Vertical 1-d inversion with thin layers of equal thickness

Abstract

Measurements made by a multicomponent logging tool in a borehole are inverted to obtain horizontal and vertical resistivities of a formation traversed by the borehole. The model includes layers of equal thickness, each layer having a horizontal resistivity and a vertical resistivity. For a vertical borehole, the inversion is done by first iteratively obtaining the horizontal resistivities of the layer using the H component of the data wherein in successive steps of the iteration, the horizontal resistivity for each layer is multiplied by a ratio of a model H output to the measured H . The vertical resistivity model is set equal to the derived horizontal resistivities and the iterative process is repeated using the ratio of the model H output to the measured H . A similar process is used for boreholes with a known inclination. For such an inclined borehole, the two horizontal components H and H are summed to give a horizontal measurement H that is independent of tool rotation. The first step uses a ratio of the model H output to the measured H data to obtain an apparent resistivity, and, in the second step, the ratio of the model H output and the measured H data are used along with a known relationship between the apparent resistivity and the horizontal and vertical resistivities in an iterative manner. No Jacobians or gradients are necessary in the method, so that computational times are small relative to prior art gradient methods.