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1

Thin interbed AVA inversion based on a fast algorithm for refectivity

Yang Zhen, Lu Jun

Acta Geophysica

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2020

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Vol. 68, no. 4

1007--1020

EN

Zoeppritz equations form the theoretical basis of most existing amplitude variation with incident angle (AVA) inversion methods. Assuming that only primary refections exist, that is, the multiples are fully suppressed and the transmission loss and geometric spreading are completely compensated for, Zoeppritz equations can be used to solve for the elastic parameters of strata efectively. However, for thin interbeds, conventional seismic data processing technologies cannot suppress the internal multiples efectively, nor can they compensate for the transmission loss accurately. Therefore, AVA inversion methods based on Zoeppritz equations or their approximations are not applicable to thin interbeds. In this study, we propose a prestack AVA inversion method based on a fast algorithm for refectivity. The fast refectivity method can compute the full-wave responses, including the refection, transmission, mode conversion, and internal multiples, which is benefcial to the seismic inversion of thin interbeds. A further advantage of the fast refectivity method is that the partial derivatives of the refection coefcient with respect to the elastic parameters can be expressed as analytical solutions. Based on the Gauss– Newton method, we construct the objective function and model-updating formula considering sparse constraint, where the Jacobian matrix takes the form of an analytical solution, which can signifcantly accelerate the inversion convergence. We validate our inversion method using numerical examples and feld seismic data. The inversion results demonstrate that the fast refectivity-based inversion method is more efective for thin interbed models in which the wave-propagation efects, such as interval multiples, are difcult to eliminate.

2

Assessing the efects of 1D assumption violation in vertical electrical sounding (VES) data processing and interpretation

Mashhadi Seyyed Reza, Ramazi Hamidreza, Asgarpour Shahreza Mohammad

Acta Geophysica

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2020

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Vol. 68, no. 1

105--122

EN

This research aimed to discover the possible efects of 1D assumption violations on VES data interpretations. In order to do so, 1D inversion results of logarithmically spaced and linearly spaced VES measurements are compared with their relevant 2D inverted models. Some real case studies are also examined by 1D and 2D inversions to test the results. It is found that linearly spaced VES measurements are not really suitable for 1D inversion in the case of 1D assumption violations and logarithmically spaced VES can better handle these problematic features. In the case of semi-infnite horizontal layers and also small surface resistivity inhomogeneities, logarithmically spaced VES datasets mostly provide a reliable 1.5D model while linearly spaced VES datasets sufer from remarkable artifacts. In the case of vertical structures, both linearly spaced and logarithmically spaced VES techniques fail. In this case (i.e., a vertical dike), artifacts in the form of “extra layer” appear in those VES stations that are adjacent to the dike. However, for VES stations on the dike structure, no extra layer appears in the 1D inversion result. It must be emphasized that 1D violating features are not improbable in many geological situations so they must be considered in mind when processing and interpreting the geophysical VES data.

3

Study on forward and inversion modeling of array laterolog logging in a horizontal/highly deviated well

Zhu Peng, Li Zhiqiang, Chen Ming, Dong Yixin

Acta Geophysica

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2019

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Vol. 67, no. 5

1307--1318

EN

Electric feld synthesis was carried out using the multi-feld superposition method according to the working principle of the array laterolog electrode system. The feld distribution of each subfeld was simulated with the 3D finite element method, and the laterolog response of the array was obtained using the linear superposition principle of electric feld. The detection depth and thin layer response at diferent angles of the array laterolog were analyzed. The forward response calculation shows that the radial detection depth of the array laterolog is smaller than the deep laterolog detection depth. When the inclination angle of the well is less than 15°, the logging response of the array laterolog is less afected by the well inclination, and the well inclination correction need not be performed. The logging response values of highly deviated wells with inclination angles exceeding 60° and horizontal wells are quite diferent from those of vertical wells; thus, well deviation correction must be performed. To improve the stability of array laterolog logging inversion using the accurate forward response, a Newton–singular value decomposition method based on particle swarm optimization is proposed to realize inversion of array laterolog logging, and the stability and reliability of logging inversion are greatly improved. Thus, application of the theoretical model and actual data processing and analysis show that the proposed method can efectively and accurately eliminate the infuence of a complex logging environment and obtain real formation parameters.

