A nehézségi erőtér potenciálfüggvényének inverziós rekonstrukciója Eötvös-inga adatok alapján

A nehézségi erőtér potenciálfüggvényének inverziós rekonstrukciójára teszünk javaslatot. A javasolt módszerrel lehetőség nyílik Eötvös-inga mérési adatok felhasználásával függővonal-elhajlás meghatározására, az eddig alkalmazott interpolációs módszerek pontosságát felülmúló számítások elvégzésére és a korábban alkalmazott eljárások során felmerülő bizonyos problémák áthidalására

FLOAT-ENCODED GENETIC ALGORITHM USED FOR THE INVERSION PROCESSING OF WELL-LOGGING DATA

In this chapter a Float-Encoded Genetic Algorithm is presented for solving the well-logging inverse problem. The aim of the global inversion of well-logging data is to provide a robust and reliable estimate of petrophysical properties of geological structures such as porosity, water saturation, shale volume and mineral content. There are two possible ways to solve the interpretation problem. The first is a conventional inversion scheme, which estimates the unknowns to different depths separately. In the forward modeling phase of the local inversion procedure the theoretical well-logging data are calculated by using locally defined probe response functions, which are then fitted to real data in order to estimate model parameters only to one depth. This procedure leads to a marginally over-determined inverse problem, which results in relatively poor parameter estimates. A further disadvantage of the above technique is that some crucial quantities such as the thickness of layered geological formations cannot be extracted by inversion, because it does not appear explicitly in local response equations. A new inversion methodology introduced by the authors gives much more freedom in choosing the inversion parameters. The so-called interval inversion method inverts all data measured from a greater depth interval in a joint inversion process. By a series expansion-based discretization of the petrophysical model a highly over-determined inverse problem can be formulated, which enables to estimate the petrophysical parameters including new unknowns such as zone parameters and layer thicknesses more accurately compared to local inversion methods. The authors give further references for several applications of the global inversion method. In this chapter, a synthetic and two field examples are presented to demonstrate the application of the Genetic Algorithm-based inversion method. It is shown that the combination of the new inversion strategy and global optimization tools forms a highly effective and adaptive algorithm for earth scientists who are interested in a more reliable calculation of the reserves of hydrocarbons and other mineral resources

Cluster Analysis Assisted Float-Encoded Genetic Algorithm for a More Automated Characterization of Hydrocarbon Reservoirs

A genetic algorithm-based joint inversion method is presented for evaluating hydrocarbon-bearing geological forma- tions. Conventional inversion procedures routinely used in the oil industry perform the inversion processing of borehole geophysical data locally. As having barely more types of data than unknowns in a depth, a set of marginally over-de- termined inverse problems has to be solved along a borehole, which is a rather noise sensitive procedure. For the reduc- tion of noise effect, the amount of overdetermination must be increased. To fulfill this requirement, we suggest the use of our interval inversion method, which inverts simultaneously all data from a greater depth interval to estimate petro- physical parameters of reservoirs to the same interval. A series expansion based discretization scheme ensures much more data against unknowns that significantly reduces the estimation error of model parameters. The knowledge of res- ervoir boundaries is also required for reserve calculation. Well logs contain information about layer-thicknesses, but they cannot be extracted by the local inversion approach. We showed earlier that the depth coordinates of layer- boundaries can be determined within the interval inversion procedure. The weakness of method is that the output of inversion is highly influenced by arbitrary assumptions made for layer-thicknesses when creating a starting model (i.e. number of layers, search domain of thicknesses). In this study, we apply an automated procedure for the determination of rock interfaces. We perform multidimensional hierarchical cluster analysis on well-logging data before inversion that separates the measuring points of different layers on a lithological basis. As a result, the vertical distribution of clusters furnishes the coordinates of layer-boundaries, which are then used as initial model parameters for the interval inversion procedure. The improved inversion method gives a fast, automatic and objective estimation to layer-boundaries and petrophysical parameters, which is demonstrated by a hydrocarbon field example

Édesvíztárolók szivárgási paramétereinek meghatározása a Csókás eljárás alkalmazásával

Csókás János (1918-2000) a Miskolci Egyetem Geofizikai Tanszékének egykori professzora 1995-ben publikált a szivárgási tényező, a vízhozam és egyéb vízminőségi paraméterek meghatározására alkalmas karotázs kiértékelési eljárást. A módszer laza törmelékes üledékes kőzetekben alkalmazható, mely a nukleáris és fajlagos ellenállás adatok alapján a szemcseátmérők ismerete nélkül adja meg a szivárgási tényező folytonos szelvényét. A tanulmányban összehasonlítást végzünk a standard Kozeny-Carman és a Csókás modell között. Ennek keretében szintetikus adatok feldolgozásával megvizsgáljuk a módszer pontosságát és zajérzékenységét. Majd terepi szelvényadatok felhasználásával bemutatjuk, hogy a Csókás eljárással és a magadatokon alapuló Kozeny-Carman módszerrel becsült szivárgási tényező értékek jól korrelálnak. A Csókás eljárással kapott eredményeket megerősítik a Hazen-formula alapján számított tapasztalati és a feltáró faktoranalízisen alapuló többváltozós statisztikus kiértékelési eredmények is. A Csókás eljárás és a faktoranalízis együttes alkalmazásával meghatározzuk néhány kőzetfizikai paraméter és a szivárgási tényező in-situ regressziós kapcsolatát. Csókás professzor alapvető törekvése az volt, hogy a víztárolók vizsgálatához szükséges kőzetfizikai és szivárgási paramétereket a fúrólyukszelvényekből származtassa. Ezt az alapgondolatot követve a módszer továbbfejlesztése ma is aktuális lehet. Ugyanis az eljárás bemenő paramétereit a korszerű mérések alapján pontosabban meghatározhatjuk, mellyel tovább javíthatjuk a kiértékelés hatékonyságát a tárolókőzetek kutatása és az édesvízkészletek kitermelése során

