Fast inversion of triaxial induction data in dipping crossbedded formations

Abstract

The tensor type measurements acquired by triaxial induction tools greatly expand the data sensitivity to formation properties, enabling the extraction of not only the resistivity but also the resistivity anisotropy and dip of the formation. The first and most popular anisotropic resistivity model for the interpretation of triaxial induction data is the transversely isotropic (TI) model in which the lamination planes are assumed to be parallel to the bedding planes. Image data and outcrops indicate that crossbedding occurs in multiple depositional environments. Modeling results have shown that the presence of crossbedding can have a considerable effect on the response of triaxial induction. Therefore, using the TI model in crossbedded formations can cause large errors in the estimation of the formation resistivity and dip. However, the strong effect suggests the possibility of performing a crossbed interpretation with triaxial induction data. We have developed an inversion method based on a fast forward solver for a crossbedded formation to automatically determine the anisotropy dip and azimuth in addition to the horizontal and vertical resistivities for each bed in the formation. The high speed and low memory requirement of the 2D Fourier transform-based forward solver allow for a pixel-based parameterization in the inversion. A weighted [Formula: see text]-norm regularization method is developed to enhance the resolution of the reconstructed model and suppress the effect of noise. The Hessian matrix is used to dynamically determine the weights of the stabilizers for the horizontal and vertical resistivities and the anisotropy dip and azimuth. The inversion delivers one bedding dip and multiple bed-to-bed anisotropy dips over the zone of interest. The method is tested on synthetic models and field data sets. Results indicate that in the presence of crossbedding, the method is able to distinguish between bedding dip and anisotropy dip, and it provides better resistivity and dip estimations.