3-D Resistivity Forward Modeling And Inversion Between Two Mine Roadways

Especially, the water-bearing structures in coal working face is more dangerousto production of the coal mine. We have developed a three-dimensional conjugategradients(CG) forward modeling and inversion algorithm to resolve interpretation ofanomaly in coal working face between two mine roadways.In this paper, we have deduced differential equation of three-dimensionalpoint-source between two mine roadways based on the basic theory of stable currentfield and through the volume divergence of space, finally the large and sparse linearequations about potential are obtained. It is need huge computer memory and poorcomputational efficiency, if we solve the linear equation systems by decompositiondirectly. The incomplete Cholesky decomposition for preconditioning conjugategradient method is used to solve the linear equation systems. In the meantime, the rowindex of sparse storage mode to store coefficient of linear equation systems is used toreduce memory requirements and accelerate forward calculation, which provided asolid foundation for three-dimensional resistivity inversion between two mineroadways.For three dimensional inversion problem, the key is the calculation of Jacobimatrix G. Directly calculating the Jacobi matrix G and the inverse matrixTG G is verydifficult, meanwhile it is need very huge memory requirements to store G andTG G.The three-dimensional conjugate gradients inversion algorithm only requires theresults of the Jacobi matrix G and its transposeTG multiplied by a vector,i.e. Gx andTG y, respectively. So, we are able to bypass the actual computation of theJacobi matrix G and the inverse matrixTG G. And the sum of integrated squares of themodel’s first derivative with respect to x, y and z is taken as the smooth factor torestrict the model. The Lagrange operator is determined by repeated experiments. Thisinversion algorithm can be used to invert potential and apparent resistivity data ofpole-pole array and pole-dipole array. The synthetic examples demonstrate thevalidity and stability of the three-dimensional conjugate gradients inversion algorithmto invert resistivity data between two mine roadways.