Data processing method developments using TAU-transformation of time-domain IP data I. Theoretical basis

The paper presents the theoretical basis of data processing method developments based on TAU-transform of the time-domain IP curves and some approximate solutions of the TAU-transform using linear system of equations, Fourier transform and inverse theory.The interpretation ways and results of field measured IP data will be presented in Part II of this paper (Turai 2011)

Determination of vertical gradients of gravity by series expansion based inversion

All the elements of the E¨otv¨os tensor can be measured by torsion balance, except the vertical gradient. The knowledge of the real value of the vertical gradient is more and more important in gravimetry and geodesy. Determination of the 3D gravity potential W(x, y, z) can be produced by inversion reconstruction based on each of the gravity data Wz(= g) measured by gravimeters and gravity gradients Wzx, Wzy, W∆, Wxy measured by torsion balance. Besides vertical gradients Wzz measured directly by gravimeters have to be used as reference values at some points. First derivatives of the potential Wx, Wy (can be derived from the components of deflection of the vertical) may be useful for the joint inversion, too. Determination of the potential function has a great importance, because all components of the gravity vector and the elements of the full E¨otv¨os tensor can be derived from it as the first and the second derivatives of this function. The second derivatives of the potential function give the elements of the full E¨otv¨ostensor including the vertical gradients, and all these elements can be determined not only in the torsion balance stations, but anywhere in the surroundings of these points. Test computations were performed at the characteristic region of a Hungarian plate area at the south part of the Csepel Island where torsion balance and vertical gradient measurements are available. There were about 30 torsion balance, 21 gravity and 27 vertical gradient measurements in our test area. Only a part of the 27 vertical gradient values was used as initial data for the inversion and the remaining part of these points were used for controlling the computatio

The pressure dependence of acoustic velocity and quality factor — New petrophysical models

In this study we introduce new rock physical models which describe the pressure dependence of seismic velocity and quality factor. The models are based on the idea (accepted in the literature) that microcracks in rocks are opened and closed under the change of pressure. The models were applied to acoustic P wave velocity data measured on core samples originated from oil-drilling wells (27 samples) and also seismic velocity and quality factor data sets published in international literature. During the measurements the pulse transmission and the spectral ratio techniques were used. Measurements were carried out at various incremental pressures and parameters of the models were determined by linearized inversion methods. The calculated data matched accurately with measured data proving that the new rock physical models apply well in practice

Robust reservoir identification by multi-well cluster analysis of wireline logging data

A novel clustering method is applied to well logs for improved rock type identification in hydrocarbon formations. For grouping the objects in the multi-dimensional data space, we propose a Most Frequent Value (MFV) based clustering technique applied to natural gamma ray, bulk density, sonic, photoelectric index, and resistivity logs. The MFV method is a robust estimator, which assists in finding the cluster centers more reliably than a more noise sensitive K-means clustering approach. The result of K-means cluster analysis highly depends on the choose of the initial centroids. To reduce the risk of inappropriately chosen starting values, we apply a histogram-based selection method to give the best position of the initial cluster centers. We assure the robustness of the solution by calculating the centroid as the MFV of the cluster elements and defining the overall deviation of cluster elements from the center by a weighted Euclidean (Steiner-) distance. The proposed workflow relies on a fully automated weighting of the cluster elements, which does not require a constraint on the statistical distribution of the observed variables. The processing of synthetic data shows high noise rejection capability and efficient cluster recognition even beside considerable amount of outlying and missing data; the accuracy is measured by the difference between the estimated and the exactly known distribution of cluster numbers. The clustering tool is first applied to single borehole data, then the procedure is extended to multi-well logging datasets to reconstruct the multi-dimensional spatial distributions of clusters revealing the lithological and petrophysical characteristics of the studied formations. A large in situ dataset acquired from several boreholes traversing Hungarian gas-bearing clastic reservoirs of Miocene age is analyzed. The accuracy of the field results is confirmed by core permeability measurements, independent well log analysis and a gradient metrics characterizing the noise rejection capability of the clustering method