3D ray tracing using a modified shortest-path method

Huang

et al. 2014

Pure Appl. Geophys.

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Traditionally, traveltime tomography entails inversion of either the velocity field and the reflector geometry sequentially, or the velocity field and the hypocenter locations simultaneously or in a cascaded fashion, but seldom are all three types (velocities, geometry of reflectors, and source locations) updated simultaneously because of the compromise between the different classes of model variable and the lack of different seismic phases to constrain these variables. By using a state-of-the-art raytracing algorithm for the first and later arrivals combined with a popular linearized inversion solver, it is possible to simultaneously recover the three classes of model variables. In the work discussed in this paper we combined the multistage irregular shortest-path ray-tracing algorithm with a subspace inversion solver to achieve simultaneous inversion of multi-class variables, using arrival times for different phases to concurrently obtain the velocity field, the reflector shapes, and the hypocenter locations. Simulation and comparison tests for two sets of source-receiver arrangements (one the ideal case and the other an approximated real case) indicate that the combined triple-class inversion algorithm is capable of obtaining nearly the same results as the double-class affect inversion scheme (velocity and reflector geometry, or velocity and source locations) even if a lower ray density and irregular sourcereceiver geometry are used to simulate the real situation. In addition, the new simultaneous inversion method is not sensitive to a modest amount of picking error in the traveltime data and reasonable uncertainty in earthquake hypocenter locations, which shows it to be a feasible and promising approach in real applications.

Section: Summary Of the Multistage Irregular Shortestpath Ray Schemementioning

confidence: 99%

Section: Summary Of the Multistage Irregular Shortestpath Ray Schemementioning

confidence: 99%

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3D Simultaneous Traveltime Inversion for Velocity Structure, Hypocenter Locations, and Reflector Geometry Using Multiple Classes of Arrivals

Huang

et al. 2014

Pure Appl. Geophys.

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“…The above definition of the velocity distribution across the cell allows us to handle arbitrary media with only a slightly increased effort in the computations to trace any ray paths, irrespective of where the sources and receivers are located. BAI et al (2004) showed that the revised 'irregular' shortest path method has a maximum relative error in 3-D situations given by:…”

Section: Velocity Function Across the Cellmentioning

confidence: 99%

“…BAI et al (2004) analyzed the relative performance between the 'irregular' and 'regular' shortest path approaches at a specified accuracy, and established the CPU ratio in terms of the level of forward star n FS ('regular' approach) and the number of nodes (n) per cell boundary ('irregular' approach) as:…”

Section: Algorithm Accuracy and Computational Efficiencymentioning

confidence: 99%

3-D Non-linear Travel-time Tomography: Imaging High Contrast Velocity Anomalies

Greenhalgh

2005

Pure appl. geophys.

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In this paper we present an approach for 3-D travel-time tomography, which works well in reconstructing high contrast velocity anomalies in both location and strength. It uses a revised 'irregular' approach to the shortest-path method as the ray tracer and a damped minimum norm, and constrained least-squares CG approach as the inversion solver. In ray tracing, the advantages of the revised 'irregular' over the 'regular' approach are that the secondary nodes introduced on the cell surfaces significantly improve accuracy of computed travel times, without dramatically increasing the total number of cells and nodes; the tri-linear velocity function defined across the cell guarantees accurate ray tracing in a high velocity contrast medium; and the capacity to calculate a relatively large 3-D model, due to the fast run speed (at least one order of magnitude over the 'regular' approach) and less number of total nodes. The introduction of 'soft' and 'hard' bounds into the inversion process changes the conditioning and makes the solution meaningful in a physical sense. Thus the artifacts caused by noise and high velocity contrasts are substantially suppressed and the image quality is considerably improved, making the solution realistic with noisy or inconsistent travel-time data. Several numerical tests indicate that we can obtain good quality images even for high velocity contrast anomalies (say more than 20%) in the target region. This means the inversion algorithm is an efficient and effective procedure. Meanwhile, the inversion procedure is not very sensitive to the quality of the travel-time data, which is promising for practical usage.

Multiple Ray Tracing Within 3‐D Layered Media with the Shortest Path Method

Tang

Chinese J of Geophysics

2009

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The purpose of this study is to introduce the multistage scheme incorporating with a modified shortestpath method (MSPM) for tracking multiple arrivals and simulating wavefront evolutions composed of any kind of combinations of transmissions, conversions and reflections in complex 3D layered media. The principle is first to divide the layered model into several different computational domains, and then to use the multistage technique to trace the multiple arrivals. It is possible to realize the multiple arrival tracking with the multistage technique because the multiple arrivals are the different combinations or conjugations of the simple incident, transmitted, reflected, and converted waves at the velocity boundaries (or discontinuities). Numerical tests and error analysis indicate that the multistage MSPM method retains the basic characteristics of the single‐stage MSPM approach, that is algorithm simplicity, numerical stability, high computational accuracy and speed, global solution and etc. Therefore it is a practical algorithm to track the multiple arrivals.