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1.
A 3D F–K dip-moveout (DMO) is developed, which is applicable to data acquired in an elementary single-fold cross-spread. The key idea is that a 3D log-stretch transform and the inherent regularity of the cross-spread geometry make it possible to transform 3D Fourier DMO. The derived theory generalizes the 2D Fourier shot-gather DMO in the log-stretch domain; 2D turns out to be a special case. Similarly to 2D, the cross-spread DMO becomes convolutional after multidimensional logarithmic stretch. The proposed method works for orthogonal and slanted acquisition geometries; the cross-spread DMO relationships are found to be independent of the intersection angle of the shot and receiver lines. In contrast to integral (Kirchhoff-style) methods, the cross-spread F–K DMO does not degrade from the inevitable irregularity in 3D sampling of offsets in a CMP gather. The newly derived F–K DMO operator can be approximated by finite-difference (FD) schemes; the low-order FD cross-spread DMO equation is shown to be the 3D extension of the Bolondi and Rocca offset continuation. It is shown that F–K and low-order FD operators are effective in a synthetic case.  相似文献   

2.
The calculation of dip moveout involves spreading the amplitudes of each input trace along the source-receiver axis followed by stacking the results into a 3D zero-offset data cube. The offset-traveltime (x–t) domain integral implementation of the DMO operator is very efficient in terms of computation time but suffers from operator aliasing. The log-stretch approach, using a logarithmic transformation of the time axis to force the DMO operator to be time invariant, can avoid operator aliasing by direct implementation in the frequency-wavenumber (f–k) domain. An alternative technique for log-stretch DMO corrections using the anti-aliasing filters of the f–k approach in the x-log t domain will be presented. Conventionally, the 2D filter representing the DMO operator is designed and applied in the f–k domain. The new technique uses a 2D convolution filter acting in single input/multiple output trace mode. Each single input trace is passed through several 1D filters to create the overall DMO response of that trace. The resulting traces can be stacked directly in the 3D data cube. The single trace filters are the result of a filter design technique reducing the 2D problem to several ID problems. These filters can be decomposed into a pure time-delay and a low-pass filter, representing the kinematic and dynamic behaviour of the DMO operator. The low-pass filters avoid any incidental operator aliasing. Different types of low-pass filters can be used to achieve different amplitude-versus-offset characteristics of the DMO operator.  相似文献   

3.
Dip‐moveout (DMO) correction is often applied to common‐offset sections of seismic data using a homogeneous isotropic medium assumption, which results in a fast execution. Velocity‐residual DMO is developed to correct for the medium‐treatment limitation of the fast DMO. For reasonable‐sized velocity perturbations, the residual DMO operator is small, and thus is an efficient means of applying a conventional Kirchhoff approach. However, the shape of the residual DMO operator is complicated and may form caustics. We use the Fourier domain for the operator development part of the residual DMO, while performing the convolution with common‐offset data in the space–time domain. Since the application is based on an integral (Kirchhoff) method, this residual DMO preserves all the flexibility features of an integral DMO. An application to synthetic and real data demonstrates effectiveness of the velocity‐residual DMO in data processing and velocity analysis.  相似文献   

4.
Almost all ray-tracing methods ignore the analysis of the amplitudes of seismic arrivals and therefore utilize only half of the available information. We propose a method which is a combination of ray-tracing imaging and transformation of the amplitudes of wide-aperture data. Seismic data in the conventional X-T domain are first transformed to the domain of intercept time τ and ray parameter p to recover the plane wave response. The next step is the derivation of a series of plane wave reflection coefficients, which are mapped as a function of τ and p. The reflection coefficients R(τ, p) for two arbitrarily chosen traces can then be used in our inversion method to derive a slowness-depth and a density-depth profile. It is shown that the inclusion of amplitudes of seismic arrivals (in this method, we consider the acoustic case) makes the inverse method highly stable and accurate. In a horizontally stratified medium one can recover separate profiles of velocity and density. Since this method utilizes large-offset data, it can be used for separate recovery of velocity and density to a greater depth.  相似文献   

