Horizontally-layered Media Research Articles

Тензор сейсмічного моменту та механізм вогнища землетрусу у Східній Словаччині 9 жовтня 2023 року

The accuracy of the focal mechanism solution mainly depends on the number of stations used and becomes problematic especially in the case of weak earthquakes and sparse networks. In our study, we retrieve the seismic moment tensor of the M=5 earthquake on 9 October 2023 (18:23:09 UTC, 21.783°E, 49.086°N, depth 11.5 km) in Eastern Slovakia from its records at only four seismic stations. Our seismic moment tensor inversion is based on the point source approach and the use of only direct waves calculated by the matrix method. Displacements on the surface of an elastic, horizontally-layered medium are generated using the frequency-wavenumber integration technique. The advantage of using only direct P- and S- waves in our inversion method is that they are less sensitive to path effects compared to reflected and converted waves, which reduces the impact of an inaccurate velocity structure and improves the accuracy and reliability of the result. Based on the forward modeling, a numerical technique was developed for the inversion of the observed waveforms for the components of the moment tensor M(t) using the generalized inversion solution. Before applying our method to the earthquake of October 9, 2023, it was also tested on the April 23, 2020 earthquake (23:18:26.42 UTC, 21.945°E, 48.781°N, magnitude M=5, depth 9 km), also in Eastern Slovakia, using data from only three stations. The resulting versions of the mechanism compare well with a very reliable version previously determined from the polarities of the first P-waves at a much larger number of stations, which only confirms the reliability of our inversion method and the very possibility of obtaining useful results from data of only limited number of stations.

Computing Theoretical Seismograms from a Point Source in a Spherical Multilayered Medium

Abstract Computing theoretical seismograms from a point source in a given Earth model is essential for modeling and inversion of observed seismic waveforms for Earth’s structure and earthquake source parameters. Here, we derived the propagator matrices and source terms for a spherical multilayered Earth model using the exact earth flattening transformation. We found that their differences from their counterparts in horizontal layered media are inversely proportional to the nondimensional horizontal wavenumber and its higher order. In addition, all the source terms in a spherical layered model have a source-depth dependent scaling factor that differs from in a horizontal layered model by up to 6% for deep earthquakes. The surface displacement produced by a point source can be obtained in a similar form as in horizontal layered media. Computation of theoretical seismograms was implemented using the generalized reflection and transmission coefficients method. Numerical tests show that our formulae and implementation are correct and efficient for computing full-wave seismograms, including the permanent displacements, at teleseismic distances up to 100°. Individual seismic phases can be isolated and analyzed semianalytically because the generalized reflection and transmission method is used. Furthermore, our analytic expression of displacement in terms of the propagator matrices and source terms can be used to derive analytic derivatives of seismograms for full-wave waveform inversion.

Amplitude-frequency characteristics of the "structure–pile foundation" layered model

Taking into account the interaction between a structure and the soil bed during an earthquake is a vital task of the seismic resistance theory. Despite a large amount of research, there is no satisfactory solution of this problem at the time being. The "platform model" applied in engineering practice can be used only for homogeneous soil beds. However, the surface stratum of soil, as a rule, has a multilayer structure, in which each individual layer has its own physical and mechanical characteristics determining the resonant properties of the entire system. The standard methods of analysis do not take into consideration the heterogeneity and layered nature of a soil bed using the averaged stiffness characteristics, which does not allow evaluating the specific features of resonance processes during the joint oscillation of a building and its soil bed. In addition, the dynamic characteristics of soils have a rather high statistical variability even within the same layer, and this can significantly affect the distribution pattern of the resonant frequencies of the system.
 The present article is aimed at investigating the dynamic response of the “building – multilayer soil bed” system based on the analytical model of a horizontal layered medium.
 The following tasks were solved:
 – an analysis of a layered system under the action of a complex sinusoidal signal was carried out with regard to damping;
 – the amplitude-frequency characteristics were constructed both for individual layers and for the system as a whole;
 – the influence of the statistical variability of the velocity of transverse seismic waves propagation on the resonant frequencies of the layered system under consideration was assessed.
 The analytical methods for the solution of the wave problem of seismology were used.

