A numerical experiment on nonlinear image reconstruction from first-arrival times for two-dimensional island arc structure.

Abstract

Many inversion studies of first P-arrival times have been made for the threedimensional upper mantle structure beneath the Japanese Islands by using the linear damped least-squares method (AKI and LEE, 1976). One of the most recent contributions relying on this method is that by HASEMI et al. (1984) on the structure beneath the Tohoku region. In the linear inversion it is assumed that the ray paths in the inverted model are the same as those in the initial model. The ray tracing experiments attempted in the early 1970 's (JACOB, 1970 showed that the ray paths are strongly guided by the high velocity slabs descending beneath the island arcs.The aim of this study is to examine the performance of a nonlinear inversion of travel times of first-arrivals for the island arc structure. We apply the Dijkstra method (DIJKSTRA, 1959) of network theory in the forward calculation of ray paths and travel times instead of the shooting or bending method (JULIAN and GUBBINS, 1977). We subdivide a two-dimensional space of 100 km x 100 km into a number of blocks of 10 km x 10 km as shown in Fig. 1. We assume an average layered velocity profile of the area under consideration a priori. We make the velocity profile by taking the value of the JMA standard P-wave structure (HAMADA, 1984) for each 10 km starting from a depth of 5 km.The algorithm proposed by DIJKSTRA (1959) is considered to be the fastest of the algorithms which find the shortest paths connecting a node and the other all nodes of a network (IRI and KOBAYASHI, 1976). For the algorithm, one should consult DIJKSTRA (1959) or IRI andKOBAYASHI (1976). We seek the shortest time paths connecting a node ns and the other all nodes ni(j_??_s) of the network. When the node ns is assigned to an event, and the nodes n;(j 0 s) include station positions, we are able to obtain the shortest time paths from the event to all the stations. When the node ns indicates a station and all the event locations are included in nj(j # s), the algorithm gives us the shortest time paths from all the events to the station. In this study we shall put the nodes on the boundaries of the blocks. Figure 1 shows a laterally heterogeneous model that corresponds to a vertical section of the uppermost mantle perpendicular to the strike of island arcs. The 195

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“…The graph method, also known as the shortest path method, was developed in network theory [e.g., Dijkstra, 1959;Gallo and Pallottino, 1986], and it can calculate the shortest connections from an origin node to all other nodes in a network. If a seismic travel time between nodes is used as a nodal distance, this global optimization scheme can be used to generate a set of first-arrival travel times and corresponding ray paths [Nakanishi and Yamaguchi, 1986;Moser, 1991], and it has recently become popular in refraction tomography [Toomey et al, 1994;Zhang and Toksbz, 1998]. The calculation of later arrivals such as reflection phases can be formulated as a two-step application of the graph method [Moser, 1991], and it has been used in refraction and reflection tomography ].…”

Seismic Traveltime Tomography of the Crust and Lithosphere

“…More recently, wavefront tracking schemes such as finite difference solutions of the eikonal equation have been employed (Vidale, 1988(Vidale, , 1990Qin et al, 1992). Another method that has seen recent application is network/graph theory, which makes direct use of Fermat's principle (Nakanishi & Yamaguchi, 1986;Moser, 1991). Each of these methods of traveltime determination is described below.…”

A three-dimensional robust seismic ray tracer for volcanic regions

“…Alternative schemes of node configuration have been proposed for the two-dimensional problem (e.g., Nakanishi and Yamaguchi, 1986;Moser, 1991;Fisher and Lees, 1993). In this node configuration, nodes are placed on the boundary of each cell, and the ray passes through to the neighbor cell via a node common to each cell.…”

“…Comparisons of the finite-difference method and graph theory are found in Klimeš and Kvasnička (1994) and Zhang and Toksöz (1998); they suggest the superiority of ray tracing by the graph theory. Nakanishi and Yamaguchi (1986) applied the idea of the shortest path (in the graph theory) to seismic ray tracing. This method regards the solution for the shortest path over a network as satisfying the Fermat's principle of stationary time for wave propagation.…”

“…Since the work of Nakanishi and Yamaguchi (1986), several improvements have increased the accuracy and the efficiency of the calculation (e.g., Saito, 1989Saito, , 1990Moser, 1991;Fisher and Lees, 1993;Klimeš and Kvasnička, 1994;Cheng and House, 1996;Zhang and Toksöz, 1998).…”