velocities are seldom used in interpretation of subsurface fault structures. This study shows that spatial velocity gradients can be used effectively in identifying subsurface discontinuities in the horizontal and vertical directions. Three-dimensional velocity models constructed through tomographic inversion of active source and/or earthquake traveltime data are generally built from an initial 1-D velocity model that varies only with depth. Regularized tomographic inversion algorithms impose constraints on the roughness of the model that help to stabilize the inversion process. Final velocity models obtained from regularized tomographic inversions have smooth three-dimensional structures that are required by the data. Final velocity models are usually analyzed and interpreted either as a perturbation velocity model or as an absolute velocity model. Compared to perturbation velocity model, absolute velocity models have an advantage of providing constraints on lithology. Both velocity models lack the ability to provide sharp constraints on subsurface faults. An interpretational approach utilizing spatial velocity gradients applied to northern Cascadia shows that subsurface faults that are not clearly interpretable from velocity model plots can be identified by sharp contrasts in velocity gradient plots. This interpretation resulted in inferring the locations of the Tacoma, Seattle, Southern Whidbey Island, and Darrington Devil's Mountain faults much more clearly. The Coast Range Boundary fault, previously hypothesized on the basis of sedimentological and tectonic observations, is inferred clearly from the gradient plots. Many of the fault locations imaged from gradient data correlate with earthquake hypocenters, indicating their seismogenic nature.

Optimization of Geophone Array for Monitoring Geologic Carbon Sequestration Using Double-Difference Tomography

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Ben Fahrman ◽  
Erik Westman ◽  
Mario Karfakis ◽  
Kray Luxbacher
Keyword(s):  
Carbon Sequestration ◽  
Injection Site ◽  
Seismic Event ◽  
Synthetic Data ◽  
Cost Effective ◽  
Velocity Model ◽  
Double Difference ◽  
Data Sets ◽  
Geologic Carbon Sequestration ◽  
Tomographic Inversion

Synthetic data were analyzed to determine the most cost-effective tomographic monitoring system for a geologic carbon sequestration injection site. Double-difference tomographic inversion was performed on 125 synthetic data sets: five stages of CO2 plume growth, five seismic event regions, and five geophone arrays. Each resulting velocity model was compared quantitatively to its respective synthetic velocity model to determine accuracy. The results were examined to determine a relationship between cost and accuracy in monitoring, verification, and accounting applications using double-difference-tomography. The geophone arrays with widely varying geophone locations, both laterally and vertically, performed best.

Practical aspects and applications of 2D stereotomography

Geophysics ◽  
2003 ◽  
Vol 68 (3) ◽  
pp. 1008-1021 ◽  
Author(s):  
Frederic Billette ◽  
Soazig Le Bégat ◽  
Pascal Podvin ◽  
Gilles Lambaré
Keyword(s):  
Estimation Method ◽  
Synthetic Data ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Common Source ◽  
Depth Migration ◽  
Reflection Seismic ◽  
Velocity Models ◽  
Automatic Picking ◽  
Iterative Inversion

Stereotomography is a new velocity estimation method. This tomographic approach aims at retrieving subsurface velocities from prestack seismic data. In addition to traveltimes, the slope of locally coherent events are picked simultaneously in common offset, common source, common receiver, and common midpoint gathers. As the picking is realized on locally coherent events, they do not need to be interpreted in terms of reflection on given interfaces, but may represent diffractions or reflections from anywhere in the image. In the high‐frequency approximation, each one of these events corresponds to a ray trajectory in the subsurface. Stereotomography consists of picking and analyzing these events to update both the associated ray paths and velocity model. In this paper, we describe the implementation of two critical features needed to put stereotomography into practice: an automatic picking tool and a robust multiscale iterative inversion technique. Applications to 2D reflection seismic are presented on synthetic data and on a 2D line extracted from a 3D towed streamer survey shot in West Africa for TotalFinaElf. The examples demonstrate that the method requires only minor human intervention and rapidly converges to a geologically plausible velocity model in these two very different and complex velocity regimes. The quality of the velocity models is verified by prestack depth migration results.

Seismic Velocity Model Building Using Neural Networks: Training Data Design and Learning Generalization

Geophysics ◽  
2021 ◽  
pp. 1-73
Author(s):  
Hani Alzahrani ◽  
Jeffrey Shragge
Keyword(s):  
Seismic Data ◽  
Model Building ◽  
Seismic Velocity ◽  
Velocity Model ◽  
Training Data ◽  
Training Process ◽  
Training Models ◽  
Velocity Models ◽  
Velocity Model Building ◽  
Layer Velocity

Data-driven artificial neural networks (ANNs) offer a number of advantages over conventional deterministic methods in a wide range of geophysical problems. For seismic velocity model building, judiciously trained ANNs offer the possibility of estimating high-resolution subsurface velocity models. However, a significant challenge of ANNs is training generalization, which is the ability of an ANN to apply the learning from the training process to test data not previously encountered. In the context of velocity model building, this means learning the relationship between velocity models and the corresponding seismic data from a set of training data, and then using acquired seismic data to accurately estimate unknown velocity models. We ask the following question: what type of velocity model structures need be included in the training process so that the trained ANN can invert seismic data from a different (hypothetical) geological setting? To address this question, we create four sets of training models: geologically inspired and purely geometrical, both with and without background velocity gradients. We find that using geologically inspired training data produce models with well-delineated layer interfaces and fewer intra-layer velocity variations. The absence of a certain geological structure in training models, though, hinders the ANN's ability to recover it in the testing data. We use purely geometric training models consisting of square blocks of varying size to demonstrate the ability of ANNs to recover reasonable approximations of flat, dipping, and curved interfaces. However, the predicted models suffer from intra-layer velocity variations and non-physical artifacts. Overall, the results successfully demonstrate the use of ANNs in recovering accurate velocity model estimates, and highlight the possibility of using such an approach for the generalized seismic velocity inversion problem.