5.
Attenuation in seismic wave propagation is a common cause for poor illumination of subsurface structures. Attempts to compensate for amplitude loss in seismic images by amplifying the wavefield may boost high‐frequency components, such as noise, and create undesirable imaging artefacts. In this paper, rather than amplifying the wavefield directly, we develop a stable compensation operator using stable division. The operator relies on a constant‐Q wave equation with decoupled fractional Laplacians and compensates for the full attenuation phenomena by performing wave extrapolation twice. This leads to two new imaging conditions to compensate for attenuation in reverse‐time migration. A time‐dependent imaging condition is derived by applying Q‐compensation in the frequency domain, whereas a time‐independent imaging condition is formed in the image space by calculating image normalisation weights. We demonstrate the feasibility and robustness of the proposed methods using three synthetic examples. We found that the proposed methods are capable of properly compensating for attenuation without amplifying high‐frequency noise in the data.  相似文献   

6.
The existing on‐line numerical integration algorithms are derived from the Newmark method, which is based on an approximation of derivatives in the differential equation. The state–space procedure (SSP), based on an interpolation of the discrete excitation signals for piecewise convolution integral, has been confirmed as more reliable than the Newmark method in terms of numerical accuracy and stability. In an attempt to enhance the pseudodynamic test, this study presents an on‐line integration algorithm (referred to as the OS–SSP method) via an integration of the state–space procedure with Nakashima's operator‐splitting concept. Numerical stability and accuracy assessment of the proposed algorithm in addition to the explicit Newmark method and the OS method were investigated via an eigenvalue, frequency‐domain and time‐domain analysis. Of the on‐line integration algorithms investigated, the OS–SSP method is demonstrated as the most accurate method with an acceptable stability (although not unconditionally stable) characteristic. Therefore, the OS–SSP method is the most desirable method for pseudodynamic testing if the numerical stability criterion (Δt/T⩽0.5) is ensured for every vibration mode involved. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

7.
The problem of the propagation of acoustic waves in a two-dimensional layered medium can be easily solved in the frequency domain if the Dix approximation is used, i.e. when only the primary reflections are considered. The migrated data at a depth z are obtained by convolving the time section with a proper two-dimensional operator dependent on z. The same result can be obtained by multiplying their two-dimensional spectra and summing for all the values of the temporal frequency. The aspect of the operator in the time-space domain has the classic hyperbolic structure together with the prescribed temporal and spatial decay. The main advantages of the frequency domain approach consist in the noticeable computer time savings and in the better approximation. On the other hand lateral velocity variations are very difficult to be taken into account. This can be done if a space variant filter is used in the time-space domain. To reduce computer time, this filter has to be recursive; the problem has been solved by Claerbout by transforming the hyperbolic partial differential equation into a parabolic one, and using the latter to generate the recursion operator. In the presentation a method is given for the generation of recursive filters with a better phase characteristics that have a pulse response with the requested hyperbolic shape instead of the parabocli one. This allows a better migration of steeper dips.  相似文献   

8.
The azimuth moveout (AMO) operator in homogeneous transversely isotropic media with a vertical symmetry axis (VTI), as in isotropic media, has an overall skewed saddle shape. However, the AMO operator in anisotropic media is complicated; it includes, among other things, triplications at low angles. Even in weaker anisotropies, with the anisotropy parameter η= 0.1 (10% anisotropy), the AMO operator is considerably different from the isotropic operator, although free of triplications. The structure of the operator in VTI media (positive η) is stretched (has a wider aperture) compared with operators in isotropic media, with the amount of stretch being dependent on the strength of anisotropy. If the medium is both vertically inhomogeneous, i.e. the vertical velocity is a function of depth (v(z)), and anisotropic, which is a common combination in practical problems, the shape of the operator again differs from that for isotropic media. However, the difference in the AMO operator between the homogeneous and the v(z) cases, even for anisotropic media, is small. Stated simply, anisotropy influences the shape and aperture of the AMO operator far more than vertical inhomogeneity does.  相似文献   

9.
Fourier transform techniques have been used to calculate the theoretical filter (amplitude) response function of Nth order vertical derivative continuation operation. The amplitude response functions of the vertical gradient and its continuation follow from the same. These response functions are subsequently used to calculate the weighting coefficients suitable for two dimensional equispaced data. A shortening operator has been incorporated to limit the extent of the operator. For comparative study, some of the developed coefficient sets and the one presented in this paper are analysed in the frequency domain and their merits and demerits are discussed.  相似文献   

