Elastic full-waveform inversion for earthquake source parameters

2-D full-waveform inversion of double-couple earthquake sources is implemented. Temporally and spatially extended sources are represented by superposition of double-couples. The source parameters solved for are the spatial location, origin time, amplitude and orientation of each double-couple. The velocity and density distribution and source time function are assumed to be known a priori but may be arbitrarily complicated. The non-linear inverse problem is solved by iterative linear approximation. The Jacobian matrix elements for source depth and rupture angle are computed by wavefield extrapolation forward in time, while those for origin time and amplitude are computed analytically. A smoothing technique that results in faster convergence and avoids local minima associated with cycle skipping is applied at each iteration. A spatial sampling interval, between discrete sources, of one-quarter wavelength of the dominant shear wave is optimal for inversion if high uniqueness of the result is desired. The presence of a fault is inferred from the spatial continuity of the rupture solution, rather than being imposed a priori. The method is illustrated by successful application to three synthetic source models: a single double-couple, a single extended rupture and a double extended rupture. The resolutions of the source depth and origin time are higher, and their posterior covariances are lower than those of the amplitude and rupture angle at each source point. Source depth, origin time and amplitude are primarily determined by the data; the rupture angle is more strongly influenced by the a priori information.     

Rapid relaxation inversion of CSAMT data

In this paper an inversion algorithm for controlled-source audio frequency magnetotelluric data is presented. This algorithm combines 2.5-D finite element forward modelling with the concepts of rapid relaxation inversion of magnetotelluric data. The inversion uses the same technique to compute sensitivities as the rapid relaxation inversion, and these approximate sensitivities are validated by comparison with exact 2.5-D sensitivities. The comparison shows that the approximate sensitivities are similar in shape to the exact sensitivities when transmitter–receiver offsets are greater than one skin depth in the Earth. The magnitudes of the two sensitivities differ but the variations with depth are similar. Tests of the algorithm on synthetic data and field data provide promising results.