共查询到20条相似文献，搜索用时 93 毫秒
1.
P. Jílek 《Pure and Applied Geophysics》2002,159(7-8):1527-1562
—?I derive converted P S-wave reflection coefficients at a planar weak-contrast interface separating two weakly anisotropic half-spaces using first-order perturbation theory. The general expressions are further specified for the interface separating any of the two following media: isotropic, transversely isotropic with a vertical symmetry axis (VTI), transversely isotropic with a horizontal symmetry axis (HTI) and orthorhombic. Relatively simple forms of small-angle reflection coefficients are also obtained. The coefficients are expressed as functions of Thomsen-type medium parameters and incidence and azimuthal phase angles. Derived expressions, as well as their application, are more complicated than the corresponding expressions for P P-wave reflection coefficients. General characteristics and pitfalls are discussed. Numerical tests reveal a good agreement between exact and approximate coefficients for most models presented. 相似文献
2.
Constraining the anisotropy structure of the crust by joint inversion of seismic reflection travel times and wave polarizations 总被引：2，自引：0，他引：2
In the context of wide-angle seismic profiling, the determination of the physical properties of the Earth crust, such as the
elastic layer depth and seismic velocity, is often performed by inversion of P- and/or S-phases propagation data supplying
the geometry of the medium (reflector depths) or any other structural parameter (P- or S-wave velocity, density...). Moreover,
the inversion for velocity structure and interfaces is commonly performed using only seismic reflection travel times and/or
crustal phase amplitudes in isotropic media. But it is very important to utilize more available information to constrain the
non-uniqueness of the solution. In this paper, we present a simultaneous inversion method of seismic reflection travel times
and polarizations data of transient elastic waves in stratified media to reconstruct not only layer depth and vertical P-wave
velocity but also the anisotropy feature of the crust based on the estimation of the Thomsen’s parameters. We carry out
a checking with synthetic data, comparing the inversion results obtained by anisotropic travel-time inversion to the results
derived by joint inversion of seismic reflection travel times and polarizations data. The comparison proves that the first
procedure leads to biased anisotropic models, while the second one fits nearly the real model. This makes the joint inversion
method feasible. Finally, we investigate the geometry, P-wave velocity structure and anisotropy of the crust beneath Southeastern
China by applying the proposed inversion method to previously acquired wide-angle seismic data. In this case, the anisotropy
signature provides clear evidence that the Jiangshan-Shaoxing fault is the natural boundary between the Yangtze and Cathaysia
blocks. 相似文献
3.
—Approximate PP plane wave displacement coefficients of reflection and transmission for weak contrast interfaces separating weakly but arbitrarily anisotropic elastic media are presented. The PP reflection coefficient for such an interface has been derived recently by Vavry?uk and P?en?ík (1997). The PP transmission coefficient presented in this paper was derived by the same approach. The coefficients are given as a sum of the coefficient for the weak contrast interface separating two nearby isotropic media and a term depending linearly on contrasts of the so-called weak anisotropy (WA) parameters (parameters specifying deviation of properties of the medium from isotropy), across the interface. While the reflection coefficient depends only on 8 of the complete set of the WA parameters describing P-wave phase velocity in weakly anisotropic media, the transmission coefficient depends on their complete set. The PP reflection coefficient depends on "shear-wave splitting parameter" γ. Tests of accuracy of the approximate formulae are presented on several models. 相似文献
4.
W. Friederich 《Pure and Applied Geophysics》1998,151(2-4):649-667
—A general relation linking the elasticity tensor of an anisotropic medium with that of the constituting single crystals and the function describing the orientation distribution of the crystals is derived. By expanding the orientation distribution function (ODF) into tensor spherical harmonics and using canonical components of the elasticity tensors, it is shown that the elastic tensor of the medium is completely determined by a finite number of expansion coefficients, namely those with harmonic degree l≤ 4. The number of expansion coefficients actually needed to determine the elastic constants of the medium depends on the symmetry of the single crystals. For hexagonal symmetry of the single crystals it is shown that only 8 real numbers are required to fix the 13 elastic constants which are for example needed to determine the azimuthal dependence of surface wave velocities. Thus, inversions of observations of seismic anisotropy are feasible which do not make any a priori assumptions on the orientation of the crystals. As a byproduct of the derivation, a formula is given which allows the easy calculation of the elastic constants of a medium composed of hexagonal crystals obeying an arbitrary ODF. An application of the theoretical results to the inversion of surface wave dispersion curves for an anisotropic 1D-mantle model is presented. For the S-wave velocities the results are similar to those of previous inversions but the new approach also yields P-wave velocities consistent with the assumption of oriented olivine. Moreover it provides a hint of the orientation distribution of the crystals. 相似文献
5.