4

On application of fractal magnetization in Curie depth estimation from magnetic anomalies

Li Chun Feng, Zhou Duo, Wang Jian

Acta Geophysica

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2019

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Vol. 67, no. 5

1319--1327

EN

As an independent geothermal proxy, the Curie-point depth has important geodynamic implications, but its estimation from magnetic anomalies requires an understanding of the spatial correlation of source magnetization, mathematically characterized by a fractal exponent. In this paper, we show that fractal exponent and Curie depth are so strongly inter-connected that attempts to simultaneous or iterative estimation of both of them often turn out to be futile. In cases of true large Curie depths, the iterative “de-fractal” method has a tendency of overcorrecting fractal exponents and thereby producing erroneously small Curie depths and smearing out true geological trends. While true fractal exponent can no way be constant over a large area, a regionally fxed fractal exponent is better than any mathematical treatments that are beyond the limit of data resolution and the underlying physics.

5

Multiples inversion imaging using a one way propagation operator

Li Qiang, Wang Deli

Acta Geophysica

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2019

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Vol. 67, no. 5

1341--1348

EN

The one-way propagation operator in the frequency-space domain has the advantages of fast calculation speed and good adaptability to medium with lateral velocity variation. The full wavefeld model constructed by the one-way propagation operator is iterative. As the number of iterations increases, the components of wavefeld are more and more abundant. In the full wavefeld model, the propagation and scattering processes are independent of each other. The former is determined by the propagation operator, while the latter is determined by the scattering operator. As each iteration increases, the wavefeld component will increase by one order. As an inverse migration operator, the full wavefeld model could feed back the imaging result to the data. By calculating the residual between the simulated data and the actual data, the refectivity is updated. This is an inversion process. In this process, multiples will be imaged. In this way, the subsurface information contained in multiples is utilized and the imaging quality is greatly improved. The L1-norm is used to constrain the imaging result, which further suppresses the artifacts and improves the imaging resolution. We have made some numerical examples in 2D case, explaining the principles and advantages of this methodology.

6

Magnetotelluric inversion of one and two dimensional synthetic data based on hybrid genetic algorithms

da Conceição Batista Joelson, Starteri Sampaio Edson Emanoel

Acta Geophysica

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2019

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Vol. 67, no. 5

1365--1377

EN

We applied the technique of the genetic algorithms and a local methodology integrating the Gauss–Newton and Conjugate Gradient (GNCG) techniques to test one-dimensional inverse modeling of synthetic magnetotelluric data. The result of this modeling applied to a homogeneous and isotropic five-layer model led to the development a hybrid algorithm (GAGNCG), combining the aforementioned techniques, for inverse modeling of one-dimensional magnetotelluric data. The GAGNCG modeling of the synthetic data performs more efciently than the local methodology in terms of both procedure and results. This showed that the hybridization procedure maximized the advantages of using the global search methodology and minimized the disadvantages of the local technique. Based on these results, we developed another hybrid methodology (GA2D), built from some characteristics of the genetic algorithm and the simulated annealing method, for the inverse modeling of two-dimensional magnetotelluric data. The results were satisfactory, and the GA2D algorithm was a good starting point for the inverse modeling of two-dimensional data.

7

Study on mine ventilation resistance coefficient inversion based on genetic algorithm

Gao K., Deng L., Liu J., Wen L., Wong D., Liu Z.

Archives of Mining Sciences

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2018

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Vol. 63, no. 4

813--826

EN

The frictional resistance coefficient of ventilation of a roadway in a coal mine is a very important technical parameter in the design and renovation of mine ventilation. Calculations based on empirical formulae and field tests to calculate the resistance coefficient have limitations. An inversion method to calculate the mine ventilation resistance coefficient by using a few representative data of air flows and node pressures is proposed in this study. The mathematical model of the inversion method is developed based on the principle of least squares. The measured pressure and the calculated pressure deviation along with the measured flow and the calculated flow deviation are considered while defining the objective function, which also includes the node pressure, the air flow, and the ventilation resistance coefficient range constraints. The ventilation resistance coefficient inversion problem was converted to a nonlinear optimisation problem through the development of the model. A genetic algorithm (GA) was adopted to solve the ventilation resistance coefficient inversion problem. The GA was improved to enhance the global and the local search abilities of the algorithm for the ventilation resistance coefficient inversion problem.