Determination of formation dip and strike from transient LWD electromagnetic measurements

An original method has been developed for estimating formation dip and strike from transient induction LWD data, based on focusing in the time domain. The focusing consists in decomposing the measured signals into a time series and diagonalizing the matrix of focused magnetic field components. We have implemented the method and comprehensively tested it in horizontally-layered media used for LWD data inversion to solve geosteering problems and evaluate the formation resistivity. Estimates of the angles contribute to reliable geosteering when choosing a direction of drilling, as well as when inverting data for a complex earth model. A significant reduction in the resource intensity of inversion and model equivalence is achieved by reducing the number of determined parameters.

Spherical-earth finite element model of coseismic slip distribution during the 2010 Mentawai earthquake

The moment magnitude (MW) 7.8 earthquake occurred along the Mentawai seismic region of Sunda Trench on 25 October 2010, which is classified as the tsunami earthquake. The GPS inversion results under the assumption of simple horizontal layered medium show that the slip near the trench is not apparent, which is inconsistent with our understanding of tsunami earthquake. Here, we construct a spherical-earth finite element model (FEM) to investigate the coseismic slip distribution of the 2010 Mentawai earthquake by geometrically combining the subducting plate with a precise subduction interface. The FEM-based coseismic slip distribution shows that there are three major slip patches on the fault interface, one is located on the shallow region and the other two are located on the deeper part of the fault plane. The largest slip patch is located near the trench with the depth less than 10 km, and the maximum amplitude is about 12 m. This significant near-trench slip is consistent with the tsunami earthquake studies. A more realistic domain of FEM is used to change the coseismic slip distribution, thus significantly improving the fitting degree of the data model. These findings suggest that the FEM-derived Green's function is essential to image a more robust and realistic coseismic slip distribution of the large earthquake in the subduction zone.

Finite element solution to 3-D airborne time-domain electromagnetic problems in complex geological media using non-conforming hexahedral meshes

We propose the approach to 3-D modeling of the electromagnetic (EM) field in time-domain airborne EM problems in complex media including rugged topography and curved borders between the geological layers, target objects of different shapes, lateral inhomogeneity within subhorizontal layers. For discretization of the electromagnetic field in space, the vector finite element method is used. We propose the approach to generating the optimized non-conforming finite element meshes with hexahedral cells in which several finite elements can be attached to the face of the other finite element which allows achieving the significant reduction of computational costs in comparison with the regular meshes on which the numerical solution has the same accuracy. The optimized non-conforming finite element mesh in a complex medium with the topography and curved borders of layers is generated with the use of special transformations. The method of constructing the finite element approximations on these non-conforming hexahedral meshes is proposed. For discretization of the electromagnetic field in time, the implicit three-point scheme “with backward overstepping” is proposed. For solving the finite element SLAE, we use the direct solver PARDISO the effectiveness of which is achieved due to the use of time stepping with a piecewise constant step and grouping the calculations of the electromagnetic field in time steps and transmitter positions. In order to increase the accuracy of calculating the signal in the receiver, a special procedure of smoothing the magnetic field B in space and special scheme of approximating the derivative of B in time are proposed. The verification of the proposed approaches is performed using the solution for the 1-D model and solutions for 3-D models obtained by other authors. We present the results of the comparative analysis of different time schemes in finite element calculating the electromagnetic field and in calculating the signal (in the form of EMF) in the receiver and choose the optimal step and the number of subintervals with the constant steps into which the entire modeling time interval is divided. We perform the comparative analysis of stair-like approximation of curved surfaces with the use of rectangular parallelepipeds and approximation with the use of the hexahedral elements and choose the optimal parameters of generating the finite element meshes. We present the results of the analysis of the possibility of replacing the model with topography with the “flat” 3-D model in which the topography is taken into account by correcting the airborne system height. For the “flat” 3-D model, we present the results of the analysis of the computational effectiveness through the use of the primary-secondary field approach with automatic choice of a horizontally-layered medium for calculating the primary field. For the complex geolelectrical model with topography, laterally-inhomogeneous overburden with curved boundaries, target objects under overburden and for a great number of airborne system positions, the computational costs are presented for sequential and parallel modes for modeling time from 0.01 ms to 1 ms and 10 ms. We present the analysis of the topography effect, the influence of the inhomogeneities in the overburden and target objects in the complex media and show that in this conditions, to discover the target objects using the form of the signal is practically impossible, i.e. in order to discover the target objects in these complex media, it is required to perform a very fine 3-D interpretation for carrying out of which fast and high accuracy forward 3-D modeling is of great importance. We obtain that for calculating the field for one transmitter and the entire modeling time interval in the sequential mode on one core of PC with processor Intel i7-8700K CPU of 3.7 GHz and 32 GB of DRAM, the required computational time is about 4–6 s. The required computational time in the parallel mode with the use of six cores of this PC is about 0.65–1 s.

