The Effects of Variable Velocity of Rupture Propagation on Fault’s Directivity Pulses

Unilateral rupture propagation along earthquake faults results in asymmetric radiation in and opposite to the direction of rupture travel, known as forward and backward directivity. Correct simulation of fault directivity pulses in ground velocity has engineering significance. Forward velocity pulses are typically recognized as short bursts of energy with large amplitude, compared to elongated and much weaker backward wave trains. A classic model of such behavior is the line source in the far field, undergoing rupture propagation with constant speed. In reality, earthquake ruptures can be reasonably expected to travel in a variable, often irregular, manner. Simulation of the distinctions introduced by the variable rupture velocity into the characteristic features of directivity should not only involve the line source but also finite sources in the near field. The differences with the case of constant rupture velocity are threefold. First, sharp amplitude contrast between the velocity pulses in the forward and reverse directions is substantially subdued by the variable fracture speed. Second, complex ruptures result in the longer duration of radiation in both directions. Third, unlike the relatively simple radiation pulses in the scenario of constant velocity, complexity in the rupture travel time creates multiple pulses of both forward and reverse directivity. Randomization of rupture velocity nearly erases the differences in the spectral content of radiation in the forward and backward directions. Well known features of fault directivity appear to be artifacts of the constant-velocity assumption and the resulting orderly interference. The complexity that randomization introduces into the directivity pulses is gradually reduced with lesser randomness. Since irregularity in the rupture travel time should be viewed as the norm rather than an exception, correct simulation of fault directivity must involve variable velocity of rupture propagation.