CSEM-regularized seismic velocity inversion: A multiscale, hierarchical workflow for subsalt imaging

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. B241-B252 ◽  
Author(s):  
Daniele Colombo ◽  
Diego Rovetta ◽  
Ersan Turkoglu
Keyword(s):  
Seismic Velocity ◽  
Fundamental Problem ◽  
Velocity Model ◽  
Seismic Inversion ◽  
Velocity Fields ◽  
Coupling Mechanism ◽  
Correct Result ◽  
Velocity Analysis ◽  
Velocity Inversion ◽  
Velocity Models

Seismic imaging in salt geology is complicated by highly contrasted velocity fields and irregular salt geometries, which cause complex seismic wavefield scattering. Although the imaging challenges can be addressed by advanced imaging algorithms, a fundamental problem remains in the determination of robust velocity fields in high-noise conditions. Conventional migration velocity analysis is often ineffective, and even the most advanced methods for depth-domain velocity analysis, such as full-waveform inversion, require starting from a good initial estimate of the velocity model to converge to a correct result. Nonseismic methods, such as electromagnetics, can help guide the generation of robust velocity models to be used for further processing. Using the multiphysics data acquired in the deepwater section of the Red Sea, we apply a controlled-source electromagnetic (CSEM) resistivity-regularized seismic velocity inversion for enhancing the velocity model in a complex area dominated by nappe-style salt tectonics. The integration is achieved by a rigorous approach of multiscaled inversions looping over model dimensions (1D first, followed by 3D), variable offsets and increasing frequencies, data-driven and interpretation-supported approaches, leading to a hierarchical inversion guided by a parameter sensitivity analysis. The final step of the integration consists of the inversion of seismic traveltimes subject to CSEM model constraints in which a common-structure coupling mechanism is used. Minimization is performed over the seismic data residuals and cross-gradient objective functions without inverting for the resistivity model, which is used as a reference for the seismic inversion (hierarchical approach). Results are demonstrated through depth imaging in which the velocity model derived through CSEM-regularized hierarchical inversion outperforms the results of a seismic-only derived velocity model.

scholarly journals Seismic velocity model of the crust in the northern Canadian Cordillera from Rayleigh wave dispersion data

2017 ◽  
Vol 54 (2) ◽  
pp. 163-172 ◽  
Author(s):  
Shutian Ma ◽  
Pascal Audet
Keyword(s):  
Rayleigh Wave ◽  
Velocity Structure ◽  
Seismic Velocity ◽  
Group Velocity Dispersion ◽  
Velocity Model ◽  
Canadian Cordillera ◽  
Seismic Velocities ◽  
Crustal Layer ◽  
Velocity Models ◽  
Moderate Earthquake

Models of the seismic velocity structure of the crust in the seismically active northern Canadian Cordillera remain poorly constrained, despite their importance in the accurate location and characterization of regional earthquakes. On 29 August 2014, a moderate earthquake with magnitude 5.0, which generated high-quality Rayleigh wave data, occurred in the Northwest Territories, Canada, ∼100 km to the east of the Cordilleran Deformation Front. We carefully selected 23 seismic stations that recorded the Rayleigh waves and divided them into 13 groups according to the azimuth angle between the earthquake and the stations; these groups mostly sample the Cordillera. In each group, we measured Rayleigh wave group velocity dispersion, which we inverted for one-dimensional shear-wave velocity models of the crust. We thus obtained 13 models that consistently show low seismic velocities with respect to reference models, with a slow upper and lower crust surrounding a relatively fast mid crustal layer. The average of the 13 models is consistent with receiver function data in the central portion of the Cordillera. Finally, we compared earthquake locations determined by the Geological Survey of Canada using a simple homogenous crust over a mantle half space with those estimated using the new crustal velocity model, and show that estimates can differ by as much as 10 km.

scholarly journals From tomography to full-waveform inversion with a single objective function

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. R55-R61 ◽  
Author(s):  
Tariq Alkhalifah ◽  
Yunseok Choi
Keyword(s):  
Objective Function ◽  
Initial Velocity ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Half Cycle ◽  
Velocity Models ◽  
Full Waveform ◽  
Single Objective

In full-waveform inversion (FWI), a gradient-based update of the velocity model requires an initial velocity that produces synthetic data that are within a half-cycle, everywhere, from the field data. Such initial velocity models are usually extracted from migration velocity analysis or traveltime tomography, among other means, and are not guaranteed to adhere to the FWI requirements for an initial velocity model. As such, we evaluated an objective function based on the misfit in the instantaneous traveltime between the observed and modeled data. This phase-based attribute of the wavefield, along with its phase unwrapping characteristics, provided a frequency-dependent traveltime function that was easy to use and quantify, especially compared to conventional phase representation. With a strong Laplace damping of the modeled, potentially low-frequency, data along the time axis, this attribute admitted a first-arrival traveltime that could be compared with picked ones from the observed data, such as in wave equation tomography (WET). As we relax the damping on the synthetic and observed data, the objective function measures the misfit in the phase, however unwrapped. It, thus, provided a single objective function for a natural transition from WET to FWI. A Marmousi example demonstrated the effectiveness of the approach.

Sign in / Sign up

Export Citation Format

Share Document