Methods of determination of spatial distribution of minor-amplitude faults and fissures in thin-layered coal-bearing geological medium

A problem of determining location of faults and fissured in geological medium which appear in the process of formation of the main types of geological structures: shears, nappes, faults, grabens, axes of folding and compression zones is considered. Areal seismic records of MCDP 3D obtained in the mine field of “Krasnolimanskaya” mine (Donetsk district) were used as initial data. It is located on the monocline of the southwestern part of Kalmius-Torets basin in the hanging wing of the Central nappe with amplitude up to 310m. Monocline occurrence of rocks is complicated by numerous disjunctive faults of the faulting type with amplitudes up to 95m. The main marker for identification for presence of a fault on the seismic records of MCDP 3D under conditions of horizontally-layered medium is interruption and (or) displacement of the axis of reflected waves phase synchronism. In some cases a diffracted wave appears in the place of horizon rupture. Provided that in the case of complicated geology it seems impossible to identify minor-amplitude displacements and discordant occurrence of reflecting margins related to faults. For spatial identification of the fault structures position the results of solving the inverse seismic problem are proposed – logarithmic decrements of fading (LDF) with their method of calculation that was put forward by the author previously. Temporal cross-sections of LDF have the same permissive ability as seismic data of MCDP 3D. Such a detail allows separating out minor-amplitude derangements related to faults and fissures. Special feature of temporal data of LDF is in the point that the identifiers of discordant occurrence of reflecting margins are their absorbing properties. The examples of vertical and horizontal LDF sections of a seismic cube 3D where a lot of deep and surface faults can be traced are given in the paper. Taking into account the complexity of mapping the planes of faults in three-dimensional space a method of automatic determination of the point of drastic change of absorbing properties of the medium (on each of horizontal cuts of the cube) with application of wavelet analysis has been proposed. A matrix of attributes is created of such points by which the planes of faults are plotted.

Моделирование электромагнитных полей систем катодной защиты трубопроводов в горизонтально-слоистых средах

Моделирование электромагнитных полей систем катодной защиты трубопроводов в горизонтально-слоистых средах

БЫСТРОЕ РЕШЕНИЕ ДВУХТОЧЕЧНОЙ ЗАДАЧИ ДЛЯ ГОРИЗОНТАЛЬНО-СЛОИСТОЙ СРЕДЫ

For the problem of reflected travel time computation in horizontal layered media, a modified parameter is suggested, providing regularization of the formula and improving the iteration solution convergence.