10.
From the past studies of acceleration records, it is generally recognised that peak acceleration is not a suitable measure of the ground motion for design purposes. Usually, peak accelerations are difficult to predict. They occur in high frequency pulses containing very little energy and therefore are of little consequence. On the other hand acceleration has direct and useful application in engineering design. A new parameter A95 is introduced in this paper which is defined as that level of acceleration which contains up to 95 per cent of the Arias Intensity. From the study of 135 records, it is noticed that the variation of the fraction of Arias Intensity with acceleration level can be described by a very well defined relationship. It is also observed that A95 and Arias Intensity bear a stable relationship. Furthermore, the Arias Intensity at a site correlates more closely with the earthquake magnitude and the distance of the site from the source in attenuation relationships. From the available data, relationships are derived which show that there is a difference between the near-field and the far-field attenuation laws. The following relationships are obtained: where Es = Arias Intensity, Ex = fraction of Arias Intensity above an acceleration level A, M = surface wave magnitude, R = nearest distance to the energy source or focal distance in km.  相似文献   

11.
The simulation of a zero-offset (ZO) stack section from multi-coverage reflection data is a standard imaging method in seismic processing. It significantly reduces the amount of data and increases the signal-to-noise ratio due to constructive interference of correlated events. Conventional imaging methods, e.g., normal moveout (NMO)/dip moveout (DMO)/stack or pre-stack migration, require a sufficiently accurate macro-velocity model to yield appropriate results, whereas the recently introduced common-reflection-surface stack does not depend on a macro-velocity model. For two-dimensional seismic acquisition, its stacking operator depends on three wavefield attributes and approximates the kinematic multi-coverage reflection response of curved interfaces in laterally inhomogeneous media. The common-reflection-surface stack moveout formula defines a stacking surface for each particular sample in the ZO section to be simulated. The stacking surfaces that fit best to actual events in the multi-coverage data set are determined by means of coherency analysis. In this way, we obtain a coherency section and a section of each of the three wavefield attributes defining the stacking operator. These wavefield attributes characterize the curved interfaces and, thus, can be used for a subsequent inversion. In this paper, we focus on an application to a real land data set acquired over a salt dome. We propose three separate one-parametric search and coherency analyses to determine initial common-reflection-surface stack parameters. Optionally, a subsequent optimization algorithm can be performed to refine these initial parameters. The simulated ZO section obtained by the common-reflection-surface stack is compared to the result of a conventional NMO/DMO/stack processing sequence. We observe an increased signal-to-noise ratio and an improved continuity along the events for our proposed method — without loss of lateral resolution.  相似文献   

12.
The transversely isotropic (TI) model with a tilted axis of symmetry may be typical, for instance, for sediments near the flanks of salt domes. This work is devoted to an analysis of reflection moveout from horizontal and dipping reflectors in the symmetry plane of TI media that contains the symmetry axis. While for vertical and horizontal transverse isotropy zero-offset reflections exist for the full range of dips up to 90°, this is no longer the case for intermediate axis orientations. For typical homogeneous models with a symmetry axis tilted towards the reflector, wavefront distortions make it impossible to generate specular zero-offset reflected rays from steep interfaces. The ‘missing’ dipping planes can be imaged only in vertically inhomogeneous media by using turning waves. These unusual phenomena may have serious implications in salt imaging. In non-elliptical TI media, the tilt of the symmetry axis may have a drastic influence on normal-moveout (NMO) velocity from horizontal reflectors, as well as on the dependence of NMO velocity on the ray parameter p (the ‘dip-moveout (DMO) signature’). The DMO signature retains the same character as for vertical transverse isotropy only for near-vertical and near-horizontal orientation of the symmetry axis. The behaviour of NMO velocity rapidly changes if the symmetry axis is tilted away from the vertical, with a tilt of ±20° being almost sufficient to eliminate the influence of the anisotropy on the DMO signature. For larger tilt angles and typical positive values of the difference between the anisotropic parameters ε and δ, the NMO velocity increases with p more slowly than in homogeneous isotropic media; a dependence usually caused by a vertical velocity gradient. Dip-moveout processing for a wide range of tilt angles requires application of anisotropic DMO algorithms. The strong influence of the tilt angle on P-wave moveout can be used to constrain the tilt using P-wave NMO velocity in the plane that includes the symmetry axis. However, if the azimuth of the axis is unknown, the inversion for the axis orientation cannot be performed without a 3D analysis of reflection traveltimes on lines with different azimuthal directions.  相似文献   

