共查询到20条相似文献，搜索用时 593 毫秒
1.
COMPUTATION OF ZERO-OFFSET VERTICAL SEISMIC PROFILES INCLUDING GEOMETRICAL SPREADING AND ABSORPTION*
Synthetic vertical seismic profiles (VSP) provide a useful tool in the interpretation of VSP data, allowing the interpreter to analyze the propagation of seismic waves in the different layers. A zero-offset VSP modeling program can also be used as part of an inversion program for estimating the parameters in a layered model of the subsurface. Proposed methods for computing synthetic VSP are mostly based on plane waves in a horizontally layered elastic or anelastic medium. In order to compare these synthetic VSP with real data a common method is to scale the data with the spherical spreading factor of the primary reflections. This will in most cases lead to artificial enhancement of multiple reflections. We apply the ray series method to the equations of motion for a linear viscoelastic medium after having done a Fourier transformation with respect to the time variable. This results in a complex eikonal equation which, in general, appears to be difficult to solve. For vertically traveling waves in a horizontally layered viscoelastic medium the solution is easily found to be the integral along the ray of the inverse of the complex propagation velocity. The spherical spreading due to a point source is also complex, and it is equal to the integral along the ray of the complex propagation velocity. Synthetic data examples illustrate the differences between spherical, cylindrical, and plane waves in elastic and viscoelastic layered media. 相似文献
2.
— A P-wave tomographic method for 3-D complex media (3-D distribution of elastic parameters and curved interfaces) with orthorhombic symmetry is presented in this paper. The technique uses an iterative linear approach to the nonlinear travel-time inversion problem. The hypothesis of orthorhombic anisotropy and 3-D inhomogeneity increases the set of parameters describing the model dramatically compared to the isotropic case. Assuming a Factorized Anisotropic Inhomogeneous (FAI) medium and weak anisotropy, we solve the forward problem by a perturbation approach. We use a finite element approach in which the FAI medium is divided into a set of elements with polynomial elastic parameter distributions. Inside each element, analytical expressions for rays and travel times, valid to first-order, are given for P waves in orthorhombic inhomogeneous media. More complex media can be modeled by introducing interfaces separating FAI media with different elastic properties. Simple formulae are given for the Fréchet derivatives of the travel time with respect to the elastic parameters and the interface parameters. In the weak anisotropy hypothesis the P-wave travel times are sensitive only to a subset of the orthorhombic parameters: the six P-wave elastic parameters and the three Euler angles defining the orientation of the mirror planes of symmetry. The P-wave travel times are inverted by minimizing in terms of least-squares the misfit between the observed and calculated travel times. The solution is approached using a Singular Value Decomposition (SVD). The stability of the inversion is ensured by making use of suitable a priori information and/or by applying regularization. The technique is applied to two synthetic data sets, simulating simple Vertical Seismic Profile (VSP) experiments. The examples demonstrate the necessity of good 3-D ray coverage when considering complex anisotropic symmetry. 相似文献
3.
We propose a finite difference method, using a hexagonal grid, to compute displacements (stresses, velocities, accelerations) in the near-field of a 2-D in-plane stress-drop crack, in both whole space (constant stress-drop) and half-space (depth-dependent stress-drop). To exercise the method, the stress field distribution is evaluated for both fundamental 2-D shear cracks, anti-plane. In order to test the method's reliability, the results are compared with some analytical and numerical solutions available in the literature (Kostrov, 1964;Virieux andMadariaga, 1982). For the in-plane source, the results emphasize that the method can resolve the stress concentration due to the rupture front from the stress peak associated with the shear wave propagating in front of the crack. Synthetic motions are computed on the fault, but also in an infinite medium and at the free surface. The rather complex waveforms generated in the near-field, even by simple sources, emphasize the contribution of all wave terms (near, intermediate and far-field) to the motion. The presence of near-field and the numerical procedure explain the significant low frequency content of the computed seismograms. The set of treated problems proves the method is stable and accurate. 相似文献
4.
Mohan D. Sharma 《Journal of Seismology》2007,11(2):187-197
A new technique relates the wave velocity of the surface waves in anisotropic elastic medium to its elastic constants. Anisotropic
propagation of surface waves is studied in a half-space occupied by a general anisotropic elastic solid. The phase velocity
expressions of quasi-waves, in three-dimensional space, are used to derive the secular equation of surface waves. The complex
secular equation is resolved, analytically, into real and imaginary parts and is then solved, numerically, for phase velocity
along a given phase direction on the surface. The complete procedure is thus analogous to the one used for conventional Rayleigh
waves in isotropic medium. A non-linear equation relates the ray direction of the surface waves to its phase direction on
the (plane) surface of the medium. The analytical differentiation of secular equation yields the directional derivative of
phase velocity. This derivative is used to calculate the wave velocity of surface waves. Spatial variations of phase velocity,
wave velocity and ray direction over the free plane surface are plotted for the numerical models of crustal rocks with orthorhombic,
monoclinic and triclinic anisotropies. 相似文献
5.
