Interval inversion of multiwell logging data for estimating laterally varying petrophysical parameters and formation boundaries

The present paper introduces a Legendre polynomials based interval inversion method for processing multi-borehole logging data. The method allows the determination of lateral changes of the layer-thicknesses together with the vertical and lateral variations of petrophysical parameters along a 2D cross-section of several boreholes. The method is assessed using noisy synthetic measurements of a petrophysical model made of two-layers structure related to hydrocarbon bearing formations. The numerical experiments aided to investigate the stability and convergence of the 2D interval inversion procedure. To ensure the accuracy and reliability of the inversion results, the misfit of data and model distance are tested, beside the calculation of estimation errors and correlation coefficients. A large amount of input data relative to the number of unknowns results in a high overdetermined ratio, consequently more precise estimates are obtained in stable and convergent procedure than in conventional local (1D) inversion schemes. The feasibility of the 2D interval inversion method is shown by analysing in-situ well logging data acquired in four wells situated in an Egyptian hydrocarbon field.