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  • Author or Editor: M. Dobróka x
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Guided waves play important role in the investigation of near surface geological structures. As it is well-known guided waves contain information about the structural- and material parameters of the wave-guide model, so - using the methods of geophysical inversion - these characteristics can be determined by means of the frequency-dependent phase- and group velocity as well as absorption coefficient data. In this paper the approximate horizontal inversion method (Dobróka 1996) is combined with a seismic tomography procedure in order to reconstruct the 3D geometry of the wave-guide structure by means of dispersion data (group traveltimes) of the guided surface waves. The inversion procedure consists of two steps: first the local group velocities are determined at various frequencies by means of tomographic inversion of the group traveltimes, the local dispersion characteristics of the Love- or Rayleigh surface waves are then inverted in the second step. In our investigations a robust SIRT method (Dobróka 1996) is used for tomography and a simple Least Squares algorithm is applied for the inversion of the group velocity data.

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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).

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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.

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Wireline logging surveys are routinely used for the reconnaissance and quantitative characterization of multi-mineral hydrocarbon structures. The interpretation of well-logging data, however, is quite a challenging task, because the conventionally used local inversion procedure becomes either an underdetermined or a slightly overdetermined problem that may result in poor parameter estimation. In order to determine the petrophysical model composed of several parameters, such as specific volumes of matrix components, water saturation, primary and secondary porosity and numerous zone-parameters, in a more reliable way a new inversion methodology is required. We suggest a joint inversion technique for the estimation of model parameters of multi-mineral rocks that inverts data acquired from a larger depth interval (hydrocarbon zone). The inverse problem is formulated assuming homogeneous intervals within the zone to get a highly overdetermined inversion procedure. The interval inversion method has been applied to shaly sandy hydrocarbon reservoirs, in this study, that is used for the estimation of petrophysical parameters of complex reservoirs. Numerical results with synthetic and field data demonstrate the feasibility of the inversion method in investigating carbonate and metamorphic structures.

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All the elements of the Eötvös 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 W z(= g) measured by gravimeters and gravity gradients W zx, W zy, W Δ, W xy measured by torsion balance. Besides vertical gradients W zz measured directly by gravimeters have to be used as reference values at some points. First derivatives of the potential W x, W y (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 Eötvös 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 Eötvöstensor 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 computation.

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In the paper a combined inversion algorithm solving the nonlinear geophysical well-logging inverse problem is presented. We apply a successive combination of a float-encoded Genetic Algorithm as a global optimization method and the well-known linearized Marquardt algorithm forming a fast inversion procedure. The technique is able to decrease the CPU run time at least one order of magnitude compared to the Genetic Algorithm and gives the parameter estimation errors having a few linearized optimization steps at the end of the iteration process. We use depth-dependent tool response equations to invert all the data of a greater depth-interval jointly in order to determine petrophysical parameters of homogeneous or inhomogeneous layers in one inversion procedure. The so-called interval inversion method gives more accurate and reliable estimation for the petrophysical model parameters than the conventional point by point inversion methods. It also enables us to determine the layer-thicknesses that can not be extracted from the data set by means of conventional inversion techniques. We test the combined interval inversion method on synthetic data, and employ it to the interpretation of well logs measured in a Hungarian hydrocarbon exploratory borehole.

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This paper presents a new algorithm for the inversion-based 1D Fourier transformation. The continuous Fourier spectra are assumed as a series expansion with the scaled Hermite functions as square-integrable set of basis functions. The expansion coefficients are determined by solving an over-determined inverse problem. In order to define a quick and easy-to-use formula in calculating the Jacobi matrix of the problem a special feature of the Hermite functions are used. It is well-known, that the basic Hermite functions are eigenfunctions of the Fourier transformation. This feature is generalized by extending its validity for the scaled Hermite functions. Using the eigenvalues, given by this generalization, a very simple formula can be derived for the Jacobi matrix of the problem resulting in a quick and more accurate inversion-based Fourier transform algorithm. The new procedure is numerically tested by using synthetic data.

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In the paper a 2D joint inversion method is presented, which is applicable for the simultaneous determination of layer thickness variation and petrophysical parameters by processing well-logging data acquired in several boreholes along the profile. The so-called interval inversion method is tested on noisy synthetic data sets generated on hydrocarbon-bearing reservoir models. Numerical experiments are performed to study the convergence and stability of the inversion procedure. Data and model misfit, function distance related to layer thickness fitting are measured as well as estimation errors and correlation coefficients are computed to check the accuracy and reliability of inversion results. It is shown that the actual inversion procedure is stable and highly accurate, which arises from the great over-determination feature of the inverse problem. Even a case study is attached to the paper in which interval inversion procedure is applied for processing of multi-borehole logging data acquired in Hungarian hydrocarbon exploratory wells in order to determine petrophysical parameters and lateral changes of layer thicknesses.

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A new L 2 norm joint inversion technique is presented and combined with the series expansion inversion method applied for different simulated erroneous Vertical Electric Sounding (VES) data sets over a complicated two dimensional structure. The applied joint inversion technique takes into consideration the complete form of the likelihood function. As a result there is no need to apply input weights to the individual objective functions. The model consists of three layers with homogeneous resistivities. The first layer boundary is a horizontal plane, the other is a two dimensional laterally varying surface. For the VES inversion the exact data sets were calculated by finite difference method, one in strike direction and the other in dip direction. These data sets were contaminated with normally distributed random errors. During inversion the second layer boundary function was determined. For comparison individual and joint inversion examples were calculated for the two data sets. The best model parameter estimate result was produced by the method of automated weighting.

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