共查询到20条相似文献，搜索用时 562 毫秒
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We propose a wave scattering approach to the problem of deconvolution by the inversion of the reflection seismogram. Rather than using the least-squares approach, we study the full wave solution of the one-dimensional wave equation for deconvolution. Randomness of the reflectivity is not a necessary assumption in this method. Both the reflectivity and the section multiple train can be predicted from the boundary data (the reflection seismogram). This is in contrast to the usual statistical approach in which reflectivity is unpredictable and random, and the section multiple train is the only predictable component of the seismogram. The proposed scattering approach also differs from Claerbout's method based on the Kunetz equation. The coupled first-order hyperbolic wave equations have been obtained from the equation of motion and the law of elasticity. These equations have been transformed in terms of characteristics. A finite-difference numerical scheme for the downward continuation of the free-surface reflection seismogram has been developed. The discrete causal solutions for forward and inverse problems have been obtained. The computer algorithm recursively solves for the pressure and particle velocity response and the impedance log. The method accomplishes deconvolution and impedance log reconstruction. We have tested the method by computer model experiments and obtained satisfactory results using noise-free synthetic data. Further study is recommended for the method's application to real data. 相似文献
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R.-G. FERBER 《Geophysical Prospecting》1985,33(2):212-223
A main problem in computing reflection coefficients from seismograms is the instability of the inversion procedure due to noise. This problem is attacked for two well-known inversion schemes for normal-incidence reflection seismograms. The crustal model consists of a stack of elastic, laterally homogeneous layers between two elastic half-spaces. The first method, which directly computes the reflection coefficients from the seismogram is called “Dynamic Deconvolution”. The second method, here called “Inversion Filtering”, is a two-stage procedure. The first stage is the construction of a causal filter by factorization of the spectral function via Levinson-recursion. Filtering the seismogram is the second stage. The filtered seismogram is a good approximation for the reflection coefficients sequence (unless the coefficients are too large). In the non-linear terms of dynamic deconvolution and Levinson-recursion the noise could play havoc with the computation. In order to stabilize the algorithms, the bias of these terms is estimated and removed. Additionally incorporated is a statistical test for the reflection coefficients in dynamic deconvolution and the partial correlation coefficients in Levinson-recursion, which are set to zero if they are not significantly different from noise. The result of stabilization is demonstrated on synthetic seismograms. For unit spike source pulse and white noise, dynamic deconvolution outperforms inversion filtering due to its exact nature and lesser computational burden. On the other hand, especially in the more realistic bandlimited case, inversion filtering has the great advantage that the second stage acts linearly on the seismogram, which allows the calculation of the effect of the inversion procedure on the wavelet shape and the noise spectrum. 相似文献
4.
Edward Szaraniec 《Geophysical Prospecting》1994,42(1):81-83
The paper by Slob and Ziolkowski (1993) is apparently a comment on my paper (Szaraniec 1984) on odd-depth structure. In fact the basic understanding of a seismogram is in question. The fundamental equation for an odd-depth model and its subsequent deconvolution is correct with no additional geological constraints. This is the essence of my reply which is contained in the following points.
- 1 The discussion by Slob and Ziolkowski suffers from incoherence. On page 142 the Goupillaud (1961) paper is quoted: “… we must use a sampling rate at least double that… minimum interval…”. In the following analysis of such a postulated model Slob and Ziolkowski say that “… two constants are used in the model: Δt as sampling rate and 2Δt as two-way traveltime”. By reversing the Goupillaud postulation all the subsequent criticism becomes unreliable for the real Goupillaud postulation as well as the odd-depth model.
- 2 Slob and Ziolkowski take into consideration what they call the total impulse response. This is over and above the demands of the fundamental property of an odd-depth model. Following a similar approach I take truncated data in the form of a source function, S(z), convolved with a synthetic seismogram (earth impulse response), R?(z), the free surface being included. The problem of data modelling is a crucial one and will be discussed in more detail below. By my reasoning, however, the function may be considered as a mathematical construction introduced purely to work out the fundamental property. In this connection there is no question of this construction having a physical meaning. It is implicit that in terms of system theory, K(z) stands for what is known as input impedance.
