Velocity rays for heterogeneous anisotropic media: Theory and implementation

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. T117-T127 ◽  
Author(s):  
Einar Iversen
Keyword(s):  
Model Updating ◽  
Seismic Velocity ◽  
Velocity Model ◽  
Media Theory ◽  
First Order ◽  
Velocity Models ◽  
Model Independent ◽  
Upper Level ◽  
The Time Domain ◽  
Seismic Images

The surface of equal two-way time referred to as the isochron is a fundamental concept in seismic imaging. The shape of an isochron depends on the source and receiver locations, on the wave type, and on the parameters constituting the seismic velocity model. A perturbation of a parameter of the velocity model forces the isochron points to move along trajectories called velocity rays, with the selected model parameter as the variable along the rays. Based on earlier work describing first-order approximations to velocity rays, I develop a general theory for velocity rays valid for 3D heterogeneous and anisotropic velocity models. By this theory, velocity rays can be obtained in a way similar to the way conventional rays are computed by numeric integration of a system of ordinary differential equations (ODEs). The process is organized with ODE solvers on two levels, where the upper level is model independent. The lower level includes conventional one-way kinematic and dynamic tracing of source and receiver rays, as well as calculation of ray perturbation quantities. Accurate velocity rays are expected to be useful for perturbation of reflectors mapped from the time domain to the depth domain, for remigration of seismic images in the depth domain, and for velocity model updating.

The isochron ray in seismic modeling and imaging

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 1053-1070 ◽  
Author(s):  
Einar Iversen
Keyword(s):  
Seismic Imaging ◽  
Model Updating ◽  
Velocity Model ◽  
Seismic Modeling ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Geometric Spreading ◽  
Model Independent ◽  
Map Migration ◽  
Upper Level

The isochron, the name given to a surface of equal two‐way time, has a profound position in seismic imaging. In this paper, I introduce a framework for construction of isochrons for a given velocity model. The basic idea is to let trajectories called isochron rays be associated with iso chrons in an way analogous to the association of conventional rays with wavefronts. In the context of prestack depth migration, an isochron ray based on conventional ray theory represents a simultaneous downward continuation from both source and receiver. The isochron ray is a generalization of the normal ray for poststack map migration. I have organized the process with systems of ordinary differential equations appearing on two levels. The upper level is model‐independent, and the lower level consists of conventional one‐way ray tracing. An advantage of the new method is that interpolation in a ray domain using isochron rays is able to treat triplications (multiarrivals) accurately, as opposed to interpolation in the depth domain based on one‐way traveltime tables. Another nice property is that the Beylkin determinant, an important correction factor in amplitude‐preserving seismic imaging, is closely related to the geometric spreading of isochron rays. For these reasons, the isochron ray has the potential to become a core part of future implementations of prestack depth migration. In addition, isochron rays can be applied in many contexts of forward and inverse seismic modeling, e.g., generation of Fresnel volumes, map migration of prestack traveltime events, and generation of a depth‐domain–based cost function for velocity model updating.

Migration velocity analysis based on focusing diffractions generated using the CRS wavefront attributes: Application to real land data

Geophysics ◽  
2021 ◽  
pp. 1-50
Author(s):  
German Garabito ◽  
José Silas dos Santos Silva ◽  
Williams Lima
Keyword(s):  
Time Domain ◽  
Real Data ◽  
Normal Incidence ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
The Time Domain

In land seismic data processing, the prestack time migration (PSTM) image remains the standard imaging output, but a reliable migrated image of the subsurface depends on the accuracy of the migration velocity model. We have adopted two new algorithms for time-domain migration velocity analysis based on wavefield attributes of the common-reflection-surface (CRS) stack method. These attributes, extracted from multicoverage data, were successfully applied to build the velocity model in the depth domain through tomographic inversion of the normal-incidence-point (NIP) wave. However, there is no practical and reliable method for determining an accurate and geologically consistent time-migration velocity model from these CRS attributes. We introduce an interactive method to determine the migration velocity model in the time domain based on the application of NIP wave attributes and the CRS stacking operator for diffractions, to generate synthetic diffractions on the reflection events of the zero-offset (ZO) CRS stacked section. In the ZO data with diffractions, the poststack time migration (post-STM) is applied with a set of constant velocities, and the migration velocities are then selected through a focusing analysis of the simulated diffractions. We also introduce an algorithm to automatically calculate the migration velocity model from the CRS attributes picked for the main reflection events in the ZO data. We determine the precision of our diffraction focusing velocity analysis and the automatic velocity calculation algorithms using two synthetic models. We also applied them to real 2D land data with low quality and low fold to estimate the time-domain migration velocity model. The velocity models obtained through our methods were validated by applying them in the Kirchhoff PSTM of real data, in which the velocity model from the diffraction focusing analysis provided significant improvements in the quality of the migrated image compared to the legacy image and to the migrated image obtained using the automatically calculated velocity model.

