2-D/3-D irregular shortest-path ray tracing for multiple arrivals and its applications

Abstract

S U M M A R YThe purpose of this study is to introduce a multistage irregular shortest-path method (ISPM) for tracking multiple seismic arrivals including any combinations of transmissions, reflections (or refractions) and mode conversions in complex 2-D/3-D layered media, incorporating irregular interfaces (or subsurface in 3-D) and velocity discontinuities. The basic principle is to first divide the model into several different layers (using irregular cells near each interface, discontinuity and the Earth's undulating surface topography) and then to apply the multistage technique to trace the multiple arrivals. It is possible to realize the multiple arrival tracking with the multistage scheme because the multiple arrivals are just different combinations or conjugations of the simple incident, transmitted, reflected (or refracted) and mode converted waves via the velocity discontinuities and the interfaces. Benchmark tests against the popular multistage fast marching method (FMM) and the multistage MSPM (modified shortest path method) are undertaken to assess the solution accuracy and the computational efficiency. The results show that the multistage ISPM is advantageous over both the multistage FMM and the multistage MSPM in both solution accuracy and CPU time. Several examples (including the Marmousi model) are used to demonstrate the viability and versatility of the multistage ISPM in heterogeneous media, even in the presence of high-velocity contrasts involving interfaces of relatively high curvature. Applications to the seismological problems, such as traveltime tomography and earthquake location, indicate that it is possible to improve the spatial resolution in traveltime tomography and solution accuracy in earthquake location if later arrival information is combined with the first arrivals.The complicated nature of multiple transmitted, reflected and mode converted seismic arrivals is caused by both continuous and discontinuous variations in seismic wave speed inside the Earth. Hence one of the most common and challenging problems in seismology is to predict the traveltimes and the corresponding ray paths of the above multiple arrivals between the sources and the receivers in the presence of lateral heterogeneous media involving irregular interfaces and undulated topography. The layer boundaries may represent a discontinuity (or continuity) in the velocity or discontinuities in the velocity gradient. These kinds of solutions are required in various applications that exploit the seismic records with high frequency energy, such as precise earthquake location (e.g. Kennett & Engdahl 1991), coincident migration of reflection data (e.g. Popovici & Sethian 2002) and resolution improvement of seismic tomography (e. g. Zhao et al. 2005).In practical applications, the above types of seismic records are obtained frequently from natural earthquakes, which take place in non-uniformly specified locations, such as subduction zones and active faults, by using seismic networks deployed sparsely and irregularly worldwide....

A Fast and Accurate Scheme for Travel-Time Computations and Ray-Path Determinations of Global Seismic Phases in a Laterally Heterogeneous Model

“…To calculate the later arrivals having stationary ray paths, we introduce the concept of Fermat's Principle of stationary minimax time paths, and extend the functionality of the multistage ISPM scheme (Bai et al, 2010), previously only developed for Cartesian coordinates. This allows us to compute ray paths and travel times in spherical coordinates for 2D velocity models to trace multiple later arriving global phases for the Earth.…”

“…(1) finite-difference eikonal equation solvers, for example, the multistage fast-marching method (Rawlinson and Sambridge, 2004a,b;de Kool et al, 2006); and (2) the shortest-path method, for example, a multistage modified shortest-path method (Bai et al, 2009), and a multistage irregular shortest-path method (Bai et al, 2010).…”

“…In such cases, the grid/ cell-based wavefront-expanding method can be useful and efficient because it predicts travel-time and ray-path information on all gridded nodes in a single computer run. For this purpose, we present in this paper a grid/cell-based wavefront-expanding method (that is an irregular shortest-path method with a multistage scheme implemented, referred as the Multistage ISPM, Bai et al, 2010) incorporated with the stationary minimax time-path concept of Fermat's Principle to calculate the travel times and the related ray paths of most global seismic phases, including 49 crust, mantle, and core phases. Accuracy of the scheme is established by comparison with the AK135 traveltime tables indicate that it has a required computational accuracy with absolute travel-time errors of less than 0.1 s. Furthermore, the method also offers high computational efficiency, taking less than a few seconds of CPU time when millions of nodes are involved in the computation.…”

Theory and Observations: Body Waves, Ray Methods, and Finite-Frequency Effects

“…Finding the shortest path between a source and a receiver leads to network ray tracing. Impressive algorithms have been developed by Bai et al (2009Bai et al ( , 2010 considering the shortest path inside each layer, while multiple arrivals are included through the interface discontinuities where transmitted, reflected (or refracted), and converted phases should obey Snell law and Huygens principle. The connection between two grid points is the ray and the related travel time between these two points is the fastest one.…”

“…The connection between two grid points is the ray and the related travel time between these two points is the fastest one. The review by Rawlinson et al (2007) is worthwhile for comparison of methods, while the shortest path algorithm is fully described by Bai et al (2010). One must be aware that this technique leads to rays, while solving first-arrival times through eikonal approaches leads to travel times.…”