- 3 Our understandings of data are divergent but Slob and Ziolkowski state erroneously that: “Szaraniec (1984) gives (21) as the total impulse response…”. This point was not made. This inappropriate statement is repeated and echoed throughout the paper making the discussion by Slob and Ziolkowski, as well as the corrections proposed in their Appendix A, ineffective. Thus, my equation (2) is quoted in the form which is in terms of the reflection response Gsc and holds true at least in mathematical terms. No wonder that “this identity is not valid for the total impulse response” (sic), which is denoted as G(z). None the less a substitution of G for Gsc is made in Appendix A, equation (A3). The equation numbers in my paper and in Appendix A are irrelevant, but (A3) is substituted for (32) (both numbers of equations from the authors’ paper). Afterwards, the mathematical incorrectness of the resulting equation is proved (which was already evident) and the final result (A16) is quite obviously different from my equation (2). However, the substitution in question is not my invention.
- 4 With regard to the problem of data modelling, I consider a bi-directional ID seismic source located just below the earth's surface. The downgoing unit impulse response is accompanied by a reflected upgoing unit impulse and the earth response is now doubled. The total impulse response for this model is thus given by where (—r0) =— 1 stands for the surface reflection coefficient in an upward direction. Thus that is to say, the total response to a unit excitation is identical with the input impedance as it must be in system theory. The one-directional 1D seismic source model is in question. There must be a reaction to every action. When only the downgoing unit impulse of energy is considered, what about the compensation?
- 5 In more realistic modelling, an early part of a total seismogram is unknown (absent) and the seismogram is seen in segments or through the windows. That is why in the usual approach, especially in dynamic deconvolution problems, synthetic data in the presence of the free surface are considered as an equivalent of the global reflection coefficient. It is implicit that model arises from a truncated total seismogram represented as a source function convolved with a truncated global reflection coefficient.
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The theme of the 2003 EAGE/SEG imaging workshop concerned the contrast between different philosophies of ‘model building’: whether an explicit, user‐determined model should be imposed throughout the processing, with user updates at each step; or alternatively, whether user intervention should be kept to a minimum so as to avoid preconceived bias, and instead to allow the data itself to guide some heuristic process to converge to an optimal solution. Here we consider a North Sea study where our initial approach was to build the subsurface model using interpreted horizons as a guide to the velocity update. This is common practice in the North Sea, where the geology ‘lends itself’ to a layer‐based model representation. In other words, we encourage preconceived bias, as we consider it to be a meaningful geological constraint on the solution. However, in this instance we had a thick chalk sequence, wherein the vertical compaction gradient changed subtly, in a way not readily discernible from the seismic reflection data. As a consequence, imposing the explicit top and bottom chalk horizons, with an intervening vertical compaction gradient (of the form v(x, y, z) =v0(x, y) +k(x, y).z), led to a misrepresentation of the subsurface. To address this issue, a gridded model building approach was also tried. This relied on dense continuous automatic picking of residual moveout in common‐reflection point gathers at each iteration of the model update, followed by gridded tomography, resulting in a smoothly varying velocity field which was able to reveal the underlying local changes within the chalk. 相似文献
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Tilted transversely isotropic formations cause serious imaging distortions in active tectonic areas (e.g., fold‐and‐thrust belts) and in subsalt exploration. Here, we introduce a methodology for P‐wave prestack depth imaging in tilted transversely isotropic media that properly accounts for the tilt of the symmetry axis as well as for spatial velocity variations. For purposes of migration velocity analysis, the model is divided into blocks with constant values of the anisotropy parameters ε and δ and linearly varying symmetry‐direction velocity VP0 controlled by the vertical (kz) and lateral (kx) gradients. Since determination of tilt from P‐wave data is generally unstable, the symmetry axis is kept orthogonal to the