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1.
We have pursued two-dimensional (2D) finite-difference (FD) modelling of seismic scattering from free-surface topography. Exact free-surface boundary conditions for the particle velocities have been derived for arbitrary 2D topographies. The boundary conditions are combined with a velocity–stress formulation of the full viscoelastic wave equations. A curved grid represents the physical medium and its upper boundary represents the free-surface topography. The wave equations are numerically discretized by an eighth-order FD method on a staggered grid in space, and a leap-frog technique and the Crank–Nicholson method in time.
In order to demonstrate the capabilities of the surface topography modelling technique, we simulate incident point sources with a sinusoidal topography in seismic media of increasing complexities. We present results using parameters typical of exploration surveys with topography and heterogeneous media. Topography on homogeneous media is shown to generate significant scattering. We show additional effects of layering in the medium, with and without randomization, using a von Kármán realization of apparent anisotropy. Synthetic snapshots and seismograms indicate that prominent surface topography can cause back-scattering, wave conversions and complex wave patterns which are usually discussed in terms of inter-crust heterogeneities. 相似文献
In order to demonstrate the capabilities of the surface topography modelling technique, we simulate incident point sources with a sinusoidal topography in seismic media of increasing complexities. We present results using parameters typical of exploration surveys with topography and heterogeneous media. Topography on homogeneous media is shown to generate significant scattering. We show additional effects of layering in the medium, with and without randomization, using a von Kármán realization of apparent anisotropy. Synthetic snapshots and seismograms indicate that prominent surface topography can cause back-scattering, wave conversions and complex wave patterns which are usually discussed in terms of inter-crust heterogeneities. 相似文献
2.
Libor Šachl 《Studia Geophysica et Geodaetica》2013,57(1):84-102
The first-order Born approximation is a weak scattering perturbation method which is a powerful tool. The combination of the Born approximation and the ray theory enables to extend the applicability of the ray theory in terms of the required smoothness of the model and ensures faster computations than with, e.g., the finite difference method. We are motivated to describe and explain the effects of the numerical discretization of the Born integral on the resulting seismograms. We focus on forward modelling and study the cases in which perturbation from the background model contains the interface. We restrict ourselves to isotropic models that contain two homogeneous layers. We compare the 2D and 3D ray-based Bornapproximation seismograms with the ray-theory seismograms. The Born seismograms are computed using a grid of finite extent. We anticipate that the computational grid should contain an appropriate number of gridpoints, otherwise the seismogram would be inaccurate. We also anticipate that the limited size of the computational grid can cause problems. We demonstrate numerically that an incorrect grid can produce significant errors in the amplitude of the wave, or it can shift the seismogram in time. Moreover, the grid boundaries work as interfaces, where spurious waves can be generated. We also attempt to explain these phenomena theoretically. We give and test the options of removing the spurious waves. We show that it is possible to compute the Born approximation in a sparser grid, if we use elastic parameters averaged from some dense grid. 相似文献
3.
Many investigations of the propagation elastic waves within the earth require a technique for producing synthetic seismograms which is capable of modelling 3D propagation effects. Ray methods are an excellent option for these problems, because they can be made fully 3D and allow a relatively quick and flexible computation of synthetic seismograms. However, the two point problem of finding the ray which connects exactly a specific source and receiver, may still be difficult and time consuming. Therefore, application of the paraxial method, which allows extrapolation of the information on a given ray to nearby receiver locations, is very valuable. With this approach, great savings in computation time and significant simplification of computer codes are possible. We investigate the application of the paraxial ray method to two problems in which the effects of 3D seismic wave propagation are important. The first is a model of a reef structure. In this case, we consider synthetic seismograms for a VSP experimental configuration. When the SV source and well are located along the axis of the reef, only 2D propagation effects are observed. If the source-receiver plane is located to the side of the reef, however, the 3D shape of the reef causes significant amplitudes to be predicted for shear-wave arrivals on the transverse component of the synthetic seismograms. The second example is a ID, layered earth model, but it includes two layers which are azimuthally anisotropic due to the presence of aligned, vertical fractures. This anisotropy leads to 3D raypaths. Synthetic seismographs are presented for a cross-hole geometry both for an equivalent isotropic model and for the direction parallel to the fractures and at an angle of 45° to the fractures in the anisotropic case. These synthetics show that the differences between the isotropic case and the case for source and receivers aligned with the plane of the fractures are small and subtle. On the other hand, the predictions for the direction at 45° to the cracks show shear-wave splitting and significant transverse component signal. These results have important implications for both modelling and for applications such as tomography. It is clear that for some of the cases considered, a 2D algorithm will lead to errors in interpretation of data. In addition, ray-based tomographic techniques will have great difficulty in obtaining a well-defined 2D planar image when the signals are propagating in regions outside the image plane. 相似文献
4.