Inversion of Travel Times in Weakly Anisotropic Rock Samples 总被引：1，自引：0，他引：1
Based on the perturbation theory, inversion formulae for travel time of qP and qS waves in arbitrary weak anisotropy media are presented. The inversion formulae are linear expressions of elastic parameters expressed in terms of weak anisotropy (WA) parameters. The formulae of qS1 and qS2 waves have the same form and they can be used without identifying which wave is considered. A synthetic experiment similar to the measurement of rock sample in the laboratory is carried out to illustrate the efficiency of the presented inversion formulae. Two data sets for qP wave travel time from rock samples in the laboratory are inverted and 15 WA parameters are obtained. 相似文献
6.
Seismic amplitude variation with offset and azimuth (AVOaz) inversion is well known as a popular and pragmatic tool utilized to estimate fracture parameters. A single set of vertical fractures aligned along a preferred horizontal direction embedded in a horizontally layered medium can be considered as an effective long-wavelength orthorhombic medium. Estimation of Thomsen’s weak-anisotropy (WA) parameters and fracture weaknesses plays an important role in characterizing the orthorhombic anisotropy in a weakly anisotropic medium. Our goal is to demonstrate an orthorhombic anisotropic AVOaz inversion approach to describe the orthorhombic anisotropy utilizing the observable wide-azimuth seismic reflection data in a fractured reservoir with the assumption of orthorhombic symmetry. Combining Thomsen’s WA theory and linear-slip model, we first derive a perturbation in stiffness matrix of a weakly anisotropic medium with orthorhombic symmetry under the assumption of small WA parameters and fracture weaknesses. Using the perturbation matrix and scattering function, we then derive an expression for linearized PP-wave reflection coefficient in terms of P- and S-wave moduli, density, Thomsen’s WA parameters, and fracture weaknesses in such an orthorhombic medium, which avoids the complicated nonlinear relationship between the orthorhombic anisotropy and azimuthal seismic reflection data. Incorporating azimuthal seismic data and Bayesian inversion theory, the maximum a posteriori solutions of Thomsen’s WA parameters and fracture weaknesses in a weakly anisotropic medium with orthorhombic symmetry are reasonably estimated with the constraints of Cauchy a priori probability distribution and smooth initial models of model parameters to enhance the inversion resolution and the nonlinear iteratively reweighted least squares strategy. The synthetic examples containing a moderate noise demonstrate the feasibility of the derived orthorhombic anisotropic AVOaz inversion method, and the real data illustrate the inversion stabilities of orthorhombic anisotropy in a fractured reservoir. 相似文献
7.
在长波长假设条件下,水平层状地层中发育一组垂直排列的裂缝构成了等效正交各向异性介质.各向异性参数与裂缝弱度参数的估算有助于非均匀各向异性介质的各向异性特征描述,而弹性逆散射理论是非均匀介质参数反演的有效途径.基于地震散射理论,我们首先推导了非均匀正交介质中纵波散射系数方程,并通过引入正交各向异性特征参数,提出了一种新颖的正交各向异性方位弹性阻抗参数化方法.为了提高反演的稳定性与横向连续性,我们发展了贝叶斯框架下的正交各向异性方位弹性阻抗反演方法,同时考虑了柯西稀疏约束正则化和平滑模型约束正则化,最终使用非线性的迭代重加权最小二乘策略实现了各向异性特征参数的稳定估算.模型和实际资料处理表明,反演结果与测井解释数据相吻合,证明了该方法能够稳定可靠地从方位叠前地震资料中获取各向异性特征参数,减小参数估算的不确定性,为非均匀正交介质的各向异性预测提供了一种高可靠性的地震反演方法. 相似文献
8.