13.
Wavenumber aliasing is the main limitation of conventional optimum least-squares linear moveout filters: it prevents adequate reject domain weighting for efficient coherent noise rejection. A general frequency domain multichannel filter design technique based on a one-to-one mapping method between two-dimensional (2D) space and one-dimensional (1D) space is presented. The 2D desired response is mapped to the 1D frequency axis after a suitable sorting of the coefficients. A min-max or Tchebycheff approximation to the desired response is obtained in the 1D frequency domain and mapped back to the 2D frequency domain. The algorithm is suitable for multiband 2D filter design. No aliasing damage is inherent in the linear moveout filters designed using this technique because the approximation is done in the frequency-wavenumber (f, k)-domain. Linear moveout filters designed by using the present coefficient mapping technique achieve better pass domain approximations than the corresponding conventional least-squares filters. Compatible reject domain approximations can be obtained from suitable mappings of the origin coefficient of the desired (f k)-response to the 1D frequency axis. The (fk)-responses of linear moveout filters designed by using the new technique show equi-ripple behavior. Synthetic and real data applications show that the present technique is superior to the optimum least-squares filters and straight stacking in recovering and enhancing the signal events with relatively high residual statics. Their outputs also show higher resolution than those of the optimum least-squares filters.  相似文献   

14.
This paper describes the development and numerical verification of a test method to realistically simulate the seismic structural response of full‐scale buildings. The result is a new field testing procedure referred to as the linear shaker seismic simulation (LSSS) testing method. This test method uses a linear shaker system in which a mass mounted on the structure is commanded a specified acceleration time history, which in turn induces inertial forces in the structure. The inertia force of the moving mass is transferred as dynamic force excitation to the structure. The key issues associated with the LSSS method are (1) determining for a given ground motion displacement, xg, a linear shaker motion which induces a structural response that matches as closely as possible the response of the building if it had been excited at its base by xg (i.e. the motion transformation problem) and (2) correcting the linear shaker motion from Step (1) to compensate for control–structure interaction effects associated with the fact that linear shaker systems cannot impart perfectly to the structure the specified forcing functions (i.e. the CSI problem). The motion transformation problem is solved using filters that modify xg both in the frequency domain using building transfer functions and in the time domain using a least squares approximation. The CSI problem, which is most important near the modal frequencies of the structural system, is solved for the example of a linear shaker system that is part of the NEES@UCLA equipment site. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

15.
Empirical attenuation relationship for Arias Intensity   总被引：1，自引：0，他引：1  
Arias Intensity is a ground motion parameter that captures the potential destructiveness of an earthquake as the integral of the square of the acceleration–time history. It correlates well with several commonly used demand measures of structural performance, liquefaction, and seismic slope stability. A new empirical relationship is developed to estimate Arias Intensity as a function of magnitude, distance, fault mechanism, and site category based on 1208 recorded ground motion data from 75 earthquakes in active plate‐margins. Its functional form is derived from the point‐source model, and the coefficients are determined through non‐linear regression analyses using a random‐effects model. The results show that for large magnitude earthquakes (M > 7) Arias Intensity was significantly overestimated by previous relationships while it was underestimated for smaller magnitude events (M ? 6). The average horizontal Arias Intensity is not significantly affected by forward rupture directivity in the near‐fault region. The aleatory variability associated with Arias Intensity is larger than that of most other ground motion parameters such as spectral acceleration. However, it may be useful in assessing the potential seismic performance of stiff engineering systems whose response is dominated by the short‐period characteristics of ground motions. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

