2.5D direct‐current resistivity forward modelling and inversion by finite‐element–infinite‐element coupled method

To reduce the numerical errors arising from the improper enforcement of the artificial boundary conditions on the distant surface that encloses the underground part of the subsurface, we present a finite‐element–infinite‐element coupled method to significantly reduce the computation time and memory cost in the 2.5D direct‐current resistivity inversion. We first present the boundary value problem of the secondary potential. Then, a new type of infinite element is analysed and applied to replace the conventionally used mixed boundary condition on the distant boundary. In the internal domain, a standard finite‐element method is used to derive the final system of linear equations. With a novel shape function for infinite elements at the subsurface boundary, the final system matrix is sparse, symmetric, and independent of source electrodes. Through lower upper decomposition, the multi‐pole potentials can be swiftly obtained by simple back‐substitutions. We embed the newly developed forward solution to the inversion procedure. To compute the sensitivity matrix, we adopt the efficient adjoint equation approach to further reduce the computation cost. Finally, several synthetic examples are tested to show the efficiency of inversion.     

A 2D finite volume model for bebris flow and its application to events occurred in the Eastern Pyrenees

FLATModel is a 2D finite volume code that contains several original approaches to improve debris-flow simulation. Firstly, FLATModel incorporates a ＂stop-and-go＂ technique in each cell to allow continuous collapses and remobilizations of the debris-flow mass. Secondly, flow velocity and consequently yield stress is directly associated with the type of rheology to improve boundary accuracy. Thirdly, a simple approach for entrainment is also included in the model to analyse the effect of basal erosion of debris flows. FLATMODEL was tested at several events that occurred in the Eastern Pyrenees and simulation results indicated that the model can represent rather well the different characteristics observed in the field.