9.
Most of P-wave anisotropic kinematic algorithms (modeling, processing, and inversion) have been developed for the case of Transverse Isotropy (TI). Does it mean that when dealing with more complex symmetry types (Arbitrarily tilted TI, orthorhombic, monoclinic or even triclinic), all these algorithms are irrelevant? In fact, not at all. It has recently been demonstrated that in 2D geometry any qP-wave TI kinematic algorithm can be simply generalized to the case of monoclinic symmetry using the so-called Azimuthally Dependent Anisotropy Parameter Transformation (ADAPT), assuming moderate anisotropy. The extension of the technique to the case of arbitrary anisotropy type (triclinic) is achieved in this paper. The method is successfully checked for seismic modeling in a full 2D model with layers of contrasted anisotropy types and with arbitrary vertical and horizontal velocity variations (non-constant gradient). Typically, the approximate travel times using ADAPT differ from the exact travel times by a few milliseconds for total travel times of the order of a few seconds. Applications to seismic processing are also described. The simplicity of the procedure and the generality of the applicability of the ADAPT recipe are striking and very convenient for practical applications. They certainly deserve further analysis. 相似文献
10.
Based on the long-wavelength approximation, a set of parallel vertical fractures embedded in periodic thin interbeds can be regarded as an equivalent orthorhombic medium. Rock physics is the basis for constructing the relationship between fracture parameters and seismic response. Seismic scattering is an effective way to inverse anisotropic parameters. In this study, we propose a reliable method for predicting the Thomsen’s weak anisotropic parameters and fracture weaknesses in an orthorhombic fractured reservoir using azimuthal pre-stack seismic data. First, considering the influence of fluid substitution in mineral matrix, porosity, fractures and anisotropic rocks, we estimate the orthorhombic anisotropic stiffness coefficients by constructing an equivalent rock physics model for fractured rocks. Further, we predict the logging elastic parameters, Thomsen’s weak parameters, and fracture weaknesses to provide the initial model constraints for the seismic inversion. Then, we derive the P-wave reflection coefficient equation for the inversion of Thomsen’s weak anisotropic parameters and fracture weaknesses. Cauchy-sparse and smoothing-model constraint regularization taken into account in a Bayesian framework, we finally develop a method of amplitude variation with angles of incidence and azimuth (AVAZ) inversion for Thomsen’s weak anisotropic parameters and fracture weaknesses, and the model parameters are estimated by using the nonlinear iteratively reweighted least squares (IRLS) strategy. Both synthetic and real examples show that the method can directly estimate the orthorhombic characteristic parameters from the azimuthally pre-stack seismic data, which provides a reliable seismic inversion method for predicting Thomsen’s weak anisotropic parameters and fracture weaknesses. 相似文献
11.
—The 3-D P-wave velocity structure of the upper crust in the region of western Greece is investigated by inversion of about 1500 residuals of P-wave arrival times from local earthquake data recorded in the year 1996 by the newly established University of Patras Seismic Network (PATNET). The resulting velocity structure shows strong horizontal variations due to the complicated structure and the variation of crustal thickness. Relatively low-velocity contours are observed in the area defined by Cephallonia—Zakynthos Islands and northwestern Peloponnesos. This is in addition to some well localized peaks of relatively higher values of P-wave velocity may be related to the zone of Triassic evaporites in the region and correspond to diapirism that breaks through to the uppermost layer. Finally, a low P-velocity ‘deeping’ zone extending from Zakynthos to the Gulf of Patras is correlated with Bouguer anomaly map and onshore and offshore borehole drillings which indicate that thick sediments overly the evaporites which exist there at depth greater than 2 km. 相似文献
12.