Series Expansion Based Tau-Transformation With Application to TDIP Dataset

Geophysical data processing in the TDIP has shown itself to be an important and effective tool in ore exploration. The recovered images from the induced polarization (IP) survey are interpreted by geologists to understand the near-surface geological structures and to guide further exploration activities such as spotting drill holes. However, it does not always provide an exact near-surface image that reliably reflects the structural and physical proper-ties of the target for many reasons. This paper aims to investigate the combination between the TAU transformation and the series expansion inverse method based on the overdeter-mined inverse problem (linearized Gaussian least squares method) in the data analysis of IP data. We also developed a stable algorithm to solve TAU transformation through the overde-termined problem (GLSQ). In this algorithm, the series expansion technique and a logarith-mic transformation have been extended to define the unknown parameters. This algorithm is useful for the quick processing of TDIP data and may assist in accuracy improvement of the interpretation of a geoelectric survey in ore exploration

Evaluation of hydraulic conductivity in shallow groundwater formations: a comparative study of the Csókás’ and Kozeny–Carman model

The Kozeny–Carman equation has achieved widespread use as a standard model for estimating hydraulic conductivity of aquifers. An empirically modified form applicable in shallow formations called Csókás’ formula is discussed, which is based on the relation between the effective grain-size and formation factor of freshwater-bearing unconsolidated sediments. The method gives a continuous estimate of hydraulic conductivity along a borehole by using electric and nuclear logging measurements without the need of grain-size data. In the first step, synthetic well-logging data sets of different noise levels are generated from an exactly known petrophysical model to test the noise sensitivity of the Csókás’ method and to assess the degree of correlation between the results of Csókás’ and Kozeny–Carman model. In the next step, borehole logs acquired from Hungarian sites are processed to make a comparison between the Csókás’ formula and the Kozeny–Carman equation including grain-size data measured on rock samples. The hydraulic conductivity logs derived separately from the Csókás’ and Kozeny–Carman formulae show reliable interpretation results, which are also validated by the Hazen’s formula and statistical factor analysis. The fundamental goal of Professor Csókás’ research was to derive some useful hydraulic parameters solely from well-logging observations. This idea may be of importance today since the input parameters can be determined more accurately by advanced measurement techniques. Hence, the Csókás’ formula may inspire the hydrogeophysicists to make further developments for a more efficient exploration of groundwater resources

Elektromágneses módszerfejlesztések a mérési adatokban lévő földtani információ hatékonyabb és stabilabb feltárása céljából = Development of Electromagnetic (EM) Methods tending to more efficient and more stable revelation of the geological information from field data

3D EM globális inverziós szoftvereket fejlesztettünk ki. A szoftverekkel felszínközeli olajszennyezések inverziós rekonstrukcióját végeztük el. Az EM módszerek esetére GIS alapú fejlesztést végeztünk, s GeoMedia Open GIS alatt működő rendszert hoztunk létre, amely lehetővé teszi az EM és IP paraméterek komplex képi és numerikus elemzését. Sikeresen pályáztunk az Intergraph RRL programjába. GeoMedia WebMap alatt kifejlesztettük a GIS alapú rendszer hálózati kliens verzióját. Vizsgáltuk a felszín közeli vetős szerkezetek és a csővezetékek hatását a Hz és az Ex/Hy térkomponensek amplitúdó- és fázisviszonyaira. A béléscsöves gerjesztésű geoelektromos szondázások adatainak inverziójára elkészült a "Cube3Dinv" elnevezésű program, melyben a direkt feladat megoldása integrálegyenletes módszerrel történik. Az IP módszer esetén elvégeztük az időállandó spektrum inverziós számításának továbbfejlesztését. Megoldottuk az időállandó spektrum, Fourier-spektrumok segítségével történő meghatározását. A korábbi terepi mérések adatainak újrafeldolgozása mellett 4 szennyezett területen új terepi méréseket is végeztünk. Az eredmények igazolták, hogy a szennyezettség mértékének a becslésére alkalmas az időállandóval súlyozott amplitúdó érték. Az időállandó spektrumok alapján a szennyezés szempontjából veszélyesebb redox és fémes hatások által érintett térrészek lehatárolhatók. A szennyezés lehatárolására bevezettük a korrigált elektromos vezetőképességet. | Some 3D EM global inversion software had been developed. We perform the inverse reconstruction of near surface oil contaminations using developed software. GIS based system under GeoMedia Open GIS had been developed for EM Methods, which makes complex image and numerical analysis of EM and IP parameters possible. Our application for the Intergraph RRL program membership was successful. We developed the network client version of GIS based system. The effects of the pipes and near surface structures with faults for the amplitude- and phase relation of Hz and Ex/Hy parameters were examined. A software named "Cube3Dinv" for the inversion of geoelectric sounding data using tube for transmission, in which integral equation method are used for the solution of forward problem had been finished. We elaborated the calculation way of the IP time constant spectra using inverse methods. Determination possibility of time constant spectrum from Fourier spectra had been solved. We performed four new field measurements over contaminated areas beside the data reprocessing of former field measurements. Results verified that the amplitude value waited with time constant suitable for the estimation of the contamination level. Seeing the dangerous contamination types, the areas touched by redox and metallic effects are able to determine on the basis of time constant spectra. Corrected electric conductivity has been introduced for the mapping of contamination