The common-ray approximation eliminates problems with ray tracing through S-wave singularities and also considerably simplifies
the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation
from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies.
It is thus of principal importance for numerical applications to estimate the errors due to the common-ray approximation applied.
The anisotropic-common-ray approximation of the coupling ray theory is more accurate than the isotropic-common-ray approximation.
We derive the equations for estimating the travel-time errors due to the anisotropic-common-ray (and also isotropic-common-ray)
approximation of the coupling ray theory. The errors of the common-ray approximations are calculated along the anisotropic
common rays in smooth velocity models without interfaces. The derivation is based on the general equations for the second-order
perturbations of travel time. 相似文献
6.
Luděk Klimeš 《Studia Geophysica et Geodaetica》2018,62(2):261-271
In an elastic medium, it was proved that the stiffness tensor is symmetric with respect to the exchange of the first pair of indices and the second pair of indices, but the proof does not apply to a viscoelastic medium. In order to indicate which phenomena could be observed in the wave field if the stiffness matrix were non–symmetric, we propose the frequency–domain ray series for viscoelastic waves with a non–symmetric stiffness tensor in this paper. 相似文献
7.
李远钦 《CT理论与应用研究》1994,3(1):30-32
本文把Ｒａｄｏｎ变换公式推广到任意ｎ维的情况。同时结合ｎ维Ｒａｄｏｎ变换和摄动理论提出了一种既能用于地面资料又能用于ＶＳＰ资料的偏移方法。 相似文献
8.
Luděk Klime? 《Studia Geophysica et Geodaetica》2012,56(2):457-482
The resolution of a general 3-D common-shot elastic prestack depth migration in a heterogeneous anisotropic medium is studied approximately, using the ray theory. It is demonstrated that the migrated section can approximately be represented by the convolution of the reflectivity function with the corresponding local resolution function. Alternatively, it can also be approximately represented by the convolution of the spatial distribution of the weak-contrast displacement reflection-transmission coefficient with the corresponding local resolution function. The derived explicit approximate equations enable us to predict the migration resolution approximately without doing the whole and expensive migration. The equations are applicable to 3-D elastic migrations in 3-D isotropic or anisotropic, heterogeneous velocity models. Both the reflectivity function and the spatial distribution of the weak-contrast displacement reflection-transmission coefficient approximately determine the linear combination of the perturbations of elastic moduli and density to which the migrated section is sensitive. The imaged linear combination of the perturbations of elastic parameters depends on the selection of the polarizations (wave types) of the incident and back-propagated wavefields and on the directions of propagation. The resolution of the linear combination of the perturbations of elastic moduli and density in the migrated section is determined by the above mentioned local resolution functions. The local resolution functions depend on the aperture and on the imaging function. The imaging function is determined by the source time function and by the form of the imaging functional. The local resolution functions are considerably sensitive to heterogeneities. The local resolution functions in elastic media differ from their acoustic counterparts, especially by the existence of converted scattered waves in elastic media. 相似文献
9.
A new method of numerical computation of elastic wavefields in regions containing caustics is tested. The method is an extension of the asymptotic ray theory (ART). The essential features of the method consist of the application of expressions which are well defined at caustics and expressed in terms of ray tracing combined with complex ray tracing in caustic shadows. The method and an outline of the underlying theory are briefly presented, followed by a comparison with finite differences on a test model involving a caustic cusp. The comparison reveals the unexpectedly high degree of accuracy of the new method. 相似文献
10.
三维VSP资料中,各种不同类型的波混杂一起形成复杂的波场.因此,波场分离是三维VSP数据处理关键的第一步.从不同波场的偏振方向和传播方向之差异着手,提出了一种高保真的VSP波场分离方法.首先通过射线追踪和偏振滤波的结合,把复杂波场(分解为简单波场;然后根据简单波场中不同波的传播方向截然相反的特点,进行方向滤波,达到波场分离的目的.实际数据处理表明,与常规波场分离方法相比,本方法大大降低了混波作用以及由此而生的波形畸变. 相似文献
11.