—Anisotropy in the subcontinental lithosphere becomes increasingly important, because it is observed in many seismic studies especially for P n -waves. Typical rocks of the uppermost mantle are peridotites, which predominantly exhibit a pronounced elastic anisotropy. This anisotropy is mainly caused by the anisotropic elastic properties and the lattice preferred orientation (here referred to as texture) of olivine. To evaluate the elastic anisotropy of peridotites from the subcontinental lithosphere, specimens of the Northern Hessian Depression (Germany) and the Balmuccia Ultramafic Massif (Northern Italy) have been used. They comprise four olivine texture types, which are characteristic for olivine textures observed worldwide. The bulk rock elastic properties have been calculated using olivine and orthopyroxene textures, their single-crystal elastic constants at ambient pressure/temperature conditions and their volume fraction. Clinopyroxene and spinel are assumed to be randomly distributed. The effect of four different orientations of the foliation within the uppermost mantle has been evaluated, since this orientation is usually unknown.¶Two of the olivine textures have a pronounced azimuthal dependence of compressional waves when a horizontal foliation within the uppermost mantle is presumed. These variations cause significant azimuthal variations of the P-wave reflections coefficients at the Moho. Primarily, we predict a significant azimuthal dependence of the critical points where the reflected amplitude increases from approximately 15% to 95%. Possibly, these azimuthal variations can be detected by seismic reflection measurements carried out at earth surface.¶The remaining two texture types only manifest a small directional dependence. When anisotropy of compressional waves is observed in seismic studies, these latter types can only be of subordinate importance. However, all of the peridotites investigated are able to explain the seismically observed azimuthal variations of compressional waves when a vertical foliation is proposed. This ambiguity can be substantially reduced when shear waves (S-waves) are considered. The directional distribution of S-wave velocities and of the S-wave splitting exhibits characteristic patterns for the different olivine texture types. This could be used to discriminate between different texture types and orientations of the foliation within the uppermost mantle. A fundamental requirement for a more comprehensive interpretation is the availability of detailed S-wave observations. The maximum S-wave splitting in the peridotites investigated coincides with the maximum of the faster (leading) S-wave. This may be of importance to detect S-wave splitting in future seismic studies. 相似文献
13.
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
14.
提出了利用人工爆破P波走时反演地壳介质方位各向异性参数的方法. 在假定介质是弱各向异性介质的情况下, 使用扰动理论得到了线性化的反演公式, 其中待反演的弱各向异性参数是P波走时的线性函数. 如果在反演公式中参考走时取相同震中距接收点的P波平均走时, 那么所获得的弱各向异性参数与参考介质速度的选取无关. 反演得到的弱各向异性参数可以看作是不同震中距和不同深度范围内介质的等效弱各向异性参数. 等效弱各向异性参数在一定程度上反映了不同深度范围内水平方向相速度随方位的变化. 这种变化可能是不同时期构造应力作用的结果. 2007年中国地震局在首都圈怀来地区实施了一次大吨位人工爆破实验, 以爆破点为中心, 布设了高密度的地震观测台网和台阵. 台站相对于爆破点具有360°的全方位覆盖, 所得到的地震记录数据为研究怀来、 延庆地区地壳介质P波方位各向异性提供了必要条件. 我们通过走时反演获得了与水平方位相关的弱各向异性参数, 并对弱各向异性参数进行坐标变换, 得到了能够直观描述岩石弱各向异性的具有水平对称轴的横向各向同性介质, 给出了对应的3个独立弱各向异性参数及其对称轴方位, 讨论了介质各向异性与构造应力场的关系. 结果表明该地区地壳介质存在明显的方位各向异性, 其最大值约为4.6%. 相似文献
15.
