Petrophysical analysis of inverted well logs includes the identification of bed boundaries and associated bed thickness values, for which it is convenient to define one set of boundaries expressed by all measurements. We have previously shown that an independent source of high axial resolution information (such as an image log) constrains the inversion of density and neutron porosity logs such that bed attributes are obtainable for beds thinner than each measurement’s intrinsic resolution. The accuracy of the inversion process is influenced by the positional uncertainty of each boundary relative to its neighbors, which − for reasons including variations in logging speed − may be several depth increments, noting that changing the position of a boundary by any amount changes the inversion result for many neighboring thin beds. The proposed solution is a fault-tolerant simultaneous determination of optimum bed locations and properties which effectively and efficiently overcomes the inherent nonlinearity of the underlying optimization problem by casting it to a bilinear problem and solving it via a well-defined series of linear problems; it is suitable for beds with apparent dip angles up to about 60 degrees (depending on bed thickness). Pre-computed response functions from tool-specific nuclear particle transport code models are combined with estimates of bed boundary positions picked automatically from high-resolution microresistivity images, each boundary having a distribution of positions. The simultaneous calculation of bed thickness and bed values is rapid, and produces reliable results in beds as thin as 0.075m; this compares to resolutions of about 0.6m for standard porosity logs, and 0.2m for enhanced resolution logs (derived by imposing the resolution of short-spaced detector readings onto standard curves using a continuous normalization process). The method is illustrated for the case of density logs, and validated using model and marker bed data, including for the challenging case of beds with high density contrast relative to adjacent formations. The method is seamlessly applicable to the simultaneous inversion of boundaries and bed values from multiple measurements. As such it provides the means to generate automatically the common boundaries for use in joint analysis.
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