Coal mine microseismic velocity model inversion based on first arrival time difference

The formation velocity is an important factor affecting the precise location of microseismic source. The establishment of elastic wave velocity model in the monitoring area to satisfy the requirements for precise location of seismic source has been a technical problem for the mine microseismic monitoring. Based on the assumption of horizontal layered medium condition, a new velocity model inversion method has been proposed. According to the concept of equal difference time surface, the first arrival travel time difference between the measured points and datum points is investigated on the basis of the observation point of first arrival travel time duration placed in the middle in the observational network. The minimal difference (double time difference) between the measured first arrival time difference and the calculated first arrival time difference is taken as the constraint condition, and the objective function is constructed to solve the velocity model. The DIRECT fast search algorithm with global optimization characteristics is applied to solve the objective function. This method is used to carry out the trial treatment for the mine microseismic model data and the measured data. The results show that the stratified velocity model under the horizontal layered medium can be obtained by his method using the microseismic data of known seismic source, with a better adaptability to different monitoring systems. Through the test for the actual data of “well-ground” joint microseismic monitoring, the velocity model obtained by the method in this paper can get more accurate location of the seismic source.

Applying TM-polarization geoelectric exploration for study of low-contrast three-dimensional targets

With using new field and theoretical data, it has been shown that applying the electromagnetic field of transverse magnetic (TM) polarization will give new opportunities for electrical prospecting by the method of transient processes. Only applying a pure field of the TM polarization permits poor three-dimensional objects (required metalliferous deposits) to be revealed in a host horizontally-layered medium. This position has good theoretical grounds. There is given the description of the transient electromagnetic method, that uses only the TM polarization field. The pure TM mode is excited by a special source, which is termed as a circular electric dipole (CED). The results of three-dimensional simulation (by the method of finite elements) are discussed for three real geological situations for which applying electromagnetic fields of transverse electric (TE) and transverse magnetic (TM) polarizations are compared. It has been shown that applying the TE mode gives no positive results, while applying the TM polarization field permits the problem to be tackled. Finally, the results of field works are offered, which showed inefficiency of application of the classical TEM method, whereas in contrast, applying the field of TM polarization makes it easy to identify the target.

Application of surface wave method in assessment of ground modification with improvement columns

Surface wave testing is considered a promising method for assessing average property and actual area replacement ratio of ground modification with improvement columns, owing to its non-destructive nature and large sampling range. However, the surface wave method is essentially a 1-D method assuming horizontally-layered medium. What it measures in highly heterogeneous improved ground remains to be investigated. This study aimed at evaluating the feasibility of surface wave method in the heterogeneous ground with improved columns, and investigating the homogenization of shear wave velocity and the lateral sampling range. Field tests on a jet grouted construction site showed that the surface wave method worked well in such heterogeneous grounds and yielded a site-representative shear wave velocity profile regardless of the survey location. This is attributed to the survey condition where the wavelength is greater than the spacing of grout columns. 1-D analytical models and 2-D numerical simulations were conducted to investigate the quantitative relation between construction parameters and the percentage increase of shear wave velocity after ground improvement. A quantitative approach to estimate the area replacement ratio and overall quality of improvement columns by surface wave testing is proposed.

Designing optimal number of receiving traces based on simulation model

Currently, the selection of receiving traces in geometry design is mostly based on the horizontal layered medium hypothesis, which is unable to meet survey requirements in a complex area. This paper estimates the optimal number of receiving traces in field geometry using a numerical simulation based on a field test conducted in previous research (Zhu et al., 2011). A mathematical model is established for total energy and average efficiency energy using fixed trace spacing and optimal receiving traces are estimated. Seismic data acquired in a complex work area are used to verify the correctness of the proposed method. Results of model data calculations and actual data processing show that results are in agreement. This indicates that the proposed method is reasonable, correct, sufficiently scientific, and can be regarded as a novel method for use in seismic geometry design in complex geological regions.