PL

Współczynnik oporu oporu wentylacji jezdni w kopalni węgla jest bardzo ważnym parametrem technicznym w projektowaniu i renowacji wentylacji kopalnianej. Obliczenia oparte na wzorach empirycznych i badaniach terenowych w celu obliczenia współczynnika oporu mają ograniczenia. W niniejszym badaniu proponuje się inwertowaną metodę obliczania współczynnika oporu wentylacji kopalni za pomocą kilku reprezentatywnych danych dotyczących przepływu powietrza i ciśnienia w węzłach. Model matematyczny metody inwersji jest opracowywany na zasadzie najmniejszych kwadratów. Zmierzone ciśnienie i obliczone odchylenie ciśnienia wraz z zmierzonym przepływem i obliczonym odchyleniem przepływu są uwzględniane przy określaniu obiektywnej funkcji, która obejmuje również ciśnienie w węźle, przepływ powietrza i ograniczenia współczynników oporu wentylacji. Problem odwrotności współczynnika oporu wentylacji został przekształcony w nieliniowy problem optymalizacji poprzez opracowanie modelu. Zastosowano algorytm genetyczny (GA) w celu rozwiązania problemu inwersji współczynnika oporu wentylacji. GA został ulepszony w celu zwiększenia globalnych i lokalnych możliwości wyszukiwania algorytmu problemu odwrotności współczynnika oporu wentylacji.

8

Stress studies in the Central Alborz by inversion of earthquake focal mechanism data

Pourbeyranvand S.

Acta Geophysica

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2018

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Vol. 66, no. 6

1273--1290

EN

The Alborz is one of the most important seismotectonic provinces in Iran. Furthermore, emplacement of Tehran as a mega city in southern part of the Alborz intensifies the seismic vulnerability in this area. In this study, the focal mechanism data from teleseismic and local seismic networks are used for stress tensor inversion. The earthquake focal mechanisms in the Central Alborz are divided into several groups with respect to their location. Two different stress tensor inversions, linear and nonlinear, are used for obtaining the principal stress orientations. The results show spatial variations in tectonic stress field, consistent with fault orientations and faulting mechanisms. The maximum compressional stress directions obtained in this study are confirmed by fast S-wave polarization axes reported by a previous shear wave splitting study. The maximum horizontal stress directions are also compared with GPS strain rates. The results indicate a partitioning of deformation in the area due to regional stresses along preexisting faults.

9

3D joint inversion of Gradient and Mise-à-la-Masse borehole IP/Resistivity data and its application to magmatic sulfide mineral deposit exploration

Wondimu H. D., Mammo T., Webster B.

Acta Geophysica

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2018

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Vol. 66, no. 5

1031--1045

EN

Gradient and Mise-à-la-Masse IP/Resistivity surveys were conducted on a group of 19 boreholes in Eagle’s Nest, Eagle One magmatic sulfide deposit in northern Ontario, Canada. The surveys were conducted as a follow-up to the many drilled boreholes, some of which missed the target. The surveys were intended to map the distribution of the ore mineralization, outline the deposit hosted by mafic and ultramafic rocks and then guide the drilling of new boreholes. Joint Gradient and Mise-à-la-Masse data inversion produced 3D chargeability and conductivity models. The inverted 3D models in turn help delineate the outline of the mineralized zone, and determine the shape, size, strength and economic viability of the deposit. The Gradient array determined the direction of the mineralization with respect to the boreholes, and the Mise-à-la-Masse array examined the highly conductive subsurface bodies and their surroundings. The mapped ore zone shows close similarity to the 0.5 Cu% and 1.05 Ni% iso-surfaces that are produced from core assay result confirming the reliability of the results obtained in this study.

