2-D/3-D multiply transmitted, converted and reflected arrivals in complex layered media with the modified shortest path method

P>Grid-cell based schemes for tracing seismic arrivals, such as the finite difference eikonal equation solver or the shortest path method (SPM), are conventionally confined to locating first arrivals only. However, later arrivals are numerous and sometimes of greater amplitude than the first arrivals, making them valuable information, with the potential to be used for precise earthquake location, high-resolution seismic tomography, real-time automatic onset picking and identification of multiple events on seismic exploration data. The purpose of this study is to introduce a modified SPM (MSPM) for tracking multiple arrivals comprising any kind of combination of transmissions, conversions and reflections in complex 2-D/3-D layered media. A practical approach known as the multistage scheme is incorporated into the MSPM to propagate seismic wave fronts from one interface (or subsurface structure for 3-D application) to the next. By treating each layer that the wave front enters as an independent computational domain, one obtains a transmitted and/or converted branch of later arrivals by reinitializing it in the adjacent layer, and a reflected and/or converted branch of later arrivals by reinitializing it in the incident layer. A simple local grid refinement scheme at the layer interface is used to maintain the same accuracy as in the one-stage MSPM application in tracing first arrivals. Benchmark tests against the multistage fast marching method are undertaken to assess the solution accuracy and the computational efficiency. Several examples are presented that demonstrate the viability of the multistage MSPM in highly complex layered media. Even in the presence of velocity variations, such as the Marmousi model, or interfaces exhibiting a relatively high curvature, later arrivals composed of any combination of the transmitted, converted and reflected events are tracked accurately. This is because the multistage MSPM retains the desirable properties of a single-stage MSPM: high computational efficiency and a high accuracy compared with the multistage FMM scheme.