Comparison of various inversion techniques as applied to the determination of a geophysical deformation model for the 1983 Borah Peak earthquake

A number of techniques are employed to overcome nonuniqueness and instability inherent in linear inverse problems. To test the factors that enter into the selection of an inversion technique for fault slip distribution, we used a penalty function with smoothness (PF + S), a damped least-squares method (DLS), damped least-squares method with a positivity constraint (DLS + P), and a penalty function with smoothness and a positivity constraint (PF + S + P) for inverting the elevation changes for slip associated with the 1983 Borah Peak earthquake. Unlike solving an ill-posed inverse problem using a gradient technique (Ward and Barrientos, 1986), we have restored the well-posed character between the elevation changes and normal slip distribution. Studies showed that the constraints based on sound understanding of the physical nature of the problem are crucial in the derivation of a meaningful solution and dictates primarily the selection of a particular inversion technique. All available geological and geophysical information were used to determine a geophysical deformation model for the earthquake. It is suggested that the PF + S + P solution for a fault length of 75 km is the preferred model. The long wavelength features in the estimated slip distribution are similar to those obtained by Ward and Barrientos (1986), whereas the shorter wavelength features differ between two solutions. The fault dips 49° to the southwest. The slipped zones deepen from the surface at the northwest to about 20-km downdip depth at the southeast. The fault extends to the southeast beyond the epicenter of the mainshock. It is also shown that only the long wavelength features of the slip distribution are well resolved. The resolution is better at shallower levels than at deeper levels. The resolution deteriorates when the deformation sources are away from the leveling lines. Smoothness constraints provide better resolution than damping does at depth. The addition of a positivity constraint significantly improves the model resolution.