Summary In this paper the multi-exponential petrophysical model describing the pressure dependence of acoustic P wave quality factor is presented. The new model considers two or more physical mechanisms (e.g. the closure of pore volume or microcracks, or friction on grain boundaries etc.) responsible for the pressure dependence of propagation characteristics (absorption coefficient or quality factor). Using the model equation as forward modeling formula, a global optimization algorithm (Metropolis algorithm) was applied to solve the inversion problem and to determine the petrophysical parameters of the model. With spectral inversion method the characteristic pressures belong to the various internal mechanisms which influences the pressure dependence of quality factor was calculated also. The global inversion results proved that the calculated data matched accurately with measured data, so the new model was tested with success on laboratory measured data.

Summary In this paper with the further development of our previously published single relaxation model (SRM), a new petrophysical model (the double relaxation model - DRM) describing the hysteretic pressure dependence of acoustic P wave velocity is presented. Since it is likely that several relaxation mechanism occur in the rock at the same time, the new model considers two or more physical mechanisms (e.g. the closure of pore volume or microcracks or friction on grain boundaries etc.) responsible for the pressure dependence of propagation velocity. Using the model equation as forward modeling formula, a global optimization algorithm (Simulated Annealing) was applied to solve the inversion problem and to determine the petrophysical parameters of the model. Inversion results proved that the calculated data matched accurately with measured data, so the new model was tested with success on laboratory measured data. On the other hand one can see that the new DRM model resulted in a more accurate fit compared to the SRM model.

Summary The rocks response as perfectly elastic materials in case of rapidly changing stresses. With the assumption of the Hooke body, the elastic moduli describe how rocks resist different deformations. Present investigations covered the examination of pressure dependence of compressional, shear and Young’s moduli. As they can be calculated from the acoustic wave velocities (longitudinal and transverse) it is important to know accurately the velocity-stress function. Therefore the authors developed a petrophysical model, which gives the physical connection between the acoustic velocities and stresses. After estimating the model parameters by joint inversion, where the rock physical parameter is the common parameter, the velocities can be calculated at any arbitrary stresses and the pressure dependent elastic moduli can be derived. To prove the applicability of this method, we measured P and S wave velocities on sandstone samples with an automatic acoustic test system under uniaxial load. This paper includes one sample from these measurements together with literature data of a Berea sandstone sample. The results show that the misfits between measured and calculated data are small, the model can be applied well in practice.

Summary It is well known that acoustic wave propagation under pressure is very nonlinear and the elastic properties of rocks are hysteretic, which behavior is important for mechanical understanding of reservoirs during depletion. Pressure strongly influences the elastic parameters of rocks, thus wave velocities too. In this study longitudinal and transverse wave velocities measured in laboratory on sandstone samples under pressure are presented. The uniaxial loading of the samples was carried out by an automatic acoustic test system. Measurement data were processed by a joint inversion technique based on the developed petrophysical model which describes the relationship between acoustic P/S wave velocities and pressure for loading and unloading phases. After Birch we assume that the main factor determining the pressure dependence is the closure of pores. The advantage of the model is that it is not based on simple curve fitting, but gives physical explanation for the process with three-parameter exponential equations. The quality checked joint inversion results showed that the misfits between measured and calculated data are small, proving that the proposed petrophysical model can be applied well in practice.

Summary The paper presents the TAU-Transform of the Time-Domain IP curves and gives an approximate solution for TAU-transformation using inverse problem theory. A method for estimation of the type and the measure of soil contaminations will also be introduced. The determination of the contamination type (metallic or chemical) comes from the time constant spectra. The estimation of the soil contamination is based on the waited amplitude values of the time constant spectra. The application of the method is demonstrated in a contaminated industrial area in Hungary.

The methods of in-mine seam-sounding and transillumination (geoelectric tomography) for the detection of tectonic disturbances of coal seams were developed by the Department of Geophysics of the University of Miskolc in the 1970–80’s with the effective support of the former “Borsod” Coal Mines Ltd.The paper gives an overview about the theory of seam-sounding and a special geoelectric tomographic inversion, and introduces the in-mine geoelectric seam-sounding and transillumination measurement systems using vertical electrode dipoles. In the second part the paper, the results of an in-mine geoelectric measurement are presented, which was carried out in order to detect tectonic disturbances of the Miocene aged coal seams situated in Slovakia. As results of the geophysical investigation, the authors forecasted the tectonic features in the coal seam. The company confirmed the results by independent information about seam disturbances and tectonic features arising from the excavation of the investigated area.

In this paper a new theory is developed which describe the pressure dependence of seismic velocity and deals with acoustic hysteresis. The model is based on the idea (accepted in the literature) that the microcracks closed during pressurization do not reopen completely during depressurization. The model was applied to acoustic P wave velocity data sets measured on core samples originated from oil-drilling wells. The model parameters of the petrophysical model were determined by inversion method. During the measurements the pulse transmission technique was used. Measurements were carried out at various incremental pressures and parameters of the model were determined by linearized inversion methods. The calculated data matched accurately with measured data proving that the new rock physical model describing acoustic hysteresis applies well in practice.