A new analysis of the complex two-dimensional multilayered anisotropic soil in time domain

The dynamic analysis of two-dimensionalmultilayered anisotropic soilwith rigid bedrock is studied. An efficient numerical approach named the modified scaled boundary finite element method (SBFEM) is proposed in the time domain. Based on introducing the continued fraction method and auxiliary variables, the time domain solution is obtained. This solution can be applied to the transversely isotropic medium without any difficulty. For the modified SBFEM, the original scaling center is replaced by a scaling line. These characteristics enable the modified SBFEM to model the horizontal layered medium. Three significant technologies have been introduced in the formula derivation and solving process. First, the dual system is used to derive the displacement equation of the modified SBFEM, which is built on a Hamilton system. According to the principle of virtual work, the displacement equation is transformed to the dynamic stiffness equation. Second, the new continued fraction method for the unbounded domain resting on rigid bedrock is proposed. By introducing auxiliary variables, the displacement equation of motion of an unbounded domain is built. Third, it is an extremely important point that the accurate precise time-integration method is first employed to solve the global equation of motion of the modified SBFEM. This numerical integral method can achieve the machine precision. By using this method in solving the equation of motion of the modified SBFEM, an extremely accurate solution can be achieved. Finally, numerical examples validate the accuracy of the new proposed method, especially for the complex inclined model with anisotropic soil.

Research on Identification of Petroliferous Unit Based on Seismic Data Structure Characteristics

The identification and classification of petroliferous unit is the key to the success in the exploration for oil-gas fields with geophysical knowledge that are the main means and ways to reduce exploration risk and improve exploration efficiency. In this paper, it analyzes geophysical response characteristics under conditions of gas, oil and water through the establishment of horizontal layered medium model. Then it extracts and analyzes seismic abnormal characteristics of the data structure combining the method of grey system theory based on the experiment, which are considered as an important reference for further objectively identifying petroliferous unit and the exploration of oil-gas fields in the practical application with comparison and analysis.

Spectral Comparison of Real Spectra with Site Effects Included vs MOC-2008 Teorical Spectra for Guadalajara City, Mexico

Guadalajara city is the capital of the Mexican federal state of Jalisco. It is located close to the Pacific coast and is subjected to a large seismic risk. We present a seismic response study for some sites along the city. We calculated response spectra of shear-waves by using seismic records of actual earthquakes registered on rock and near the source as Green functions and propagated them trough a flat and horizontal layered media using a linear equivalent method to compare them with the response spectra calculated according to the Federal Commission of Electricity (CFE) seismic design buildings Manual (MOC-2008, 2008) which is widely used as reference on construction projects in Mexico. Our results show that MOC-2008 manual underestimates the spectral amplitudes and frequency band for the response spectra.

Mathematical modeling of seismic gravity effect of oil and gas reservoir in crystalline basement

A new seismic and gravitational method for the decompacted zones detection in crystalline basement, based on a multi-crack-cavernous pore (gas or oil saturated) model of crystalline reservoir is proposed. To estimate the capabilities of the proposed method mathematical modeling of effective elastic and acoustic properties of granite reservoir rocks with different pore space structure is realized. The algorithm and software for solving the problem of joint inversion of seismic and gravimetric data based on Born's approximation for the space-time Green's function with root mean square background velocity for the horizontally-layered medium has been developed and tested. It has been determined that the most reliable estimation of density and seismic velocity can be obtained by joint inversion. Convincingly is illustrated on an example of the Prykerch shelf model that the presence of decompacted oil or gas saturated zone in granite basement can be confidently identified based on results of seismic and precise gravity observations.

A novel fast algorithm of electromagnetic dyadic Green's function in horizontal layered medium

In this paper, a novel fast algorithm is presented for electromagnetic (EM) dyadic Green’s functions in horizontal layered medium using direct-waves’ extraction combining with self-adaptive digital filter method. First of all, the direct-waves which characterize effects of homogeneous medium in spectral domain Green’s functions(SDGF) are extracted, and their integrals are obtained by analytical calculations. In this method, the singularity of SDGF is reduced and the integral convergence range is shortened remarkably. Then, we transform the remnant integrals of SDGF into three rapid declining integrals, and self-adaptive digital filter method is introduced to obtain solution quickly. Finally, our numerical results validate the efficiency of the algorithm.

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低速度層をいくつかもつ水平成層媒質のための走時計算

低速度層をいくつかもつ水平成層媒質のための走時計算