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1.
An efficient inverse scattering method is developed for imaging near-surface heterogeneities using scattered surface waves. Three dimensional elastodynamic wave propagation and scattering in a laterally invariant embedding medium is considered. The Born Approximation is used and the scattered wavefield is expressed as a domain type integral representation. The computation time of Green's tensor elements is reduced by considering the radial symmetry of the medium. The method is validated by numerical tests. Ultrasonic laboratory data obtained from a scale model experiment are used for imaging the near-surface inhomogeneities caused by an epoxy-filled hole in the surface of an aluminum block. Both synthetic and the scale model tests show that the location, the actual density contrast and the depth of the inhomogeneities are reasonably well estimated.  相似文献   

2.
Summary. Scattering of surface waves by lateral heterogeneities is analysed in the Born approximation. It is assumed that the background medium is either laterally homogeneous, or smoothly varying in the horizontal direction. A dyadic representation of the Green's function simplifies the theory tremendously. Several examples of the theory are presented. The scattering and mode conversion coefficients are shown for scattering of surface waves by the root of an Alpine-like crustal structure. Furthermore a 'great circle theorem'in a plane geometry is derived. A new proof of Snell's law is given for surface wave scattering by a quarter-space. It is shown how a stationary phase approximation can be used to simplify the Fourier synthesis of the scattered wave in the time domain. Finally a procedure is suggested to do 'surface wave holography'.  相似文献   

3.
We present a technique based on the single-scattering approximation that relates time-lapse localized changes in the propagation velocity to changes in the traveltime of singly scattered waves. We describe wave propagation in a random medium with homogeneous statistical properties as a single-scattering process where the fluctuations of the velocity with respect to the background velocity are assumed to be weak. This corresponds to one of two end-member regimes of wave propagation in a random medium, the first being single scattering, and the second multiple scattering. We present a formulation that relates the change in the traveltime of the scattered waves to a localized change in the propagation velocity by means of the Born approximation for the scattered wavefield. We validate the methodology with synthetic seismograms calculated with finite differences for 2-D acoustic waves. Potential applications of this technique include non-destructive evaluation of heterogeneous materials and time-lapse monitoring of heterogeneous reservoirs.  相似文献   

4.
Non-linear elastic response of rocks has been widely observed in laboratory, but very few seismic studies are reported in the literature, even though it is the most natural environment where this feature could be observed. Analytic solutions to the non-linear wave propagation phenomena are not readily available, and there is a need to use approximated techniques. It is clear that when a seismic wave propagates through a homogeneous non-linear elastic media, it will be perturbed by the non-linearity. This perturbation can be treated as a source of scattering, spreading the energy of the primary wave in space and time, contributing to the seismic coda. This is in some sense similar to the effect of heterogeneities. The properties of the coda due to the non-linearity depend on the amount of non-linearity and the seismic moment. Using a perturbation approach we calculate the amplitude of the scattered waves, and show that it can describe reasonably well the main features of real seismic codas.  相似文献   

5.
A Gaussian correlation function characterizes smoothly heterogeneous media, while real heterogeneities in the Earth are often non-Gaussian in nature. Using the Born approximation, mean square amplitudes of the scattered waves have been derived for an elastic media characterized by the Von Karman correlation function. Heterogeneities with different power laws can be defined by the Von Karman correlation function. The sensitivity of fore- and backscattering to heterogeneities with different scales and properties (that is velocity and impedance) is discussed in this paper. The analytical expression for total scattered energy for the incident P waves is also derived for a random medium having the Von Karman correlation function. We find that at high frequencies, the scattered power of converted waves is a function of frequency. In the case of codawave excitation by local earthquakes, which must be handled by the full elastic-wave theory, we can define any type of inhomogeneity by the Von Karman correlation function. It also supports the idea that the lithosphere might have multiple-scale inhomogeneities.  相似文献   