reflectors in all trial velocity models. It is also assumed that the velocity VP0 is either known at the top of each block or remains continuous in the vertical direction. The velocity analysis algorithm estimates the velocity gradients kz and kx and the anisotropy parameters ε and δ in the layer‐stripping mode using a generalized version of the method introduced by Sarkar and Tsvankin for factorized transverse isotropy with a vertical symmetry axis. Synthetic tests for several models typical in exploration (a syncline, uptilted shale layers near a salt dome and a bending shale layer) confirm that if the symmetry‐axis direction is fixed and VP0 is known, the parameters kz, kx, ε and δ can be resolved from reflection data. It should be emphasized that estimation of ε in tilted transversely isotropic media requires using nonhyperbolic moveout for long offsets reaching at least twice the reflector depth. We also demonstrate that application of processing algorithms designed for a vertical symmetry axis to data from tilted transversely isotropic media may lead to significant misfocusing of reflectors and errors in parameter estimation, even when the tilt is moderate (30°). The ability of our velocity analysis algorithm to separate the anisotropy parameters from the velocity gradients can be also used in lithology discrimination and geologic interpretation of seismic data in complex areas. 相似文献
7.
Simultaneous estimation of velocity gradients and anisotropic parameters from seismic reflection data is one of the main challenges in transversely isotropic media with a vertical symmetry axis migration velocity analysis. In migration velocity analysis, we usually construct the objective function using the l2 norm along with a linear conjugate gradient scheme to solve the inversion problem. Nevertheless, for seismic data this inversion scheme is not stable and may not converge in finite time. In order to ensure the uniform convergence of parameter inversion and improve the efficiency of migration velocity analysis, this paper develops a double parameterized regularization model and gives the corresponding algorithms. The model is based on the combination of the l2 norm and the non‐smooth l1 norm. For solving such an inversion problem, the quasi‐Newton method is utilized to make the iterative process stable, which can ensure the positive definiteness of the Hessian matrix. Numerical simulation indicates that this method allows fast convergence to the true model and simultaneously generates inversion results with a higher accuracy. Therefore, our proposed method is very promising for practical migration velocity analysis in anisotropic media. 相似文献
8.
G. Kwiatek 《Journal of Seismology》2008,12(4):499-517
The relative source time function (RSTF) inversion uncertainty assessment was performed for two small, mining-induced seismic
events (M
W
=2.9 and 3.0) that occurred at Rudna copper mine in Poland. The seismograms of selected events were recorded by the seismic
net work composed of over 60, short-period, vertical seismometers, recording ground velocity, located in the distance ranging
from 400 m up to 8 km from their hypocenters. The RSTFs were calculated for each seismic station independently, using the
empirical Green’s function technique. The pseudospectral approximation of the sought RSTF by a finite sum of Gaussian kernel
functions was used and the inverse problem was solved with the adaptive simulated annealing algorithm. Both methods improved
the stability of the deconvolution procedure and physical correctness of the final solution in comparison to the classical
deconvolution methods. To estimate the inversion uncertainties, classical Markov-chain Monte-Carlo techniques were used. The
uncertainty analysis allows for improved selection of a priori data to the following inversion for kinematic rupture process. 相似文献
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Soil water content vertical profiles under natural conditions: matching of experiments and simulations by a conceptual model 总被引：1，自引：0，他引：1 
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下载免费PDF全文 The prediction of soil moisture content, θ, as a function of depth, z, and time, t, is of fundamental importance for applications in many hydrological processes. The main objective of this paper is to provide an approach to solve this problem at a local scale in soils with vegetation. The matching of soil moisture vertical profiles observed under natural conditions in grassy plots and their simulations by a conceptual model is presented. Experimental measurements were performed in a plot located in Central Italy, complete with hydrometeorological sensors specifically set up and equipped with a time domain reflectometry system providing the water