Wellsite quasi-2D inversion of array resistivity logging data

New generation galvanic array tools can provide high-resolution resistivity logging data in conductive borehole environments. Fast and accurate interpretation of these array data is required for timely decisions on well completions. Due to the high nonlinearity between the galvanic data and the earth formation, inversion is necessary in interpreting resistivity logging data. A typical array tool data set, however, consists of several tens of measurements at each logging depth, acquired at a dense sampling of 4 cm. Such a large amount of data makes traditional inversion-based interpretation very slow and thus it is impossible to deliver the results to customers at the well site.

In this paper, we develop a quasi-2D wellsite deliverable inversion algorithm that utilises trained back-propagation (BP) neural networks as forward modelling engines. We first reduce the 2D data into quasi-1D data via numerical focusing. We further simplify the quasi-1D data by performing borehole correction. The numerically focused and borehole effect corrected data are then inverted to provide information about the 2D resistivity structure. Synthetic tool responses are first generated over a set of cylindrically 1D earth models covering a large range of resistivity contrasts and invasion lengths. The earth model parameters are input to the neural network as the stimuli while the associated responses are used as the desired neural network output. The neural network is then trained to model the tool response. After validation, the trained neural network is applied in an inversion algorithm as a forward modelling engine that combines the computation of the potentials and numerical focusing into a single step and allows the inversion to be performed at real time. We tested our inversion algorithm on both synthetic and field data. The numerical examples show that this fast inverse algorithm is a useful tool in providing information about the formation resistivity at wellsite.