Common-ray tracing and dynamic ray tracing for S waves in a smooth elastic anisotropic medium 总被引：1，自引：0，他引：1
L. Klimeš 《Studia Geophysica et Geodaetica》2006,50(3):449-461
Anisotropic common S-wave rays are traced using the averaged Hamiltonian of both S-wave polarizations. They represent very
practical reference rays for calculating S waves by means of the coupling ray theory. They eliminate problems with anisotropic-ray-theory
ray tracing through some S-wave slowness-surface singularities and also considerably simplify the numerical algorithm of the
coupling ray theory for S waves.
The equations required for anisotropic-common-ray tracing for S waves in a smooth elastic anisotropic medium, and for corresponding
dynamic ray tracing in Cartesian or ray-centred coordinates, are presented. The equations, for the most part generally known,
are summarized in a form which represents a complete algorithm suitable for coding and numerical applications. 相似文献
12.
2.5-D modeling and inversion techniques are much closer to reality than the simple and traditional 2-D seismic wave modeling
and inversion. The sensitivity kernels required in full waveform seismic tomographic inversion are the Fréchet derivatives
of the displacement vector with respect to the independent anisotropic model parameters of the subsurface. They give the sensitivity
of the seismograms to changes in the model parameters. This paper applies two methods, called ‘the perturbation method’ and
‘the matrix method’, to derive the sensitivity kernels for 2.5-D seismic waveform inversion. We show that the two methods
yield the same explicit expressions for the Fréchet derivatives using a constant-block model parameterization, and are available
for both the line-source (2-D) and the point-source (2.5-D) cases. The method involves two Green’s function vectors and their
gradients, as well as the derivatives of the elastic modulus tensor with respect to the independent model parameters. The
two Green’s function vectors are the responses of the displacement vector to the two directed unit vectors located at the
source and geophone positions, respectively; they can be generally obtained by numerical methods. The gradients of the Green’s
function vectors may be approximated in the same manner as the differential computations in the forward modeling. The derivatives
of the elastic modulus tensor with respect to the independent model parameters can be obtained analytically, dependent on
the class of medium anisotropy. Explicit expressions are given for two special cases—isotropic and tilted transversely isotropic
(TTI) media. Numerical examples are given for the latter case, which involves five independent elastic moduli (or Thomsen
parameters) plus one angle defining the symmetry axis. 相似文献
13.
Numerical solution of the scalar and elastic wave equations has greatly aided geophysicists in modeling seismic wave fields
in the complicated geologic structures containing hydrocarbons and hence increases the geologic interpretation. Finite-difference
method offers a versatile approach to compute synthetic seismograms numerically for given subsurface complex geological structures.
To avoid the spatial derivative of the elastic parameters and density, elastodynamic equation (first-order hyperbolic equation)
has been solved using the Lax-Wendroff scheme. A numerical finite-difference modeling program has been developed for the P-SV
wave using the above solution. A line source with a time delay of 0.015s and dominant frequency of 120 Hz has been utilized
in the simulation. In order to avoid the large values of the displacement vector in the source region,Alterman andKaral's method (1968) has been utilized. Horizontal and vertical component synthetic seismograms have been computed for two different
geological models with and without oil and gas bearing zones. It has been concluded from the response that a finite-difference
technique not only yields the relative arrival times but also accounts for the variation in amplitude and phase according
to the elastic impedance contrast across the interfaces. It should come as no surprise to learn that in spite of the limitation
of this numerical method, the scheme has provided a valid response for the thin layer, high acoustic impedance contrast and
the pinch out. 相似文献
14.
Konstantin Latychev Jerry X. Mitrovica Miaki Ishii Ngai-Ham Chan James L. Davis 《Earth and Planetary Science Letters》2009,277(1-2):86-90
The deformational and gravitational response of the Earth to the tide generating potential has generally involved 1-D (i.e., depth varying) Earth models. Progressive improvement in observational constraints on body tides, generated from both ground and space-based surveys, suggests that an examination of the potential impact of lateral variations in Earth structure is warranted. We present a suite of predictions of the body tide response within the semi-diurnal, diurnal and long-period tidal bands computed using a finite-volume numerical code. The calculations adopt 3-D density and elastic structure taken from seismic inferences and, in a subset of the calculations, dynamic topography on the surface and internal interfaces. We find that perturbations in the radial displacement and surface gravity within the semi-diurnal band reach ~ 1 mm and 0.15 µgal, respectively. The perturbations in the diurnal band are comparable to these values, and within the long-period band they are a factor of 3–5 smaller. We also demonstrate that lateral variations in the elastic moduli, which have been ignored in recent work, contribute greater than 50% of the total perturbation. The level of perturbation associated with 3-D structure exceeds the current observational uncertainty obtainable using space-geodetic methods, and this suggests the possibility of performing tidal tomographic inversions of such data. 相似文献
15.