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.

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.

Applications of the trend-match attribute for interpreting seismic velocity data

2019 ◽  
Vol 7 (2) ◽  
pp. SB1-SB10
Author(s):  
Mingya Chen ◽  
Damian O’Grady
Keyword(s):  
Case Studies ◽  
Seismic Velocity ◽  
Regional Scale ◽  
Velocity Model ◽  
Velocity Data ◽  
Thickness Estimation ◽  
Velocity Modeling ◽  
Modeling Techniques ◽  
Seismic Images

A seismic velocity model is one of the products generated from a seismic imaging project. Recent advances in velocity modeling techniques have significantly improved the quality of seismic velocity data. Yet, the use of seismic velocity to guide geologic interpretations is still limited. This is mainly due to the overwhelming effect of compaction and the low-resolution nature of the seismic velocity model. Geologic boundaries and anomalies are often difficult to visualize from seismic velocity data alone. A new attribute called the trend-match attribute is proposed to reveal changes in velocity compaction trends from seismic velocity. The attribute is computed by comparing seismic velocity data with the regional velocity depth trends defined for different lithofacies using wells. We applied the trend-match attribute on several case studies to facilitate stratigraphic interpretation, horizon mapping, and erosion thickness estimation. Integration of the trend-match attribute volume with migrated seismic images can further constrain the geologic and stratigraphic interpretation at a regional scale.

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.

Illumination compensation for image-domain wavefield tomography

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. U65-U76 ◽  
Author(s):  
Tongning Yang ◽  
Jeffrey Shragge ◽  
Paul Sava
Keyword(s):  
Model Building ◽  
Velocity Model ◽  
Model Errors ◽  
Image Domain ◽  
Illumination Compensation ◽  
Illumination Problem ◽  
Velocity Models ◽  
Velocity Model Building ◽  
Penalty Operator ◽  
Seismic Images

Image-domain wavefield tomography is a velocity model building technique using seismic images as the input and seismic wavefields as the information carrier. However, the method suffers from the uneven illumination problem when it applies a penalty operator to highlighting image inaccuracies due to the velocity model error. The uneven illumination caused by complex geology such as salt or by incomplete data creates defocusing in common-image gathers even when the migration velocity model is correct. This additional defocusing violates the wavefield tomography assumption stating that the migrated images are perfectly focused in the case of the correct model. Therefore, defocusing rising from illumination mixes with defocusing rising from the model errors and degrades the model reconstruction. We addressed this problem by incorporating the illumination effects into the penalty operator such that only the defocusing by model errors was used for model construction. This was done by first characterizing the illumination defocusing in gathers by illumination analysis. Then an illumination-based penalty was constructed that does not penalize the illumination defocusing. This method improved the robustness and effectiveness of image-domain wavefield tomography applied in areas characterized by poor illumination. Our tests on synthetic examples demonstrated that velocity models were more accurately reconstructed by our method using the illumination compensation, leading to a more accurate model and better subsurface images than those in the conventional approach without illumination compensation.

Improving seismic image using the common-horizon panel

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. S449-S458
Author(s):  
Lu Liu
Keyword(s):  
Time Lag ◽  
Velocity Model ◽  
Migration Velocity ◽  
Quantitative Information ◽  
Time Shift ◽  
Velocity Models ◽  
Seismic Image ◽  
The Common ◽  
Seismic Images ◽  
Zero Time

Generating high-quality seismic images requires accurate velocity models. However, velocity errors are predictably brought into the models. To mitigate the influences of velocity errors, we have used the common-horizon panel (CHP) for migration velocity analysis. CHP provides quantitative information to adjust mispositioned interfaces or correct deformed wavefields, which leads to improved image quality. It is generated by extrapolating seismic gathers to a selected target horizon and applying the time-shift imaging condition. Compared with the commonly used common-image gathers, the events in CHPs are more trackable because geologic interfaces are typically continuous in space. For a correct velocity model, the panel indicates a flat event at zero time lag, whereas in the case of an erroneous velocity model, the event becomes kinematically oscillating. This distinguishing difference provides a practical criterion to verify whether the migration velocity model is correct and to estimate the velocity or wavefield errors based on how much the event deviates from zero time lag. Tests on synthetic and field data sets have shown that the seismic images are improved by using the proposed CHP technique.

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.

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