6.
Velocity estimation remains one of the main problems when imaging the subsurface with seismic reflection data. Traveltime inversion enables us to obtain large-scale structures of the velocity field and the position of seismic reflectors. However, as the media currently under study are becoming more and more complex, we need to know the finer-scale structures. The problem is that below a certain range of velocity heterogeneities, deterministic methods become difficult to use, so we turn to a probabilistic approach. With this in view, we characterize the velocity field as a random field defined by its first and second statistical moments. Usually, a seismic random medium is defined as a homogeneous velocity background perturbed by a small random field that is assumed to be stationary. Thus, we make a link between such a random velocity medium (together with a simple reflector) and seismic reflection traveltimes. Assuming that the traveltimes are ergodic, we use 2-D seismic reflection geometry to study the decrease in the statistical traveltime fluctuations as a function of the offset (the source–receiver distance). Our formulae are based on the Rytov approximation and the parabolic approximation for acoustic waves. The validity and the limits are established for both of these approximations in statistically anisotropic random media. Finally, theoretical inversion procedures are developed for the horizontal correlation structure of the velocity heterogeneities for the simplest case of a horizontal reflector. Synthetic seismograms are then computed (on particular realizations of random media) by simulating scalar wave propagation via finite difference algorithms. There is good agreement between the theoretical and experimental results.  相似文献   

7.
Elastic scattered waves from a continuous and heterogeneous layer   总被引：3，自引：0，他引：3  
Elastic scattering from a continuous and laterally unbounded heterogeneous layer has been formulated using the Born approximation. A general solution of the scattered wave equation for the above-stated medium has been given in terms of a Fourier integral over plane waves. Far-field asymptotic expressions for weak elastic scattering by a finite, continuous and inhomogeneous layer have been presented which agree with earlier results. For perturbations of the two elastic parameters and the density having the same form of spatial variation, the spectrum of plane waves scattered from a heterogeneous layer is expressed as a product of an 'elastic scattering factor'and a 'distribution factor'. As in earlier results for small-scale heterogeneity, the scattering pattern depends on various combinations of perturbations of elastic parameters and density. In order to show the general characteristics of the elastic wave scattering, some scattering patterns have been given.  相似文献   

8.
The Born approximation is applied to the modelling of the propagation of deeply turning longperiod body waves through heterogeneities in the lowermost mantle. We use an exact Green's function for a spherically symmetric earth model that also satisfies the appropriate boundary conditions at internal boundaries and the surface of the earth. The scattered displacement field is obtained by a numerical quadrature of the product of the Green's function, the exciting wavefield and structural perturbations. We study three examples: scattering of longperiod P waves from a plume rising from the coremantle boundary (CMB), generation of longperiod precursors to PKIKP by strong, localized scatterers at the CMB, and propagation of corediffracted P waves through largescale heterogeneities in D". The main results are as follows: (1) the signals scattered from a realistic plume are small with relative amplitudes of less than 2 per cent at a period of 20 s, rendering plume detection a fairly difficult task; (2) strong heterogeneities at the CMB of appropriate size may produce observable longperiod precursors to PKIKP in spite of the presence of a diffraction from the PKP B caustic; (3) corediffracted P  waves ( P diff) are sensitive to structure in D" far off the geometrical ray path and also far beyond the entry and exit points of the ray into and out of D"; sensitivity kernels exhibit ringshaped patterns of alternating sign reminiscent of Fresnel zones; (4) P diff also shows a nonnegligible sensitivity to shear wave velocity in D"; (5) down to periods of 40 s, the Born approximation is sufficiently accurate to allow waveform modelling of P diff through largescale heterogeneities in D" of up to 5 per cent.  相似文献   

9.
The use of the Born approximation in seismic scattering problems   总被引：5，自引：0，他引：5  
Summary. In view of recent work on seismic scattering by small-scale heterogeneities in the Earth, which has been based on single-scattering perturbation theory (that is, the Born approximation), we attempt to define the region within which this approximation may be regarded as reasonably accurate. Comparison with the exact solution for scattering by an embedded sphere shows that the inequalities obtained, governing the ranges of the parameters of the problem, are appropriate.
However, application of these constraints on the parameters imply that, in almost all cases, application of the Born approximation to upper and lower mantle scattering is probably invalid.  相似文献   