The common ray approximation considerably simplifies the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies. It is thus of principal importance for numerical applications to estimate the errors due to the common ray approximation.We derive the equations for estimating the travel-time errors due to the isotropic and anisotropic common ray approximations of the coupling ray theory. These equations represent the main result of the paper. The derivation is based on the general equations for the second-order perturbations of travel time. The accuracy of the anisotropic common ray approximation can be studied along the isotropic common rays, without tracing the anisotropic common rays.The derived equations are numerically tested in three 1-D models of differing degree of anisotropy. The first-order and second-order perturbation expansions of travel time from the isotropic common rays to anisotropic-ray-theory rays are compared with the anisotropic-ray-theory travel times. The errors due to the isotropic common ray approximation and due to the anisotropic common ray approximation are estimated. In the numerical example, the errors of the anisotropic common ray approximation are considerably smaller than the errors of the isotropic common ray approximation.The effect of the isotropic common ray approximation on the coupling-ray-theory synthetic seismograms is demonstrated graphically. For comparison, the effects of the quasi-isotropic projection of the Green tensor, of the quasi-isotropic approximation of the Christoffel matrix, and of the quasi-isotropic perturbation of travel times on the coupling-ray-theory synthetic seismograms are also shown. The projection of the travel-time errors on the relative errors of the time-harmonic Green tensor is briefly presented. 相似文献
16.
Petr Bulant 《Pure and Applied Geophysics》1996,148(3-4):421-447
Algorithm for determination of all two-point rays of a given elementary wave by means of the shooting method is presented. The algorithm is designed for general 3-D models composed of inhomogeneous geological blocks separated by curved interfaces. It is independent of the initial conditions for rays and of the initial-value ray tracer. The algorithm described has been coded in Fortran 77, using subroutine packages MODEL and CRT for model specification and for initial-value ray tracing. 相似文献
17.
研究了三维弱各向异性近似下,利用伪P波(伪纵波)模拟弹性波场P分量在倾斜对称轴的横向各向同性(TTI)介质中的传播过程,并对比了分别基于弹性Hooke定律、弹性波投影和运动学色散方程所建立的三种二阶差分伪P波方程的正演特点.目前这些伪P波方程数值计算主要采用规则网格差分,但是规则网格在TTI模拟中有低效率、低精度以及不稳定的缺点.为了提高计算的精度,本文构建出相应方程的交错网格有限差分格式.通过对比伪P波方程在三维TTI介质中不同的数值模拟的表达形式,本文认为基于色散方程所建立的伪P波方程在模拟弹性波中P波传播的过程中具有最小的噪声.本文分析不同的各向同性对称轴空间角度的频散特征,并引入适当的横波速度维持计算的稳定.二维模型算例表明,本文提出的交错网格正演算法可以得到稳定光滑的伪P波正演波场.使用本文交错网格算法对二维BP TTI模型的逆时偏移也具有较稳定的偏移结果. 相似文献
18.
19.
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
20.
The behaviour of the actual polarization of an electromagnetic wave or elastic S–wave is described by the coupling ray theory, which represents the generalization of both the zero–order isotropic and anisotropic ray theories and provides continuous transition between them. The coupling ray theory is usually applied to anisotropic common reference rays, but it is more accurate if it is applied to reference rays which are closer to the actual wave paths. In a generally anisotropic or bianisotropic medium, the actual wave paths may be approximated by the anisotropic–ray–theory rays if these rays behave reasonably. In an approximately uniaxial (approximately transversely isotropic) anisotropic medium, we can define and trace the SH (ordinary) and SV (extraordinary) reference rays, and use them as reference rays for the prevailing–frequency approximation of the coupling ray theory. In both cases, i.e. for the anisotropic–ray–theory rays or the SH and SV reference rays, we have two sets of reference rays. We thus obtain two arrivals along each reference ray of the first set and have to select the correct one. Analogously, we obtain two arrivals along each reference ray of the second set and have to select the correct one. In this paper, we suggest the way of selecting the correct arrivals. We then demonstrate the accuracy of the resulting prevailing–frequency approximation of the coupling ray theory using elastic S waves along the SH and SV reference rays in four different approximately uniaxial (approximately transversely isotropic) velocity models. 相似文献