Determining fault orientations from seismic wave observations

There exists today a large number of inversion procedures for obtaining information about the seismic source. The simplest techniques use only P wave first motions to constrain the three angles of the fault plane solution. More advanced schemes use amplitudes or amplitude ratios to obtain the fault plane solution and a measure of the seismic moment $M_0$. Even more complex inversions estimate the entire moment tensor with both double-couple and non-double-couple contributions. The stress tensor inversion technique described in paper II of this thesis and the spectral amplitude correlation scheme in paper III, were developed on the basis of the source mechanism inversion by Slunga [1981], later extended by Rögnvaldsson and Slunga [1993]. The techniques in paper II and III are not limited to a certain focal mechanism inversion technique, but their development was inspired by features of the Slunga [1981] technique, which is why I will point out the main ideas behind his approach, which I will refer to as the RS-technique.

Developed for use in local networks with source-receiver distances of less than 100 km, the RS-technique assumes a pure double-couple source without over-shoot in the source-time function. Under such circumstances the P and S wave far-field impulses are only dependent on the fault plane solution and the seismic moment. Using the absolute values of the spectral amplitudes (the low-frequency asymptote) for P, SV and SH waves plus the first motion directions of the P wave, the RS-technique performs a grid search over strike, dip and rake, calculates the radiation pattern and, if the radiation pattern agrees with the polarity readings, performs a direct, least-squares inversion for the seismic moment. The misfits from the inversions are compared and an optimal, best-fitting focal mechanism is found. Of great importance for the stress tensor inversion in paper II is the fact that the RS-technique not only yields an optimal focal mechanism with associated errors, but also produces a range of well fitting, acceptable, focal mechanisms. These acceptable mechanisms have source orientations and slip directions that satisfy the recorded spectral amplitudes and polarities and give sufficiently small least-square misfits, which we will refer to as amplitude errors. The number of acceptable mechanisms obtained in the inversion depends on the shape of the objective function and usually varies between 10 and 90. Events with poorly restricted focal mechanisms have a larger number of acceptable mechanisms. This provides the stress inversion routine with a measure of the non-uniqueness of the focal mechanism and a range of mechanisms, that all fit the data, to test in the inversion scheme.

The RS-technique was successfully tested on Swedish earthquakes in the 1970s and 1980s and is incorporated into the routine analysis of the Icelandic seismic network SIL (Section 5.2). Focal mechanisms produced using the RS-technique have been compared to moment tensors produced using full waveform inversion [Shomali and Slunga, 2000]. Icelandic earthquakes of $M_L \sim 4$ were used and there was generally good agreement between the two approaches.