Patent GB-1405311-A (GB)
Title: Method of generating subsurface characteristic models
IPC: G01V3/38
Filed: 1972-09-06
Abstract: 1405311 Data processing SCHLUMBERGER INLAND SERVICES Inc 6 Sept 1972 [7 Sept 1971 (4)] 41346/72 Heading G4A A subsurface characteristic model consistent with readings taken by a well-logging device with a known response characteristic is machine generated by selecting a trial model of the subsurface characteristic within a given depth interval, generating a set of simulated measurement values by applying the response characteristic of the well-logging device to the model, comparing the simulated and actual measurement values and modifying the model according to the result of the comparison. The logging device may measure conductivity of the surrounding subsurface, a measurement made at any given depth level being influenced by the characteristics of the subsurface at neighbouring depth levels. The model generated is an approximation to the true conductivity of the subsurface at the various depth levels of the well. In a first embodiment, the log measurements taken at unit intervals of depth are used to compute the variance at each depth level z and the boundaries BB between beds of the model are defined at points of maximum variance. To complete the trial model, the simulated conductivity <SP>#</SP> # (J) of each model bed J is obtained by (a) selecting the maximum measured value of # if the gradient of the log is positive and negative at the upper and lower boundary respectively, (b) selecting the minimum measured value of # if the gradient of the log is negative and positive at the upper and lower boundary respectively, or (c) selecting the measured value of # at the point of minimum variance if the gradients of the log at the upper and lower boundaries are equal. For each unit depth bed in the main part of the depth interval over which the log was   taken a simulated measurement value #L(z) is calculated as the sum over all J of terms G(z, J), ##(J) where G(z, J) is the sum of weighting factors appropriate to the contribution made to the measurement value L(z) by unit beds in the same and neighbouring model beds J, according to the response characteristic of the   log. The simulated measurement values #L(z) for model beds near the ends of the depth interval are calculated as the sum over all J of G(z, J).##(J)+D(z) where D(z) is the sum of terms representing the weighted effect of unit beds in the end beds of the model on the unit bed z. From the simulated and actual measurement values #L(z) and L(z) a set of error values   E(z)=ln[#L(z)/L(z)] is calculated and an error function #=#/E(z)/is obtained for all z except in the end beds of the model. The model is then modified in successive iterations to minimize the error function #, for example by calculating the conjugate gradient direction of #, recalculating # after each of a number of trial steps in that direction and selecting the optimum step size Mb obtain new simulated values ##<SP>1</SP>(J)=##(J)+ (- ##/##(J)).Mb for use in the next iteration. In an alternative embodiment matrix elements G(J, Jy) each representing the effect of a model bed Jy on a single measurement point at or approximately at the centre of a model bed Jx are derived as the sum over all z in bed Jy of W(Zx, Zy). Simulated measurement values #L(J)=###(J)G(J, Jy) are calculated, error and values E(J)=L(J)-#(J) are used to obtain a new model in which ##<SP>1</SP>(J)=#(J)+E(J)/G(J, Jy). In another embodiment, the initial model is obtained by assigning the measured values of #(z) to the unit beds, calculating simulated measurement values #L(z) = ### over all relevant unit beds, deriving error values E(z)= L(z) - #L(z), and, for all values of E(z) exceeding a given tolerance, modifying the values of #(z) to form an enhanced model in which ##(z) = #(z) + #E(z) where # is chosen to ensure high probability of convergence. Successive iterations are performed until the desired degree of convergence is reached or a given number of iterations has been completed. A further embodiment involves calculation of #L(z) and E(z) for a particular depth level z as in the preceding embodiment and the value of E(z)   is apportioned to the unit beds affecting #L(z) according to the weighting factors of the response characteristic to obtain modified values of # for those beds. A similar step is performed for the next depth level (z+1), that one of the modified values #<SP>1</SP> obtained in the preceding step and not required in the new step. The stored values #<SP>1</SP> represent an enhanced model for the next iteration of the above steps. Algorithms for performing the above methods are described.