F. AMINZADEH 《Geophysical Prospecting》1989,37(8):893-906
Data from offshore Norway is used to study applications of elastic VSP modelling in detecting shear waves and observing the effects of successive mode conversion in field-recorded VSP data. The shear-wave velocities and densities from log data are used in conjunction with compressional wave velocities determined from surface seismic and log data in the VSP modelling. The time domain non-normal incidence elastic VSP modelling technique of Aminzadeh and Mendel is used as the modelling algorithm. Two surface seismograms are computed first. One is the vertical component and the other is the horizontal component for plane waves that have specified incident angles. A downward continuation method is then applied to generate seismograms at different depth points. The collection of these seismograms constitutes non-normal incidence VSPs. Both vertical and horizontal components of VSP data can be obtained by this procedure. In this paper non-normal incidence VSPs are generated for a 12.5° incident plane wave. The modelling results of layered earth systems of thin layers and thick layers are both compared with field data, and the effect of mode conversions in thin layers is observed. Several events in the field data can be explained by this elastic VSP modelling. Comparison of the model data and field data enabled a probable tube wave or out-of-plane event to be identified, the removal of which significantly improved the final VSP section. This study also shows how the VSP data helped the interpretation of the surface 3D data. 相似文献
5.
数值计算方法是考察非线性弹性波在介质中（如岩石）传播特征的重要手段.非线性弹性波的数值模拟存在陡峭间断面（点）、数值振荡以及误差的指数级增长等现象而破坏数值解的稳定性、收敛性，能否消减上述现象的不利影响成为制约数值方法有效与否的重要因素.文中同时引入了FCT算子和幅值限制器，采用中心差分格式对具有垂直对称轴的横向各向同性（VTI）介质中的二维非线性弹性波进行数值模拟，从而克服了上述困难；介绍了适用于非线性弹性波的吸收边界条件，给出了差分方程的稳定性条件.在验证了方法的有效性后成功地获取了二维VTI介质中非线性弹性波的三分量地震正演记录，表明非线性波在传播过程中会发生波形畸变等现象. 相似文献
6.
XIAOHONG XU 《Geophysical Prospecting》1990,38(2):139-168
A multichannel lattice filter structure is utilized to represent seismic waves propagating in adjacent layers in an elastic medium. Using this model, an explicit time-domain solution for arbitrary source and receiver locations is obtained as an ARMA (AutoRegressive and Moving-Average) process. The lattice and ARMA structures have given rise to an effective algorithm for the calculation of offset/downhole synthetic seismograms. A large range of recently developed offset/downhole seismic survey geometries, such as the ‘Yo-Yo’ arrangement, can thus be simulated. In addition, the explicit solutions for upgoing and downgoing waves provide new insight into the properties of general downhole seismic signals, including wave-mode conversion effects and multiple reflections. Furthermore, offset/downhole seismograms generated by a line source (i.e. 2D point source) can also be constructed by superposition of plane waves with different incidence angles. Synthetic seismograms generated using a different source-receiver arrangement indicate that the properties especially associated with offset/downhole seismic signals can be predicted by this modelling method. These properties include arrival times, amplitude attenuation and wave-mode conversion effects. Finally, utilizing this numerical modelling method to a real downhole survey with Yo-Yo geometry may lead to a proper data acquisition and processing procedure, and improves the interpretation confidence of the field section. 相似文献
7.
