Interval inversion approach for an improved interpretation of well logs

Dobróka, Mihály and Szabó, Norbert Péter and Tóth, József and Vass, Péter (2016) Interval inversion approach for an improved interpretation of well logs. GEOPHYSICS, 81 (2). pp. 163-175. ISSN 0016-8033, ESSN: 1942-2156

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Abstract

The quality analysis of well-logging inversion results has always been an important part of formation evaluation. The precise calculation of hydrocarbon reserves requires the most possible accurate estimation of porosity, water saturation, and shale and rock-matrix volumes. The local inversion method conventionally used to predict the above model parameters depth-by-depth represents a marginally overdetermined inverse problem, which is rather sensitive to the uncertainty of observed data and limited in estimation accuracy. To reduce the harmful effect of data noise on the estimated model we suggest the interval inversion method, in which an increase of the overdetermination ratio allows a more accurate solution of the well-logging inverse problem. The interval inversion method inverts the data set of a longer depth-interval to predict the vertical distributions of petrophysical parameters in a joint inversion procedure. In formulating the forward problem, we extend the validity of probe response functions to a greater depth-interval assuming the petrophysical parameters depth-dependent, and then we expand the model parameters into series by using Legendre polynomials as basis functions for modeling inhomogeneous formations. We solve the inverse problem for much smaller number of expansion coefficients than data to derive the petrophysical parameters in a stable overdetermined inversion procedure. The added advantage of the interval inversion method is that the layer-thicknesses and suitably chosen zone parameters can be estimated automatically by the inversion procedure to refine the results of both inverse and forward modeling. We define depth-dependent model covariance and correlation matrices to compare the quality of the local and interval inversion results. A detailed study using well logs measured from a Hungarian gas-bearing unconsolidated formation demonstrates that the greatly overdetermined interval inversion procedure can be effectively used in reducing the estimation errors in shaly sand formations, which may refine significantly the results of reserve calculation.

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