10

Interpretation of magnetic anomalies using a genetic algorithm

Kaftan İ.

Acta Geophysica

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2017

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Vol. 65, no. 4

627--634

EN

A genetic algorithm (GA) is an artificial intelligence method used for optimization. We applied a GA to the inversion of magnetic anomalies over a thick dike. Inversion of nonlinear geophysical problems using a GA has advantages because it does not require model gradients or welldefined initial model parameters. The evolution process consists of selection, crossover, and mutation genetic operators that look for the best fit to the observed data and a solution consisting of plausible compact sources. The efficiency of a GA on both synthetic and real magnetic anomalies of dikes by estimating model parameters, such as depth to the top of the dike (H), the half-width of the dike (B), the distance from the origin to the reference point (D), the dip of the thick dike (δ), and the susceptibility contrast (k), has been shown. For the synthetic anomaly case, it has been considered for both noise-free and noisy magnetic data. In the real case, the vertical magnetic anomaly from the Pima copper mine in Arizona, USA, and the vertical magnetic anomaly in the Bayburt–Sarıhan skarn zone in northeastern Turkey have been inverted and interpreted. We compared the estimated parameters with the results of conventional inversion methods used in previous studies. We can conclude that the GA method used in this study is a useful tool for evaluating magnetic anomalies for dike models.

11

Various Approaches to Forward and Inverse Wide-Angle Seismic Modelling Tested on Data from DOBRE-4 Experiment

Janik T., Środa P., Czuba W., Lysynchuk D.

Acta Geophysica

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2016

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Vol. 64, no. 6

1989--2019

EN

The interpretation of seismic refraction and wide angle reflection data usually involves the creation of a velocity model based on an inverse or forward modelling of the travel times of crustal and mantle phases using the ray theory approach. The modelling codes differ in terms of model parameterization, data used for modelling, regularization of the result, etc. It is helpful to know the capabilities, advantages and limitations of the code used compared to others. This work compares some popular 2D seismic modelling codes using the dataset collected along the seismic wide-angle profile DOBRE-4, where quite peculiar/uncommon reflected phases were observed in the wavefield. The ~505 km long profile was realized in southern Ukraine in 2009, using 13 shot points and 230 recording stations. Double PMP phases with a different reduced time (7.5-11 s) and a different apparent velocity, intersecting each other, are observed in the seismic wavefield. This is the most striking feature of the data. They are interpreted as reflections from strongly dipping Moho segments with an opposite dip. Two steps were used for the modelling. In the previous work by Starostenko et al. (2013), the trial-and-error forward model based on refracted and reflected phases (SEIS83 code) was published. The interesting feature is the high-amplitude (8-17 km) variability of the Moho depth in the form of downward and upward bends. This model is compared with results from other seismic inversion methods: the first arrivals tomography package FAST based on first arrivals; the JIVE3D code, which can also use later refracted arrivals and reflections; and the forward and inversion code RAYINVR using both refracted and reflected phases. Modelling with all the codes tested showed substantial variability of the Moho depth along the DOBRE-4 profile. However, SEIS83 and RAYINVR packages seem to give the most coincident results.

12

On Choosing Effective Elasticity Tensors Using a Monte-Carlo Method

Danek T., Slawinski M. A.

Acta Geophysica

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2015

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Vol. 63, no. 1

45--61

EN

A generally anisotropic elasticity tensor can be related to its closest counterparts in various symmetry classes. We refer to these counterparts as effective tensors in these classes. In finding effective tensors, we do not assume a priori orientations of their symmetry planes and axes. Knowledge of orientations of Hookean solids allows us to infer properties of materials represented by these solids. Obtaining orientations and parameter values of effective tensors is a highly nonlinear process involving finding absolute minima for orthogonal projections under all three-dimensional rotations. Given the standard deviations of the components of a generally anisotropic tensor, we examine the influence of measurement errors on the properties of effective tensors. We use a global optimization method to generate thousands of realizations of a generally anisotropic tensor, subject to errors. Using this optimization, we perform a Monte Carlo analysis of distances between that tensor and its counterparts in different symmetry classes, as well as of their orientations and elasticity parameters.