A. B. Druzhinin 《Pure and Applied Geophysics》1996,148(3-4):637-683
A comprehensive approach, based on the general nonlinear ray perturbation theory (Druzhinin, 1991), is proposed for both a fast and accurate uniform asymptotic solution of forward and inverse kinematic problems in anisotropic media. It has been developed to modify the standard ray linearization procedures when they become inconsistent, by providing a predictable truncation error of ray perturbation series. The theoretical background consists in a set of recurrent expressions for the perturbations of all orders for calculating approximately the body wave phase and group velocities, polarization, travel times, ray trajectories, paraxial rays and also the slowness vectors or reflected/transmitted waves in terms of elastic tensor perturbations. We assume that any elastic medium can be used as an unperturbed medium. A total 2-D numerical testing of these expressions has been established within the transverse isotropy to verify the accuracy and convergence of perturbation series when the elastic constants are perturbed. Seismological applications to determine crack-induced anisotropy parameters on VSP travel times for the different wave types in homogeneous and horizontally layered, transversally isotropic and orthorhombic structures are also presented. A number of numerical tests shows that this method is in general stable with respect to the choice of the reference model and the errors in the input data. A proof of uniqueness is provided by an interactive analysis of the sensitivity functions, which are also used for choosing optimum source/receiver locations. Finally, software has been developed for a desktop computer and applied to interpreting specific real VSP observations as well as explaining the results of physical modelling for a 3-D crack model with the estimation of crack parameters. 相似文献
16.
Patrick N.J. Rasolofosaon 《Geophysical Prospecting》2010,58(4):637-655
Seismic anisotropy in geological media is now widely accepted. Parametrizations and explicit approximations for the velocities in such media, considered as purely elastic and moderately anisotropic, are now standards and have even been extended to arbitrary types of anisotropy. In the case of attenuating media, some authors have also recently published different parametrizations and velocity and attenuation approximations in viscoelastic anisotropic media of particular symmetry type (e.g., transversely isotropic or orthorhombic). This paper extends such work to media of arbitrary anisotropy type, that is to say to triclinic media. In the case of homogeneous waves and using the so‐called ‘correspondence principle’, it is shown that the viscoelastic equations (for the phase velocities, phase slownesses, moduli, wavenumbers, etc.) are formally identical to the corresponding purely elastic equations available in the literature provided that all the corresponding quantities are complex (except the unit vector in the propagation direction that remains real). In contrast to previous work, the new parametrization uses complex anisotropy parameters and constitutes a simple extension to viscoelastic media of previous work dealing with non‐attenuating elastic media of arbitrary anisotropy type. We make the link between these new complex anisotropy parameters and measurable parameters, as well as with previously published anisotropy parameters, demonstrating the usefulness of the new parametrization. We compute the explicit complete directional dependence of the exact and of the approximate (first and higher‐order perturbation) complex phase velocities of the three body waves (qP, qS1 and qS2). The exact equations are successfully compared with the ultrasonic phase velocities and phase attenuations of the three body waves measured in a strongly attenuating water‐saturated sample of Vosges sandstone exhibiting moderate velocity anisotropy but very strong attenuation anisotropy. The approximate formulas are checked on experimental data. Compared to the exact solutions, the errors observed on the first‐order approximate velocities are small (<1%) for qP‐waves and moderate (<10%) for qS‐waves. The corresponding errors on the quality factor Q are moderate (<6%) for qP‐waves but critically large (up to 160%) for the qS‐waves. The use of higher‐order approximations substantially improves the accuracy, for instance typical maximum relative errors do not exceed 0.06% on all the velocities and 0.6% on all the quality factors Q, for third‐order approximations. All the results obtained on other rock samples confirm the results obtained on this rock. The simplicity of the derivations and the generality of the results are striking and particularly convenient for practical applications. 相似文献
17.
18.
A technique allowing inversion of the shale stiffness tensor from standard logging data: sonic velocities, density, porosity and clay content is developed. The inversion is based on the effective medium theory. The testing of the technique on laboratory measurements of the elastic wave velocities in shale samples shows that the inversion makes it possible to predict the elastic wave velocities VP, VS1 and VS2 in any direction within an error of a few per cent. The technique has been applied for the stiffness tensor inversion along a well penetrating a shale formation of the Mississippian age altered by thin layers of limestone. It is demonstrated that the symmetry of a stiffness tensor inverted at the sonic frequency (2 kHz) is slightly orthorhombic and taking into account the experimental errors, can be related to the vertical transverse isotropy symmetry. For the productive interval of the shale formation, the Thomsen parameters ?, γ, and δ average, respectively, 0.32, 0.25 and 0.21, which indicate anelliptic behaviour of the velocities in this shale. The coefficients of anisotropy of this shale interval are around 24% and 20% for the compressional and shear waves, respectively. The values of the inverted velocities in the bedding plane for this interval are in good agreement with the laboratory measurements. The technique also allows inversion of the water saturation of the formation (Sw) and the inverted values are in agreement with the Sw values available for this formation. A Backus‐like upscaling of the inverted stiffness tensors is carried out for the lower and upper bounds of the frequency band used in the crosswell tomography (100 Hz and 500 Hz). These results can serve as an initial velocity model for the microearthquake location during hydrofracking of the shale formation. 相似文献
19.
