Improvement and application of Jacobian matrix for 2D resistivity sounding fast inversion
Naibin Li
Abstract
Naibin Li
Abstract
In the traditional resistivity sounding method,the pole distance increases little by little with equal logarithm interval,which brings on grid irregular elements.In comparison with the HD measured configuration,it can't make full use of all poles.It takes much longer time to inverse only several sounding points,and in the calculation of partial derivatives Jacobian matrix.So in the inversion,the partial derivatives of the apparent resistivity is calculated with respect to model resistivity by means of the relationship between the source and receiver locations and Broyden's method,to save the inversion time and satisfy the inversion precision.It is proved that the algorithms of this paper is workable through inversing the modeling data and practical data.
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In the traditional resistivity sounding method,the pole distance increases little by little with equal logarithm interval,which brings on grid irregular elements.In comparison with the HD measured configuration,it can't make full use of all poles.It takes much longer time to inverse only several sounding points,and in the calculation of partial derivatives Jacobian matrix.So in the inversion,the partial derivatives of the apparent resistivity is calculated with respect to model resistivity by means of the relationship between the source and receiver locations and Broyden's method,to save the inversion time and satisfy the inversion precision.It is proved that the algorithms of this paper is workable through inversing the modeling data and practical data.
Key concepts: Jacobian matrix and determinant, Inversion (geology), Depth sounding, Electrical resistivity and conductivity, Logarithm, Inverse, Matrix (chemical analysis), Mathematical analysis