New Results in Modeling the Phenomenon of Acoustic Hysteresis

Interpretation of seismic data is significantly constrained by the extrapolation of measured acoustic properties - in laboratory - of rocks in a given physical (pressure) environment. To reasonably interpret laboratory measurements, a quantitative model - which provides the physical explanation - of the mechanism of pressure dependence is required. It is well known that the change of acoustic wave velocity propagating in rocks is nonlinear with respect to pressure and the quasistatic elastic properties of rocks are hysteretic. In this paper a petrophysical model is presented which provides the connection between the propagation velocity of acoustic wave and rock pressures both in case of pressurization and depressurization cycles. The developed model also describes well and explains the mechanism of acoustic hysteresis. The model is based on the idea that the microcracks in rocks close during pressurization and reopen during depressurization. The model was applied to acoustic P wave velocity data sets. Measurements were carried out at various incremental pressures and the parameters of the petrophysical model were determined by a linearized inversion method. The calculated data matched accurately with measured data proving that the new rock physical model describing acoustic hysteresis applies well in practice

Hilbert Transform Using the Most Frequent Value Method

Hilbert Transform Using The Most Frequent Value Method Omar Al Marashly – Mihály Dobróka In the study, we present a robust inversion method for calculating Hilbert trans-form, a process that also provides resistance to outlier noise. The inversion-based Fourier transform process combined with the Most Frequent Value method (MFV) developed by Steiner can effectively make the Fourier transform more robust. The resistance of the robust Fourier transform process (IRLS-FT) to outliers and its outstanding noise suppression capa-bility justify the method being tried in the field of seismic data processing. As the first stage, we present the production of the Hilbert transform based on a robust inversion, and as an application example we calculate the absolute value of the analytical signal that can be pro-duced as an attribute gauge (instantaneous amplitude). The new algorithm is based on a dual inversion: we determine the Fourier spectrum of the time signal (channel) by inversion, and the spectrum obtained by the transformation required for the Hilbert transform is transformed into the time range with a robust inversion. The latter operation is carried out using the Steiner weights calculated using the Iterative Reweighting Least Squares (IRLS) method (robust in-verse Fourier transform based on inversion). To discretize the spectrum of the time signal, we use the scaled Hermite functions in a series expansion. The expansion coefficients are the unknowns in the inversion. The new Hilbert transform procedure was tested on a Ricker wavelet loaded with Cauchy post-distribution noise. The results show that the procedure has remarkable resistance to outlier noises and noise suppression an order of magnitude better than that calculated by the conventional (DFT) method

Testing The Noise Rejection Capability Of The Inversion Based Fourier Transformation Algorithm Applied To 2d Synthetic Geomagnetic Datasets

For signal processing, different algorithms can be applied to enhance the quality of measured datasets that contain simple or complex noises during the field survey. Treating these noisy data can be done using the discrete Fourier transform (DFT based noise filtering) which converts the data from time to a frequency domain but in some cases is not preferable due to its low noise suppression capability. Therefore, a robust and effective 2D inversion called the iteratively reweighted least-squares Fourier transformation (IRLS-FT) method is applied. In the framework of this inversion, the continuous Fourier spectrum is discretized using the series expansion to solve our inverse problem in the form of the expansion coefficients. Moreover, the Hermite functions are used as basis functions with the distinguishing feature of the Fourier transform eigenfunctions to facilitate and speed up the calculation of the Jacobian matrix without complex integration. In the robust inversion studied in the article, the Steiner weights are calculated through an internal iteration loop instead of Cauchy weights to overcome the problem of scale parameters. In this paper, the 2D IRLS-FT inversion method is applied to synthetic magnetic datasets and their reduction to the pole. The results demonstrated that the method is very stable during the procedures as well as its robustness, resistance, and effectiveness in the process of noise rejection