许康生 《地震地磁观测与研究》1992,13(2):15-19
地震泼由多种频率成份组成,在其传播过程中。由于地球介质的滤波作用,随着传播距离的增大。高频成份逐渐被衰减。周期越大的成份传播越远。因此,在地震观测上,不同频带的地震仪用于观测不同震中距范围的地震,使仪器较好地响应,就我国台网而言,短周期仪用于地方震、近震的监测,中长周期仪和长周期仪用于远震,极远震的监测,其中长周期仪偏重于记录极远震。但作者在实际分析工作中注意到,短周期仪的记录应用于远震,极远震的分析,显示出独特的作用,充分挖掘和利用短仪资料,将会更加丰富远震、极远震的震相资料。本文以高台地震台的资料为依据,从震中距和震级角度,与中长仪和长仪作比较,对短仪记录远震、极远震的震相及特征作了统计分析与初步探讨,并对新疆地区“影区”地震S波的记录、日本地区地震_PPcP等震相的出现提出了现象的存在,给出了相应的观测结果,以待步一步研究。 相似文献
8.
１９８０年和１９９２年分别在昆明和北京白家疃台架设了ＩＤＡ观测仪器，１９８５年开始又陆续在北京，兰州，海拉尔等地布设和完善了ＣＤＳＮ数字化地震观测台网，为开展长周期面波研究提供了方便。本文结合国内外研究现状，论述了超长周期地震观测在地球自由振荡，震源物理面波理论地震图合成及非均匀地球介质结构研究中的应用。同时结合１９８９年５月６日发生在秘鲁的Ｍｓ７．０地震，介绍了利用简正振型资料开发地震矩张量反演 相似文献
9.
A hybrid seismic modelling technique has been developed to investigate complex geological phenomena. Those parts of a geological structure which are too complicated to be treated theoretically are studied by two-dimensional physical models; other sections of the structure which can be treated theoretically, i.e., inhomogeneities in the vertical direction, are modelled by computer methods. A feedback process is used to combine the results of both physical and computer modelling. Horizontally layered coal-seam models are presented to test the hybrid modelling technique for normal incidence. A comparison of the hybrid seismograms with pure synthetic seismograms shows an acceptable conformity for normal incidence. A hybrid zero-offset section is shown to investigate a complex geological structure in the Ruhr coalfield in Germany. 相似文献
10.
A. T. DE HOOP 《Geophysical Prospecting》1988,36(5):465-477
Large horizontal offset and large vertical offset approximations in the modified Cagniard method for computing synthetic seismograms in a horizontally layered model of the earth are derived. They apply to each of the generalized-ray constituents into which the seismic wave motion is decomposed. For the results applying to large horizontal offset, which are known in the seismological literature, a simplified derivation is given. The results for large vertical offset, which are of particular interest to vertical seismic profiling, are new. The use of the large-offset approximations, both horizontal and vertical, leads to a considerable reduction in computation time for synthetic seismograms compared with the full three-dimensional version of the modified Cagniard method. 相似文献
11.
It is important to include the viscous effect in seismic numerical modelling and seismic migration due to the ubiquitous viscosity in an actual subsurface medium. Prestack reverse‐time migration (RTM) is currently one of the most accurate methods for seismic imaging. One of the key steps of RTM is wavefield forward and backward extrapolation and how to solve the wave equation fast and accurately is the essence of this process. In this paper, we apply the time‐space domain dispersion‐relation‐based finite‐difference (FD) method for visco‐acoustic wave numerical modelling. Dispersion analysis and numerical modelling results demonstrate that the time‐space domain FD method has great accuracy and can effectively suppress numerical dispersion. Also, we use the time‐space domain FD method to solve the visco‐acoustic wave equation in wavefield extrapolation of RTM and apply the source‐normalized cross‐correlation imaging condition in migration. Improved imaging has been obtained in both synthetic and real data tests. The migration result of the visco‐acoustic wave RTM is clearer and more accurate than that of acoustic wave RTM. In addition, in the process of wavefield forward and backward extrapolation, we adopt adaptive variable‐length spatial operators to compute spatial derivatives to significantly decrease computing costs without reducing the accuracy of the numerical solution. 相似文献
12.
