VERTICAL 1-D INVERSION WITH THIN LAYERS OF EQUAL THICKNESS

摘要

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_zz 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_zz output to the measured H_zz. 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_xx output to the measured H_xx. A similar process is used for boreholes with a known inclination. For such an inclined borehole, the two horizontal components H_xx and H_yy are summed to give a horizontal measurement H_xxyy that is independent of tool rotation. The first step uses a ratio of the model H_zz output to the measured H_zz data to obtain an apparent resistivity, and, in the second step, the ratio of the model H_xxyy output and the measured H_xyy 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.