Vertical Response Function Research Articles

An iterative inversion of Dual Induction Tool logs from thin-bedded sandy\u2013shaly formations of the Carpathian Foredeep using a modified simulated annealing method

In thin-bedded sandy–shaly Miocene formations of the Carpathian Foredeep, the main source of errors in gas saturation evaluation is the underestimation of resistivity of thin, hydrocarbon-bearing beds, which is the result of the low vertical resolution of induction logging tools. This problem is especially visible in older boreholes drilled in times where the Dual Induction Tool (DIT) was the primary induction tool used for determining the formation resistivity, and in shallowest depth intervals of newer boreholes where the DIT was used instead of newer array tools for cost-saving reasons. In this paper, we show how a global inversion algorithm was used to improve the vertical resolution of DIT logs. Our implementation of an iterative inversion utilizes a one-dimensional formation model, vertical response functions of the DIT, and a modified simulated annealing algorithm to determine the true vertical distribution of the formation resistivity. The algorithm was tested on resistivity logs recorded in a borehole drilled in the Carpathian Foredeep in Poland, where the DIT and the High-Resolution Array Induction (HRAI) tool were run in the same depth interval.

Evaluation of laminated shaly sand sequences in Ahwaz oil field using (via) high-resolution square logs

Thinly bedded and laminated shale-sand sequences are very common in most of the producing formations in Iran. Historically, traditionally well logging methods such as conventional resistivity measurement is employed to evaluate pay intervals in order to extract information about hydrocarbon saturation. However, there is the practical matter of resolution of these methods to detect thin laminated shaly sand layers. In order to cope with this limitation, other technique such as: high-resolution method should be utilized. For doing this method, we receive low-resolution logs and a high-resolution log from a well logging tool that is disposed in a wellbore which has laminated shaly sand layers. Firstly, square log is produced then these logs are convolved with vertical response function of well logging tools to generate constructed log. The constructed logs are compared with low-resolution logs, if these two logs are matched we choose that square logs as optimum square logs and analyze them. But if these two logs do not match, the square logs undergo interactive refinement then these refined logs are subsequently convolved with a vertical response function of the well logging tool thereby producing a constructed log. Then these constructed logs compare with low-resolution logs. This work repeated until these logs are matched and the optimum square logs are chosen. High-resolution square log method is an iterative method, time consuming and also has very mathematical calculations because we developed a computer program with MATLAB software which can do all these works with high accuracy and low time.

An absolute method of vertical seismometer calibration by reference to a falling mass with application to the measurement of the gain

Abstract We measure the gain of a vertical seismometer by simultaneously recording the output of the seismometer and repeatedly measuring the displacement between the seismometer and a free-falling mass in a vacuum. The falling object provides an inertial reference frame. By comparing the ground motion measured by the seismometer with the independent record of displacement between the seismometer and inertial space, we obtain the gain. It is an absolute measurement of the gain relative to the local Lorentz reference frame. Bootstrap error estimates show that a high precision in the estimate of the gain can be obtained with a small number of individual drops. The method derived can be extended to multi-parameter searches of the vertical response function. The technique is also shown to reduce noise in absolute gravity measurements due to ground noise. Finally, we discuss the potential for replacing vibration isolation schemes in absolute gravity systems with digital noise reduction.

A New Resolution Index for Resistivity Electrode Arrays

Historical arguments about the ‘sensitivity’ of an electrode array to different volume elements in the subsurface have been satisfied by the concept of signal contribution sections, although they address only homogeneous Earths. Similar arguments on the ‘depth of investigation’ of various electrode arrays have been put to rest by the concept of effective depth. The effective depth is a well-defined characteristic of the vertical response function of an electrode array obtained by integrating horizontal planes of the corresponding signal contribution section. Debate on the ‘resolution’ of various electrode arrays has not reached a firm conclusion. The ranking of arrays in order of resolving power varies according to the definition of resolution. A new resolution index is proposed here. It builds on the successful effective depth concept by introducing new concepts called effective thickness and extended depth. The index is quantified by formulating the cumulative vertical response function of a general electrode array. The dipole-dipole arrays are found to have the best vertical resolution, and the Schlumberger array is found to be better than the conventional Wenner array.

Eliminating the Rugosity Effect From Compensated Density Logs by Geometrical Response Matching

Summary A theoretical and experimental effort to understand the effects of borehole rugosity on individual detector responses yielded an improved method of processing compensated density logs. Historically, the spine/ribs technique for obtaining borehole and mudcake compensation of dual-detector, gamma-gamma density logs has been very successful as long as the borehole and other environmental effects vary slowly with depth and the interest is limited to vertical features broader than several feet. With the increased interest in higher vertical resolution, a more detailed analysis of the effect of such quickly varying environmental effects as rugosity was required. A laboratory setup simulating the effect of rugosity on Schlumberger Litho-DensitySM tools (LDT) was used to study vertical response functions. These functions were used to derive matching filters, enabling a significant improvement in the compensated log response in the presence of rugosity. The data served as a benchmark for the Monte Carlo models used to generate synthetic density logs in the presence of more complex rugosity patterns. The results show that proper matching of the two detector responses before application of conventional compensation methods can eliminate rugosity effects without degrading the measurement's vertical resolution. The accuracy of the results is as good as that obtained in a parallel mudcake or standoff with the conventional method. Application to both field and synthetic logs confirmed the validity of these results.