A layeredP- andS-wave velocity model is obtained for the Friuli seismic area using the arrival time data ofP- andS-waves from local earthquakes. A damped least-squares method is applied in the inversion.The data used are 994P-wave arrival times for 177 events which have epicenters in the region covered by the Friuli seismic network operated by Osservatorio Geofisico sperimentale (OGS) di Trieste, which are jointly inverted for the earthquake hypocenters andP-wave velocity model. TheS-wave velocity model is estimated on the basis of 978S-wave arrival times and the hypocenters obtained from theP-wave arrival time inversion. We also applied an approach thatP- andS-wave arrival time data are jointly used in the inversion (Roecker, 1982). The results show thatS-wave velocity structures obtained from the two methods are quite consistent, butP-wave velocity structures have obvious differences. This is apparent becauseP-waves are more sensitive to the hypocentral location thanS-waves, and the reading errors ofS-wave arrival times, which are much larger than those ofP-waves, bring large location errors in the joint inversion ofP- andS-wave arrival time. The synthetic data tests indicated that when the reading errors ofS-wave arrivals are larger than four times that ofP-wave arrivals, the method proposed in this paper seems more valid thanP- andS-wave data joint inversion. Most of the relocated events occurred in the depth range between 7 and 11 km, just above the biggest jump in velocity. This jump might be related to the detachment line hypothesized byCarulli et al. (1982). From the invertedP- andS-wave velocities, we obtain an average value 1.82 forV
p
/V
s
in the first 16 km depth. 相似文献
20.
J.L. Rodríguez-Zúñiga C. Ortiz-Alemán G. Padilla R. Gaulon 《Soil Dynamics and Earthquake Engineering》1997,16(3):223-234
Among the class of global optimization techniques, which includes Monte Carlo and simulated annealing methods, the Genetic Algorithms constitute a new class of methods to solve highly non-linear optimization problems. The issue has generated considerable interest in the field of artificial intelligence, and recently, in some multi-parameter optimization geophysical problems. In this study, we explore the applicability of genetic algorithms to the inversion of high resolution ground inclination measurements produced by known loads placed at known distances. Our objective is to find a model for dynamic properties of the subsoil such as shear and compressional wave velocities and depth distributions of the uppermost strata, which are related to elastic moduli. Three parameters are needed for describing elastic isotropic horizontally homogeneous media: mass density ρ and Lame constants λ and μ or mass density and P-wave and S-wave velocities. In general, the choice of parameters is not always a simple matter. In fact, although theoretically equivalent, if they are not adequately chosen, the numerical algorithms in the inversion can be inefficient.Ground inclination surveys were performed at the virgin Texcoco Lake, near Mexico City, and at the European Synchrotron radiation facility (ESRF) of Grenoble, France. From both sets of data we study the feasibility of applying genetic algorithms to rapidly and effectively explore the model space to find an optimal model for the shallow structure under study. Forward solution of vertical and radial displacements in a layered medium, under static loads, is calculated by means of the stiffness matrix approach (Kausel, E. & Roesett, J. M. Stiffness matrices for layered soil. Bulletin of the Seismological Society of America, 1981, 71(6), 1743–1761.) Comparisons with results from common established techniques such as seismic wave refraction profiles, cone resistance values and inversion of surface wave dispersion curves were used for validation purposes. Our procedure represents a fast and accurate alternative method to infer the shallow elastic parameters in surficial soils. 相似文献