Synthetic seismograms can be very useful in aiding understanding of wave propagation through models of real media, verification of geologic models derived from interpretation of field seismic data, and understanding the nature and complexity of wave phenomena. If meaningful results are to be obtained from synthetic seismograms, the method of their computation must, in general, include three-dimensional geometrical spreading of wavefronts associated with highly concentrated (i.e., point) sources. The method should also adequately represent the seismic response of solid-layered media by including enough primaries, multiples, and converted phases to accurately approximate the total wavefield. In addition to these features, it is also very helpful, although not always essential, if the method of seismogram computation provides for explicit identification of wave type and ray path for each arrival. Various seismograms, computed via asymptotic ray theory and an automatic ray generation scheme, are presented for a highly simplified North Sea velocity structure. This is done to illustrate the importance of the above features and to demonstrate the inadequacy of the plane-wave synthesis method of seismogram computation for point sources and the limitations of acoustic models of solid-layered media. 相似文献
13.
利用2004～2005年Hi-CLIMB计划架设在藏南日喀则附近由28台宽频带数字地震仪组成的二维台阵的地震记录,应用双差层析定位方法(TomoDD)对454个区域地震进行了精确重定位,共确定了340个地震的精确位置.发现区域震源深度呈明显的双层分布,其中有21 个地震的深度在50～80 km之间,与该地区的莫霍面深度相近.通过不同深度震源的理论地震图与实际地震图对比的方法,发现震源位置位于莫霍面上下地震图的震相存在明显差异,从而给出了存在地幔地震的直接观测证据.这一发现,对长期争论的地幔地震是否存在及大陆岩石圈流变结构的“三明治”模型有重要参考意义. 相似文献
14.
We characterize the seismic response of Lake Vostok, an Antarctic subglacial lake located at nearly 4 km depth below the ice sheet. This study is relevant for the determination of the location and morphology of subglacial lakes. The characterization requires the design of a methodology based on rock physics and numerical modelling of wave propagation. The methodology involves rock-physics models of the shallow layer (firn), the ice sheet and the lake sediments, numerical simulation of synthetic seismograms, ray tracing, τ–p transforms, and AVA analysis, based on the theoretical reflection coefficients. The modelled reflection seismograms show a set of straight events (refractions through the firn and top-ice layer) and the two reflection events associated with the top and bottom of the lake. Theoretical AVA analysis of these reflections indicates that, at near offsets, the PP-wave anomaly is negative for the ice/water interface and constant for the water/sediment interface. This behaviour is shown by AVA analysis of the synthetic data set. This study shows that subglacial lakes can be identified by using seismic methods. Moreover, the methodology provides a tool for designing suitable seismic surveys. 相似文献
15.
16.
Numerical simulation of 2D wave propagation on unstructured grids using explicit differential operators 总被引：2，自引：0，他引：2
We present a numerical method of simulating seismic wave propagation on unstructured 2D grids. The algorithm is based on the velocity–stress formulation of the elastic wave equation and therefore uses a staggered grid approach. Unlike finite-element or spectral-element methods, which can also handle flexible unstructured grids, we use explicit differential operators for the calculation of spatial derivatives in each time step. As shown in previous work, three types of these operators are used, and their particular performance is analysed and compared with standard explicit finite-difference operators on regular quadratic and hexagonal grids. Our investigations are especially focused on the influence of grid irregularity, sampling rate (i.e. gridpoints per wavelength) and numerical anisotropy on the accuracy of numerical seismograms. The results obtained from the various methods are therefore compared with analytical solutions. The algorithm is then applied to a number of models that are difficult to handle using (quasi-)regular grid methods. Such alternative techniques may be useful in modelling the full wavefield of bodies with complex geometries (e.g. cylindrical bore-hole samples, 2D earth models) and, because of their local character, they are well suited for parallelization. 相似文献
17.