10.
Scattering of surface waves modelled by the integral equation method   总被引：1，自引：0，他引：1  
The integral equation method is used to model the propagation of surface waves in 3-D structures. The wavefield is represented by the Fredholm integral equation, and the scattered surface waves are calculated by solving the integral equation numerically. The integration of the Green's function elements is given analytically by treating the singularity of the Hankel function at   R = 0  , based on the proper expression of the Green's function and the addition theorem of the Hankel function. No far-field and Born approximation is made. We investigate the scattering of surface waves propagating in layered reference models imbedding a heterogeneity with different density, as well as Lamé constant contrasts, both in frequency and time domains, for incident plane waves and point sources.  相似文献   

11.
We have developed a new array method combining conventional migration with a slowness-backazimuth deviation weighting scheme. All seismic traces are shifted based on the theoretical traveltime of the scattered wave from specific gridpoints in a 3-D volume. Observed slowness and backazimuth are calculated for each raypath and compared with theoretical values in order to estimate slowness and backazimuth deviations. Subsequently, stacked energy calculated by a conventional migration method is weighted by the slowness and backazimuth deviations to suppress any arrival energy whose slowness and backazimuth are inconsistent with the expected theoretical values. This new method was applied to two P- wave data sets which comprise (1) underside reflections at the 410 and 660 km mantle discontinuities and (2) D" reflections as well as their corresponding synthetic data sets. The results show that the weighting scheme dramatically increases the resolution of the migrated images and enables us to obtain well-constrained, focused images, making upper-mantle discontinuities and D" reflections more distinct by reducing their surrounding energy.  相似文献   

12.
Summary . In this paper the accuracy of velocity-depth profiles derived by matching WKBJ seismograms to observations is quantitatively evaluated. Seismograms computed with the WKBJ method are generally quite reliable but possess predictable, systematic inaccuracies in the presence of strong velocity gradients. The effects of these inaccuracies on models derived through WKBJ waveform inversion are studied, using reflectivity seismograms as 'data'. The velocity structure used is an oceanic lithosphere model that contains several transition regions separated by relatively homogeneous layers, producing partially-reflected reverberations in the reflectivity synthetics that are absent from the WKBJ seismograms. The inversion incorporates the 'jumping' strategy to solve for the smoothest models consistent with the data. We find these solutions to be independent of the starting model and to have a stable basic structure that agrees well with the correct model. The differences, everywhere less than a seismic wavelength, depend on the frequency content of the seismograms. Reverberations in the reflectivity seismograms that are well separated from WKBJ arrivals are treated as 'noise' in the inversion.  相似文献   

13.
Numerical simulation of the propagation of P waves in fractured media   总被引：1，自引：0，他引：1  
We study the propagation of P waves through media containing open fractures by performing numerical simulations. The important parameter in such problems is the ratio between crack length and incident wavelength. When the wavelength of the incident wavefield is close to or shorter than the crack length, the scattered waves are efficiently excited and the attenuation of the primary waves can be observed on synthetic seismograms. On the other hand, when the incident wavelength is greater than the crack length, we can simulate the anisotropic behaviour of fractured media resulting from the scattering of seismic waves by the cracks through the time delay of the arrival of the transmitted wave. The method of calculation used is a boundary element method in which the Green's functions are computed by the discrete wavenumber method. For simplicity, the 2-D elastodynamic diffraction problem is considered. The rock matrix is supposed to be elastic, isotropic and homogeneous, while the cracks are all empty and have the same length and strike direction. An iterative method of calculation of the diffracted wavefield is developed in the case where a large number of cracks are present in order to reduce the computation time. The attenuation factor Q −1 of the direct waves passing through a fractured zone is measured in several frequency bands. We observe that the attenuation factor Q −1 of the direct P wave peaks around kd = 2, where k is the incident wavenumber and d the crack length, and decreases proportionally to ( kd ) −1 in the high-wavenumber range. In the long-wavelength domain, the velocity of the direct P wave measured for two different crack realizations is very close to the value predicted by Hudson's theory on the overall elastic properties of fractured materials.  相似文献   

