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 accurate possible 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 have suggested 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 have extended the validity of probe response functions to a greater depth interval assuming the petrophysical parameters are depth dependent, and then we expanded the model parameters into a series using the Legendre polynomials as basis functions for modeling inhomogeneous formations. We solved the inverse problem for a 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 inverse and forward modeling. We have defined 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 revealed 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.

A novel clustering method is applied to well logs for improved rock type identification in hydrocarbon formations. For grouping the objects in the multi-dimensional data space, we propose a Most Frequent Value (MFV) based clustering technique applied to natural gamma ray, bulk density, sonic, photoelectric index, and resistivity logs. The MFV method is a robust estimator, which assists in finding the cluster centers more reliably than a more noise sensitive K-means clustering approach. The result of K-means cluster analysis highly depends on the choose of the initial centroids. To reduce the risk of inappropriately chosen starting values, we apply a histogram-based selection method to give the best position of the initial cluster centers. We assure the robustness of the solution by calculating the centroid as the MFV of the cluster elements and defining the overall deviation of cluster elements from the center by a weighted Euclidean (Steiner-) distance. The proposed workflow relies on a fully automated weighting of the cluster elements, which does not require a constraint on the statistical distribution of the observed variables. The processing of synthetic data shows high noise rejection capability and efficient cluster recognition even beside considerable amount of outlying and missing data; the accuracy is measured by the difference between the estimated and the exactly known distribution of cluster numbers. The clustering tool is first applied to single borehole data, then the procedure is extended to multi-well logging datasets to reconstruct the multi-dimensional spatial distributions of clusters revealing the lithological and petrophysical characteristics of the studied formations. A large in situ dataset acquired from several boreholes traversing Hungarian gas-bearing clastic reservoirs of Miocene age is analyzed. The accuracy of the field results is confirmed by core permeability measurements, independent well log analysis and a gradient metrics characterizing the noise rejection capability of the clustering method.