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The response characteristics of a combination of hole-centered electric logging tools in a variety of borehole conditions can be obtained by means of impedance values as entries of a matrix resulting from measurements over a series of depth increments, utilizing an array of 2M-1 electrode assemblies

The response characteristics of a combination of hole-centered electric logging tools in a variety of borehole conditions can be obtained by means of impedance values as entries of a matrix resulting from measurements over a series of depth increments, utilizing an array of 2M-1 electrode assemblies of equal incremental spacing positioned on a rigid mandrel. While the array moves continuously along the borehole, current is continuously emitted from the centrally located current electrode allowing the impedance matrix to be formed by the principle of linear superposition in terms of voltage and voltage difference measurements between adjacent electrodes. The impedance matrix is inverted and used to generate a set of tool responses, which when properly compared to a set of tool responses previously generated by computer simulation and addressable by sets of borehole parameters and calibration factors, allows the corresponding borehole conditions to be deduced from the measured data.

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Method of synthesizing the true response characteristics of a combination of different hole-centered electric logging tools in a variety of difficult borehole conditions as provided by (1) determining impedance values of an earth formation penetrated by a borehole filled with a drilling mud of resis

Method of synthesizing the true response characteristics of a combination of different hole-centered electric logging tools in a variety of difficult borehole conditions as provided by (1) determining impedance values of an earth formation penetrated by a borehole filled with a drilling mud of resistivity (Rm), and forming impedance matices with said impedance values, and (2) selectively manipulating the impedance values of the impedance matrixes so as to synthesize operations of different hole-centered tools over an associated depth increment with surprising accuracy, wherein each of said impedance matrices is associated with a matrix gather indexed to one of a series of finite, overlapping depth scan increments of the formation measured along the borehole, each scan increment being dependent on the array length L of an electrode array to define shallow and deep depth markers as well as being centrally indexed to the depth in the borehole of a mid-central electrode assembly of the array at the time of data collection, and thereby provide a true indication of the formation resistivity (Rt) even though the formation is interspaced from the borehole by an invaded zone of resistivity (Rxo) of unknown lateral extent due to drilling mud filtrate invasion, comprising the steps of: (i) calibrating an array of hole centered M electrode assemblies of equal incremental electrode spacing “a”to obtain sets of calibration factors normalized to known voltage patterns in a known resistivity zone of response, said electrode assemblies havinq a known internally ordered numbering index, said sets of calibration factors each being addressable as a function of borehole conditions including said difficult borehole conditions as well as by particular synthetic computer focused array type; (ii) positioning a field array in the borehole, said array comprising a mid-central electrode assembly comprising a current electrode and a potential electrode, and a series of additional electrode assemblies each comprising a potential measuring electrode only, the absolute depth of at least one electrode assembly being continuously known with respect to a predetermined depth datum level measured from the earth\s surface; (iii) continuously moving the array along the borehole, and continuously injecting current of a known value from the current electrode of the mid-cental assembly, through the drilling mud of resistivity (Rm) and the invaded zone of resistivity Rxo and thence into the formation of resistivity Rt; (iv) during current injection, measuring the absolute potential at each potential electrode as well as the potential differences between adjacent pairs of potential electrodes in a rapid manner wherein the potential measurements can be indexed to common logging stations of a series of equi-spaced logging stations located along the borehole having a spacing incremental distance of “a”where “a”is the distance between adjacent electrode assemblies; (v) calculating impedance values from the measured absolute and difference potential values and their associated injection currents, each value being indexed to said known internal indexing numbers of active current and potential electrodes used in the measurements; (vi) reindexing the impedance values into impedance entries of a series of overlapping matrix gathers, each gather being associated with a predetermined segment of said formation equal in vertical extent, to M logging stations, and comprising M×M impedance entries where 2M-1 the largest number of the numbering index of the electrode assemblies comprising said array and in which the ratio of the number of difference impedance entries to absolute entries is about M-1:1; (vii) inverting each to form inverted oberlapping matrix gathers; (viii) generating computer focused response parameters using voltage patterns of step (i) and said inverted overlapping matrix gathers; (ix) searching sets of calibration factors of step (i) whereby the difficult borehole condition is deduced even in the presence of high true resistivity to mud resistivity contrasts and irrespective of the fact that synthetic sets of potential patterns have been used as initiators of the subsequently generated computer focused response parameters.