14.
Offset-dependent characteristics of seismic scattering are useful for characterizing fractured reservoirs. We use two models that have different background medium properties and different azimuthal AVO responses to study elastic wave propagation and scattering in gas-saturated, heterogeneously fractured reservoirs. Heterogeneous fracture density distributions are built through stochastic modelling. Synthetic seismograms are generated by 3-D finite difference modelling, and waveforms along crack-normal and strike directions are considered in this paper. The multiple signal classification (MUSIC) frequency estimator is used in waveform estimation to provide frequency-domain attributes related to seismic wave scattering by fracture heterogeneity. Our results indicate that the strength of the scattering field is a function of the background medium. The strength also increases with increasing fracture scatterer density and with decreasing correlation length of spatial variations of fracture density. The scattering field is weak at the top of the fractured reservoir. The first-order results are dominated by velocity anisotropy of the mean fracture density field. However, the base of the fractured reservoir corresponds to a strong scattering field on which fracture heterogeneity has a larger effect and is characterized by the loss of coherence.  相似文献   

15.
The phase velocity and the attenuation coefficient of compressional seismic waves, propagating in poroelastic, fluid-saturated, laminated sediments, are computed analytically from first principles. The wavefield is found to be strongly affected by the medium heterogeneity. Impedance fluctuations lead to poroelastic scattering; variations of the layer compressibilities cause inter-layer flow (a 1-D macroscopic local flow). These effects result in significant attenuation and dispersion of the seismic wavefield, even in the surface seismic frequency range, 10–100 Hz. The various attenuation mechanisms are found to be approximately additive, dominated by inter-layer flow at very low frequencies. Elastic scattering is important over a broad frequency range from seismic to sonic frequencies. Biot's global flow (the relative displacement of solid frame and fluid) contributes mainly in the range of ultrasonic frequencies. From the seismic frequency range up to ultrasonic frequencies, attenuation due to heterogeneity is strongly enhanced compared to homogeneous Biot models. Simple analytical expressions for the P -wave phase velocity and attenuation coefficient are presented as functions of frequency and of statistical medium parameters (correlation lengths, variances). These results automatically include different asymptotic approximations, such as poroelastic Backus averaging in the quasi-static and the no-flow limits, geometrical optics, and intermediate frequency ranges.  相似文献   

16.
Summary. In order to separate the scattering effect from the intrinsic attenuation, we need a multiple scattering model for seismic wave propagation in random heterogeneous media. In this paper, we apply radiative transfer theory to seismic wave propagation and formulate in the frequency domain the energy density distribution in space for a point source. We consider the cases of isotropic scattering and strong forward scattering. Some numerical examples are shown. It is seen that the energy density–distance curves have quite different shapes depending on the values of medium seismic albedo B 0=ηs/(ηs+ηa) where ηs is the scattering coefficient and ηa is the absorption coefficient of the medium. For a high albedo ( B > 0.5) medium, the energy–distance curve is of arch shape and the position of the peak is a function of the extinction coefficient of the medium ηe=ηs+ηa. Therefore it is possible to separate the scattering effect and the absorption based on the measured energy density distribution curves.  相似文献   

17.
Large scale seismic anisotropy in the Earth's mantle is likely dynamically supported by the mantle's deformation; therefore, tomographic imaging of 3-D anisotropic mantle seismic velocity structure is an important tool to understand the dynamics of the mantle. While many previous studies have focused on special cases of symmetry of the elastic properties, it would be desirable for evaluation of dynamic models to allow more general axis orientation. In this study, we derive 3-D finite-frequency surface wave sensitivity kernels based on the Born approximation using a general expression for a hexagonal medium with an arbitrarily oriented symmetry axis. This results in kernels for two isotropic elastic coefficients, three coefficients that define the strength of anisotropy, and two angles that define the symmetry axis. The particular parametrization is chosen to allow for a physically meaningful method for reducing the number of parameters considered in an inversion, while allowing for straightforward integration with existing approaches for modelling body wave splitting intensity measurements. Example kernels calculated with this method reveal physical interpretations of how surface waveforms are affected by 3-D velocity perturbations, while also demonstrating the non-linearity of the problem as a function of symmetry axis orientation. The expressions are numerically validated using the spectral element method. While challenges remain in determining the best inversion scheme to appropriately handle the non-linearity, the approach derived here has great promise in allowing large scale models with resolution of both the strength and orientation of anisotropy.  相似文献   