Introduction to the Phasor Dual Induction Tool

Barber, T.D., Schlumberger Well Services Summary Automatic environmental corrections to the induction log have been an elusive goal for many years. Recent work in induction response has been combined with modern signal processing theory to derive an automatic shoulder-effect correction algorithm, but the method requires measurement of the induction quadrature or X-signals. The Phasor* dual induction tool incorporates these Phasor* dual induction tool incorporates these measurements and makes automatic shoulder corrections for induction a reality. Introduction The dual induction-electrode logging tool has evolved into the primary logging tool for openhole formation evaluation. The induction log, however, must be corrected by hand for environmental distortions, such as shoulder effect and borehole effect. Although the environmental distortions are fully understood and predictable, automatic correction algorithms have not been successful. Recent work on computing the response of the induction tool in realistic formation models, combined with modern signal processing theory, has allowed the development of a nonlinear deconvolution technique that corrects the induction log for shoulder effect over the full range of formation conductivities. This algorithm, however, requires additional measurements that are not made with the present commercial tools. These measurements are the induction quadrature signals. or X-signals. The introduction of digital telemetry to well logging has opened up new data channels, and the Phasor dual induction tool has incorporated new measurements that use these new channels. The most important new measurements are the X-signals on both deep induction (ID) and medium induction (IM) arrays, which are required by the new shoulder-effect algorithm. In addition, quality control of the log is improved by continuous calibration along with independent measurements of the calibration signals. Shoulder Effect and Deconvolution Shoulder effect is the response of an induction tool to distant conductive beds when in a relatively nonconductive bed. This is illustrated in Fig. 1, which is a computed simulation of an Oklahoma field log using Anderson's method. In the resistive zones, the ID raw log reads too low, even in the thicker beds. This fact implies that, for the ID array, a "thick bed" is one much thicker than any shown on this log. The traditional processing, labeled in Fig. I as "panel," squares up the corners of the raw log and leaves the center-bed readings unchanged. Development of deconvolution filters has been simplified by modern signal processing theory. A well-known technique is to tailor the response in the frequency domain after Fourier-transforming the spatial response function. The deconvolution filter is computed with the Remez algorithm. Such a filter was derived for the ID array using its response in low-conductivity formations, with emphasis on low spatial frequency response to correct the shoulder effect of the array. The use of this filter is illustrated in Fig. 1 by the curve labeled "deconvolved. "The log reading in the high-resistivity beds is much closer to the true resistivity than either the raw or panel logs. panel logs. During the 1950's, a lot of work was done on the induction deconvolution problem, with Doll and others making significant contributions. The commercial result of this work was the three-point filter shown as the panel log in Fig. 1. Why is a more sophisticated filter not used for induction? The answer to this is in the nature of the induction response itself. The induction signal does not change linearly with formation conductivity, nor is the response function that maps the formation conductivity into the measured signal a constant function. In fact, Gianzero and Anderson demonstrate that the response function is different at every point in the log. This variation of the response with formation conductivity is referred to as "skin effect" or "propagation effect."Because the induction response is not constant, at higher conductivities the deconvolution filter that worked well at low conductivities no longer suffices. The induction response function has changed at higher conductivities from the one for which the filter was computed. Fig. 2 shows a computed log using the same resistivity contrasts and bed thickness as the formation of Fig. 1, but with all magnitudes shifted down one decade in resistivity (or up one decade in conductivity). Clearly, the deconvolution filter no longer works at these resistivities. Induction Response The response of an induction tool in a layered formation can be computed by solving Maxwell's equations for the fields from an induction transmitter coil in the given formation geometry. The usual methods of solution lead to an equation involving a volume integral over all regions of space in which induced currents are flowing. Gianzero and Anderson show that the resulting integrand, suitably normalized, is in the form of a mapping function. They write the kernel of the integration in the form g(z, a) and call it the vertical response function. JPT p. 1699

Statistical determination of geophysical well log response functions

The vertical response function of induction logging tools is shown to be derivable from a power spectrum analysis of the measurement. The vertical response function is the one‐dimensional sequence of weights that characterizes how the tool combines the rock conductivities along the borehole to form an output called the apparent conductivity; it is the system impulse response. The value of knowing this function lies in the possible use of filter theory to aid in data processing and interpretation. Two general notions establish the framework for the analysis. The first is that logging is a linear, convolutional operation. Second, the earth’s conductivity profile forms a stochastic process. The probabilistic component is fleshed out by reasonably based assumptions about the occurrence of bed boundaries and nature of conductivity changes across them. Brought together, these tenets create a characterization of the conductivity sequence that is not a stationary process, but rather is intrinsic, as defined in the discipline of geostatistics. Such a process is described by a variogram, and it is increments of the process that are stationary. The connection between the power spectrum of the measurement and the system response function is made when the convolutional model is merged with the conductivity process. Some examples of induction log functions are shown using these ideas. The analysis is presented in general terms for possibly wider application.