D40 Nonlinear inversion algorithm for all types of geodetic data – NVI

This deliverable is presented in a paper entitled “Fault slip distribution of two June 2000 Mw 6.5 earthquakes in South Iceland estimated from joint inversion of InSAR and GPS measurements” by Pedersen et al. (2003). The deliverable is a nonlinear inversion algorithm suitable for all types of geodetic data and is presented in the paper. Observed ground displacements d can be written as a function g of the deformation model parameters m:

d = g(m) + e

where e are observational errors. The algorithm finds the best-fitting model parameters. As input, the algorithm needs information on the ground displacements, and the function g describing the behavior of the assumed model. For a single earthquake fault, the model vector m consists of 10 fault parameters (seven describing the fault geometry, three describing the slip on the fault). For a magmatic point source of pressure (Mogi model), the model vector consists of four parameters (three for location, one for strength). For earthquake faults, the surface displacements are a non-linear function of the fault geometry but change linearly with slip components for a fixed geometry. This is considered in the algorithm as described by Pedersen et al. (2003).

Prior to running the algorithm, the input data needs to be prepared. InSAR data needs special treatment because of the large number of highly correlated data points, compared to the number of GPS points. The number of InSAR data is reduced by quadtree partitioning, a two-dimensional quantization algorithm to speed up model computations. The algorithm divides the scene into four quadrants, then calculates the mean of each quadrant and subsequently evaluates the RMS scatter against a specific threshold (e.g., 10 mm). If the misfit exceeds the threshold, the quadrant is sub-divided into four new quadrants recursively until convergence. The resulting quadtree partitioning of the data is used as input for the inversion, as well as other available data.

The algorithm is described in details in the paper by Pedersen et al. (2003). In that paper the algorithm is tested and implemented using InSAR and GPS data covering the two June 2000 Mw 6.5 earthquakes in South Iceland. The algorithm was further tested and implemented in a paper by Pagli et al. (2003) using InSAR data to constrain triggered fault slip on the Reykjanes Peninsula in 2003. The algorithm has also been used for magmatic sources in Iceland (abstracts by Pedersen et al., 2003).