16.
The JMA (Japan Meteorological Agency) seismic intensity scale has been used in Japan as a measure of earthquake ground shaking effects since 1949. It has traditionally been assessed after an earthquake based on the judgment of JMA officials. In 1996 the scale was revised as an instrumental seismic intensity measure (IJMA) that could be used to rapidly assess the expected damage after an earthquake without having to conduct a survey. Since its revision, Japanese researchers have developed several ground motion prediction equations (GMPEs) for IJMA using Japanese ground motion data. In this paper, we develop a new empirical GMPE for IJMA based on the strong motion database and functional forms used to develop similar GMPEs for peak response parameters as part of the PEER (Pacific Earthquake Engineering Research Center) Next Generation Attenuation (NGA) project. We consider this relationship to be valid for shallow crustal earthquakes in active tectonic regimes for moment magnitudes ( M ) ranging from 5.0 up to 7.5–8.5 (depending on fault mechanism) and rupture distances ranging from 0 to 200 km. A comparison of this GMPE with relationships developed by Japanese researchers for crustal and shallow subduction earthquakes shows relatively good agreement among all of the relationships at M 7.0 but relatively poor agreement at small magnitudes. Our GMPE predicts the highest intensities at small magnitudes, which together with research on other ground motion parameters, indicates that it provides conservative or upwardly biased estimates of IJMA for M <5.5. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

17.
This paper describes an effective implementation of the inverse data-space multiple elimination method via the three-dimensional (3D) curvelet domain. The method can separate the surface-related operator (A) and primaries (P 0) through seismic data matrix inversion. A 3D curvelet transform is introduced to sparsely represent the seismic data in the inverse data space. Hence, this approach is suitable for obtaining an accurate solution because of its multiscale and multidirectional analysis properties. The L1 norm is used to promote sparseness in the transform domain. Then, a high-fidelity separation of the operator (A) and the primaries (P 0) is realized. The proposed method is applied to synthetic data from a model containing a salt structure. We compare the results with that of the traditional inverse data-space multiple elimination method and also with that of two-dimensional surface-related multiple elimination. The findings fully demonstrate the superiority of the proposed method over the traditional inverse method; moreover, the proposed method protects the primary energy more effectively than the SRME method.  相似文献   

18.
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19.
In the Taiwan region, the empirical spectral models for estimating ground-motion parameters were obtained recently on the basis of recordings of small to moderate (5.0≤ML≤6.5) earthquakes. A large collection of acceleration records from the ML=7.3 Chi-Chi earthquake (21 September, 1999) makes it possible to test the applicability of the established relationships in the case of larger events. The comparison of ground-motion parameters (Fourier amplitude spectra, peak accelerations and response spectra), which were calculated using the models, and the observed data demonstrates that the models could provide an accurate prediction for the case of the Chi-Chi earthquake and the largest aftershocks. However, there are some peculiarities in the ground-motion frequency content and attenuation that, most probably, are caused by the features of the rupture process of the large shallow earthquake source.  相似文献   

20.
Migration to zero offset (MZO) is a prestack partial migration process that transforms finite-offset seismic data into a close approximation to zero-offset data, regardless of the reflector dips that are present in the data. MZO is an important step in the standard processing sequence of seismic data, but is usually restricted to constant velocity media. Thus, most MZO algorithms are unable to correct for the reflection point dispersal caused by ray bending in inhomogeneous media. We present an analytical formulation of the MZO operator for the simple possible variation of velocity within the earth, i.e. a constant gradient in the vertical direction. The derivation of the MZO operator is carried out in two steps. We first derive the equation of the constant traveltime surface for linear V(z) velocity functions and show that the isochron can be represented by a fourth-degree polynomial in x, y and z. This surface reduces to the well-known ellipsoid in the constant-velocity case, and to the spherical wavefront obtained by Slotnick in the coincident source-receiver case. We then derive the kinematic and dynamic zero-offset corrections in parametric form by using the equation of the isochron. The weighting factors are obtained in the high-frequency limit by means of a simple geometric spreading correction. Our analytical results show that the MZO operator is a multivalued, saddle-shaped operator with marked dip moveout effects in the cross-line direction. However, the amplitude analysis and the distribution of dips along the MZO impulse response show that the most important contributions of the MZO operator are concentrated in a narrow zone along the in-line direction. In practice, MZO processing requires approximately the same trace spacing in the in-line and cross-line directions to avoid spatial aliasing effects.  相似文献   

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