Approximate inverse mappings in DC resistivity problems

Hybrid algorithm for inverse DC/AC resistivity logging measurement simulations

We present a hybrid algorithm for solving inverse 3D resistivity logging measurement simulation problem with DC and AC tools in deviated wells. The term “simulation of measurements” is widely used by the geophysical community. A quantity of interest, voltage, is measured at a receiver electrode located in the logging instrument. Computer simulations are used to explain obtained measurements. We...

Inverse problems in approximate uniform generation

We initiate the study of inverse problems in approximate uniform generation, focusing on uniform generation of satisfying assignments of various types of Boolean functions. In such an inverse problem, the algorithm is given uniform random satisfying assignments of an unknown function f belonging to a class C of Boolean functions (such as linear threshold functions or polynomial-size DNF formula...

DC resistivity surveys

Using the same colour scheme as the flow diagram above, Figure 2 shows how this conceptual framework applies for DC methods. The energy source is a pair of electrodes that inject a well-known current into the ground at known locations (Fig. 2a). The earth affects this energy because variations in the electrical conductivity of subsurface structures will bend the current flow lines (Fig. 2b). Th...

Data-sparse Approximate Inverse in Elliptic Problems: Green’s Function Approach

hp-HGS strategy for inverse 3D DC resistivity logging measurement simulations

In this paper we present a twin adaptive strategy hp-HGS for solving inverse problems related to 3D DC borehole resistivity measurement simulations. The term ”simulation of measurements” is widely used by the geophysical community. A quantity of interest, voltage, is measured at a receiver electrode located in the logging instrument. We use the self-adaptive goal-oriented hp-Finite Element Meth...