The application of seismic refraction methods is very widespread in near-surface geological investigations for e.g. hydrogeological, geophysical engineering and geotechnical purposes [1, 2]. In a surface seismic measurement various source types can be used, related to which trigger error may occur during field measurements. If elastic waves are generated by explosion, an approx. 1–4 ms triggering error can occur due to the error of the geophysical blasting cap. Generating the waves with weight dropping or hammer strike, a piezoelectric ceramic or a geophone serves the trigger signal – cycle skipping may occur. These triggering errors can cause problems in the interpretation of measured data and the estimation of the parameters, especially in shallow explorations as the accuracy or the errors of the trigger time have greater importance there compared to that of deeper explorations. This problem was examined earlier in the inversion of three-component seismic VSP surveys in a coal mine using the traveltime differences between the upper and lower geophone-triplet [3]; and in shallow seismic reflection exploration, estimating the shot distortion on each common shot gather and eliminating them by shifting all the traces [4]. In this paper the idea of double-trace data is applied to refraction traveltime data, a concept that was developed by Dobroka et al. [5] for tomographic interpretation. The modified conjugate gradient and SIRT algorithms proved to be effective for solving the problem described above. With this theory the problem of the inaccurate trigger time is attempted to be solved in the field of seismic refraction.

Refraction seismic methods are widely used in near surface investigations of geological structures. In the Department of Geophysics (University of Miskolc) a series expansion based inversion method was developed for the interpretation of refraction traveltime data. The experiences that we gained using this method show that the accuracy (or the errors) of trigger time have greater importance in near surface application than in the exploration of deeper regions. In this paper an experiment is described for the development of this inversion method for avoiding the interpretation problems originated from the inaccurate source time. In the presented inversion procedure traveltime differences are used instead of the measured simple traveltime dataset. Therefore a significant improvement is detected in the results of those cases where triggering error occurred. The method is tested on synthetic and field datasets as well. Further upgrade of this theory and its implementation into the series expansion based inversion method is planned in the near future.

The paper discusses the characteristics and feasibility of a multilayer kinematic refraction inversion method that is applicable to estimate the — even laterally changing — parameters of a geological model in the simultaneous evaluation of refraction data. The studied method has been developed at the Department of Geophysics of the University of Miskolc for the interpretation of parameters (layer thicknesses and seismic velocities) using series expansion based on adequately chosen basis functions. Besides revealing its resolution properties, ambiguity studies are also presented on synthetic data sets. In the terminology of refraction inversion uncertain and ambiguous results are frequently encountered problems in multilayer cases when all parameters (or all coefficients describing the parameters) are estimated simultaneously in the same inversion procedure. Results of resolution and ambiguity analyses of synthetic data sets and field examples are shown in this study.

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.

For the description of realistic geological models it is important to develop an inversion method that is able to calculate slow lateral changes in the model parameters. But laterally varying parameters of a multilayered structure can cause ambiguity in the inversion process. This is a problem in the use of the kinematic multilayer refraction inversion method developed in the University of Miskolc, because it can interpret laterally changing model parameters (layer thicknesses, and propagation velocities) (for a maximum of 5 geological layers in the same process) described by continuous basis functions expanded in series. The reduction of the arising ambiguity question could be reached by searching for the optimal number of coefficients in the inversion method and it is also important to use different coefficient numbers or different basis functions for the description of the ambiguous parameters. Thus no joint or constrained inversion techniques are needed for the interpretation; our inversion method with simple, quick ray tracing forward modelling is able to handle the ambiguity problem.

This paper presents the principles of a new inversion method used for determining 2-D geological structures. The basis of the method is that horizontal changes in layer-thicknesses and resistivities of the geological structure are discretized in the form of series expansion. The unknown expansion coefficients are determined by linearized iterative least-squares (LSQ) inversion of data provided by surface geoelectric measurements. The discretization of the 2-D model by means of series expansion gives the possibility to reduce the number of model parameters. Thus, the resulting inverse problem becomes overdetermined and can be solved without the application of additional regularization, e.g., by smoothness constraints, which is usually required for traditional 2-D/3-D inversion. By knowing the expansion coefficients, the local layer parameters are calculated along the profile, point by point. In conformity with the complexity of the model, 1-D forward modeling is applied in the initial iteration steps, then as a continuation the direct problem is handled as a real 2-D problem by means of a finite difference (FD) procedure—i.e., the forward modeling is combined, whereas the unknowns (the expansion coefficients) are the same. This combination of the 1-D and 2-D forward modeling procedures makes it possible to analyze quickly the geological models having considerable lateral variation.

In this paper a refraction inversion technique developed in the Department of Geophysics, University of Miskolc is investigated for different laterally changing geological models. It is important because the solution of the forward problem uses several approximations for significant reduction of the calculation time and these can affect the inversion results. The effects of these approximations depend on the investigated geological structure. According to our investigations it can be stated that the applied approximation gives very good results in case of slowly changing structures, while even in case of a highly changing model the inversion technique gives a result where the target model is recognizable.

In-mine geoelectric methods - the geoelectric seam-sounding and geoelectric transillumination - were applied for detection of fault zones in a coal mine. The measured data were interpreted using geoelectric tomography algorithm. Appreciable agreements were found between the location of tectonic zones predicted by the interpretation and those observed during the mining extraction.

The paper shortly presents the TAU-Transform of the Time-Domain IP curves and the approximate solution of the TAU-Transform using inverse theory. A method for estimation of the type and the value of soil contaminations will be introduced. The calculation of contamination type comes from the time constant value of the time constant spectra. The value estimation of the soil contamination is based on the waited amplitude values of the time constant spectra In this paper we show two new interpretation results measured over a slag ash site (Tiszapalkonya - 2004) and near a communal waste site (Berekböszörmény - 2007). The analysis of the IP data measured over the ash sludge site shows that relatively higher specific resistivity is connected with relatively higher polarizability in slag ash body, and the types of the polarization are membrane and redox.

In-mine geoelectric methods – the geoelectric seam-sounding and geoelectric transillumination – were applied for detection of fault zones in a coal mine. The measured data were inter-preted using geoelectric tomography algorithm. An appreciable agreement were found between the location of tectonic zones predicted by the interpretation and those observed during the mining extraction.