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What is Poly3Dinv?
Poly3Dinv is a 3D-boundary element method that uses triangular dislocations in a linear-elastic, homogeneous, isotropic, whole- or half-space to solve linear inverse problems such as slip inversion for earthquake study. The elastic fields around the elements are derived from the solution for a single angular dislocation in elastic half-space or whole-space (Comninou and Dundurs, 1975, Journal of Elasticity, v. 5, p. 203-216). Geologically, a polygonal element may represent some portion of a fracture or fault surface across which the discontinuity in displacement is postulated to be constant. Several polygonal dislocation elements may be used to model faults or fractures or even joined to form a closed surface. This superposition provides the means to model geological structures with complex, three dimensional boundaries and shapes that are not possible to model effectively with the commonly used rectangular dislocations.
Using a Weighted Damped Least Squares method (WDLS), one can retrieve the Burgers vectors b on elements, given the model geometry and a set of measure displacements u (GPS, InSAR…), using the equation:
(1)
In eq.1, We represents the data-weighting matrix. The smoothing operator 
, called the Umbrella operator, is a finite approximation of the Laplacian operator for 2-manifolds and e serves as a measure of the roughness of the Burgers's vectors. The operator is constructed using the equation:
, with 
(2)
where hij represents the distance from the ith element center to the jth element center. n is the number of elements around element i, and can be chosen according to a valence, as shown below. The valence controls the local degree of smoothness for the considered element, and can vary from one element to another if necessary.
