Body wave directivity functions for two-dimensional fault model and kinematic parameters of a deep focus earthquake

The earthquake focus is represented by a bilateral bidirectional fault model in which the final fault area is rectangular. The transfer functions for body waves for this fault model have been derived. The directivity functions for body waves are defined by taking the ratio of the transfer functions corresponding to two observation stations. The sensitivity of the directivity function for P waves to the kinematic parameters and to the orientation of the fault plane is demonstrated. The S wave directivity function appears to be relatively insensitive to the change in the kinematic parameters. A deep focus earthquake (H = 600 km, mb = 7.0) has been investigated and the kinematic parameters have been successfully recovered using the modulus of the P wave directivity function. The kinematic parameters are as follows: The fault plane is the y-z nodal plane of the focal mechanism solution, the faulting is of the bilateral bidirectional type with total rupture along the y axis of 75 km and total rupture along the z axis of 29.5 km; the rupture speed along the y axis is 3.97 km/sec and along the z axis is 2.98 km/sec. The fault area is 2212 km2 and the dislocation is estimated to be 26 cm.