Helga Emmerich 《Physics of the Earth and Planetary Interiors》1993,80(3-4):125-134
Computing synthetic seismograms for media with localized heterogeneous regions can be performed using hybrid methods. Here, a combination of a finite-difference (FD) technique and a frequency-wavenumber (ω − k) filtering is applied to model wave reflection at different kinds of core-mantle boundary (CMB) topography. The FD method is only applied in the neighbourhood of the CMB, while the ω − k filter is used to continue the reflected wavefield to the Earth's surface. Synthetic SH-seismograms for ScS with a dominant frequency of 0.5 Hz are computed at epicentral distances from 44° to 69°. The topography varies in amplitude (maximum amplitude of 1.0–2.7 km) and in its wavenumber spectrum; it is either monochromatic (wavelengths from 55 to 270 km) or statistical (coloured noise). The seismograms for a CMB with topography are compared with those for a plane CMB. We observe that monochromatic topography with short wavelengths (less than 100 km) results in amplitude reduction and shorter travel times than in the case of a plane CMB, but no variations with epicentral distance appear, whereas greater wavelengths exhibit amplitude variations with distance as well as travel time residuals, which both correlate with the CMB topography. Statistical models show amplitude variations with epicentral distance, while the travel time residuals are very small (less than 0.1 s). All synthetics illustrate that wavefront healing occurs along the ray path from the CMB to the Earth's surface. While the seismograms at the CMB exhibit strong fluctuations, the fluctuations at the surface are smoothed and reduced. This demonstrates that it is necessary to use wave theoretical methods for computing synthetic seismograms for complicated structures at greater depth. It also follows that travel times are less sensitive to the structure than the amplitudes. 相似文献
18.
The presence of natural gas in the pore space of reservoir rocks results in a significant decrease in P-wave velocity. Even low gas saturation can generate seismic anomalies (DHI) and false image of gas accumulation of economic importance. This article presents an attempt to evaluate gas saturation from 2D seismic section in the Miocene sandstone strata in the south-eastern part of the Carpathian Foredeep. The ESTYMACJA program and the Biot-Gassmann model were used to study the dependence between elastic parameters and saturating fluids (water and gas) recorded in wells. Series of calculations was carried out using a method of fluid substitution for various gas saturation. The applicability of seismic data for evaluating gas saturation of reservoir beds was assessed with the use of 1D modelling (synthetic seismograms) and 2D modelling (theoretical seismic section) calculated for different gas saturation. The proposed methodology can be used to identify low and high gas-saturated zones and contour the reservoir. 相似文献
19.
When treating the forward full waveform case, a fast and accurate algorithm for modelling seismic wave propagation in anisotropic inhomogeneous media is of considerable value in current exploration seismology. Synthetic seismograms were computed for P-SV wave propagation in transversely isotropic media. Among the various techniques available for seismic modelling, the finite-difference method possesses both the power and flexibility to model wave propagation accurately in anisotropic inhomogeneous media bounded by irregular interfaces. We have developed a fast high-order vectorized finite-difference algorithm adapted for the vector supercomputer. The algorithm is based on the fourth-order accurate MacCormack-type splitting scheme. Solving the equivalent first-order hyperbolic system of equations, instead of the second-order wave equation, avoids computation of the spatial derivatives of the medium's anisotropic elastic parameters. Examples indicate that anisotropy plays an important role in modelling the kinematic and the dynamic properties of the wave propagation and should be taken into account when necessary. 相似文献
20.
Love waves from five earthquakes in southwest Germany, Italy, Yugoslavia, Greece and Algeria, as recorded at the broadband Gräfenberg array in eastern Bavaria, are modelled in detail using an extended reflectivity method. The focal mechanisms are taken from the literature or determined from long-period WWNSS data. The theoretical double-couple moment function used for modelling increases smoothly during the risetime T from zero to the seismic moment M0. T and M0 are determined by matching the observed and theoretical Love-wave seismograms in the long-period WWNSS frequency band. T is approximately equal to the rupture duration; values from 1.4 to 20 s are found. Seismic moments generally agree within a factor of about two with those found by other authors from larger data sets. The earthquakes in southwest Germany and Greece were simple events and can be modelled very well by one double couple. In the case of the other earthquakes, the theoretical Love-wave seismograms are too short. For these earthquakes there is some independent evidence for a multiple-event nature. This evidence is condensed into source models consisting of two or three double couples representing separate and complete sub-earthquakes, which then explain the observations quite well. In the case of the Algerian earthquake, the long Love-wave duration may also be due to complications in structure along the wavepath across the Mediterranean and the Alps. The present results show that accurate Love-wave modelling for a single station at regional distance from an epicentre is a reliable method for estimation of seismic moment and rupture duration. Use of a digitally recording station with large dynamic range allows events over a large magnitude interval to be studied. The Gräfenberg array is well suited for such an investigation of European and North African earthquakes. 相似文献