Grid-based Ray Theory Amplitude Calculation for Teleseismic Moment Tensor Sources

Direct numerical modeling of seismic wave propagation at high frequencies remains a computational challenge despite ever-increasing processing capabilities. Ray theory, which is based on a high-frequency solution of the seismic wave equation, provides an alternative to direct numerical modeling for sufficiently smooth velocity models. Here, we present a hybrid 1D-3D approach to model grids of seismic amplitudes of P-phases based on ray theory and dynamic ray tracing. They may serve to construct P-phase synthetic seismograms to be used in high-frequency teleseismic full waveform inversion or the interpretation of scattered and converted waves as done, for example, in receiver function analysis.

The modeling domain is split into two parts: 1D bulk earth and a box encompassing a regional study area for which a 3D model is used. 1D dynamic ray tracing and amplitude calculation for a moment tensor source is performed using ray paths calculated with Obspy TauP and the resulting transformation matrices and amplitudes are stored at the box boundaries. In the regional box ray paths from the box boundary to each grid point are calculated using the FM3D software by Rawlinson and Sambridge (2005) and de Kool, Rawlinson and Sambridge (2006). Subsequently, 3D dynamic ray tracing along all calculated rays is initialized from the box boundaries yielding amplitudes at each grid point.

The 1D method is tested by comparing amplitude ratios with those calculated using the software Gemini (Friederich and Dalkolmo 1995). The 3D method is tested using a 1D model and comparing amplitudes calculated using the hybrid 1D-3D method with amplitudes calculated using only the 1D method. Additionally, a 3D spherical velocity anomaly is inserted into a 1D background model to test the plausibility of the resulting amplitude grid for this model. The calculated amplitude grid clearly shows the expected focusing effects caused by the anomaly.