The effect of focal depth error on moment tensor inversion

Abstract

In the determination of focal mechanism and rupture process of earthquake sources by using moment tensor inversion technique, it is difficult to guarantee the focal depth used in calculating the Green’s functions (theoretical focal depth) is exactly equal to the real focal depth. The difference between the theoretical and real focal depths, i. e., the focal depth error, will affect the moment tensor inversion to some extent. Using synthetic seismograms, the effect of the focal depth error on moment tensor inversion for three basic types of faults is discussed systematically. For the normal and thrust fault, the focal depth error mainly affects the explosive (EP) component and the compensated linear vector dipole (CLVD) component. In the case that the theoretical focal depth is greater than the real focal depth, the focal depth error causes a false positive EP component and a false negative CLVD component for the normal fault. However, it produces a false negative EP component and a false positive CLVD component for the thrust fault. The absolute values of the false EP and CLVD components for both normal fault and thrust fault cases increase with increasing focal depth error. In the case that the theoretical focal depth is smaller than the real focal depth, the focal depth error causes a false negative EP component and a false positive CLVD component for the normal fault. However, it produces a false positive EP component and a false negative CLVD component for the thrust fault. Similarly, the absolute values of the false EP and CLVD components for both normal fault and thrust fault cases increase with increasing focal depth error. For a pure strike-slip fault the focal depth error mainly affects the shape of source the function, unlike for the normal and thrust faults. The source time functions have artificially extended tails when either the theoretical focal depth is greater or smaller than the real focal depth. The numerical experiments show that the focal depth error less than 20 km has no significant effect on the overall focal mechanism of the earthquake. In addition, the effect of the focal depth error on the inversion result is slighter in case that the theoretical focal depth is greater than the real focal depth than in the case that the theoretical focal depth is smaller than the real focal depth.