18.
Small-scale elastic heterogeneities (<5  km) are found in the upper lithosphere underneath the Gräfenberg array, southeast Germany. The results are based on the analysis of broadband recordings of 17 intermediate-depth (201–272  km) events from the Hindu Kush region. The wavefront of the first P arrival and the following 40  s coda are separated into coherent and incoherent (scattered) parts in the frequency range from 0.05 to 5  Hz. The frequency-dependent intensities of the mean and fluctuation wavefields are used to describe the scattering characteristics of the lithosphere underneath the receivers. It is possible to discriminate a weak-fluctuation regime of the wavefield in the frequency range below approximately 1.5–2.5  Hz and a strong-fluctuation regime starting at 2.0–2.5  Hz and continuing to higher frequencies. In order to explain the observed wavefield fluctuations, an approach with seismic scattering at random media-type structures is proposed. The preferred model contains heterogeneities with 3–7 per cent perturbations in seismic velocity and correlation lengths of 0.6–4.8  km in the crust. This is compatible with models from active seismic experiments. Scattering in the lithospheric mantle is not required, but cannot be excluded at weak velocity contrasts (<3 per cent).  相似文献   

19.
The Kirchhoff (or tangent plane) approximation, derived from the theoretically complete Kirchhoff–Helmholtz integral representation for the seismic wavefield, has been used extensively for the analysis of seismic-wave scattering from irregular interfaces; however, the accuracy of this method for curved interfaces has not been rigorously established. This paper describes an efficient Kirchhoff algorithm to simulate scattered waves from an arbitrarily curved interface in an elastic medium. Synthetic seismograms computed using this algorithm are compared with exact synthetics computed using analytical formulae for scattering of plane P waves by a spherical elastic inclusion. A windowing technique is used to remove strong internal reverberations from the analytical solution. Although the Kirchhoff method tends to underestimate the total scattering intensity, the accuracy of the approximation improves with increasing value of the wavenumber-radius product, kR . The arrival times and pulse shapes of primary reflections from the sphere are well approximated using the Kirchhoff approach regardless of curvature of the scattering surface, but the amplitudes are significantly underestimated for kR ≤ 5. The results of this work provide some new guidelines to assess the accuracy of Kirchhoff-synthetic seismograms for curved interfaces.  相似文献   

20.
Wide-angle seismic velocities in heterogeneous crust   总被引：5，自引：0，他引：5  
Seismic velocities measured by wide-angle surveys are commonly used to constrain material composition in the deep crust. Therefore, it is important to understand how these velocities are affected by the presence of multiscale heterogeneities. The effects may be characterised by the scale of the heterogeneity relative to the dominant seismic wavelength (λ); what is clear is that heterogeneities of all scales and strengths bias wide-angle velocities to some degree. Waveform modelling was used to investigate the apparent wide-angle P -wave velocities of different heterogeneous lower crusts. A constant composition (50 per cent felsic and 50 per cent ultramafic) was formed into a variety of 1- and 2-D heterogeneous arrangements and the resulting wide-angle seismic velocity was estimated. Elastic, 1-D models produced the largest velocity shift relative to the true average velocity of the medium (which is the velocity of an isotropic mixture of the two components). Thick (width > λ) horizontal layers, as a result of Fermat's Principle, provided the largest increase in velocity; thin (width ≪λ) vertical layers produced the largest decrease in velocity. Acoustic 2-D algorithms were shown to be inadequate for modelling the kinematics of waves in bodies with multiscale heterogeneities. Elastic, 2-D modelling found velocity shifts (both positive and negative) that were of a smaller magnitude than those produced by 1-D models. The key to the magnitude of the velocity shift appears to be the connectivity of the fast (and/or slow) components. Thus, the models with the highest apparent levels of connectivity between the fast phases, the 1-D layers, produced the highest-magnitude velocity shifts. To understand the relationship between measured seismic velocities and petrology in the deep crust it is clear that high-resolution structural information (which describes such connectivity) must be included in any modelling.  相似文献   

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