content, θe(z, t). A conceptual model framework earlier proposed for two‐layered soil vertical profiles was modified and adopted for simulations. The changes concern the incorporation of evapotranspiration, the reduction of the original model for applications also to homogeneous soil vertical profiles, and a correction for the differences existing between assumed and observed initial moisture contents. In the model calibration, it was found that the effects of vegetation could be represented adequately by a fictitious soil vertical profile with a more permeable upper layer of saturated hydraulic conductivity, Ks, independent of time. Then, for the validation events, the model simulations in the stages of both infiltration and redistribution/evapotranspiration reproduced appropriately θe(z, t) with typical values of root mean square error in the range 0.0017–0.0657. Similar results were obtained by applying the modified two‐layered model for simulations of experimental data observed in three other plots located in Northern Italy and Germany. For all four vegetated sites, the two‐layer profile better matched the experimental data than the assumption of a homogeneous profile. Thus, the conceptual approach based on a two‐layered scheme for representing θ(z, t) in soils with vegetation appears to be appropriate for many hydrological applications. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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Various exact methods of inverting the complete waveform of vertical seismic reflection data to produce acoustic impedance profiles have been suggested. These inverse methods generally remain valid for nonvertical, plane-wave data, provided total reflection does not occur. Thus, in principle, the “seismogram” at each ray parameter in a slant stack can be interpreted separately. Rather than invert each plane-wave seismogram separately, they can all be interpreted simultaneously and an “average” model thus obtained. Inversion for both the velocity and the density also becomes possible when two or more plane-wave seismograms are simultaneously inverted. The theory for a noniterative inversion method, based on the time-domain Riccati equation, is discussed. Numerical examples of inversions using this technique on synthetic data demonstrate its numerical stability and the advantage of simultaneous inversion of several seismograms to reduce the effect of noise in the data and increase the stability of the inversion process. 相似文献
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The purpose of deconvolution is to retrieve the reflectivity from seismic data. To do this requires an estimate of the seismic wavelet, which in some techniques is estimated simultaneously with the reflectivity, and in others is assumed known. The most popular deconvolution technique is inverse filtering. It has the property that the deconvolved reflectivity is band-limited. Band-limitation implies that reflectors are not sharply resolved, which can lead to serious interpretation problems in detailed delineation. To overcome the adverse effects of band-limitation, various alternatives for inverse filtering have been proposed. One class of alternatives is Lp-norm deconvolution, L1norm deconvolution being the best-known of this class. We show that for an exact convolutional forward model and statistically independent reflectivity and additive noise, the maximum likelihood estimate of the reflectivity can be obtained by Lp-norm deconvolution for a range of multivariate probability density functions of the reflectivity and the noise. The L∞-norm corresponds to a uniform distribution, the L2-norm to a Gaussian distribution, the L1-norm to an exponential distribution and the L0-norm to a variable that is sparsely distributed. For instance, if we assume sparse and spiky reflectivity and Gaussian noise with zero mean, the Lp-norm deconvolution problem is solved best by minimizing the L0-norm of the reflectivity and the L2-norm of the noise. However, the L0-norm is difficult to implement in an algorithm. From a practical point of view, the frequency-domain mixed-norm method that minimizes the L1norm of the reflectivity and the L2-norm of the noise is the best alternative. Lp-norm deconvolution can be stated in both time and frequency-domain. We show that both approaches are only equivalent for the case when the noise is minimized with the L2-norm. Finally, some Lp-norm deconvolution methods are compared on synthetic and field data. For the practical examples, the wide range of possible Lp-norm deconvolution methods is narrowed down to three methods with p= 1 and/or 2. Given the assumptions of sparsely distributed reflectivity and Gaussian noise, we conclude that the mixed L1norm (reflectivity) L2-norm (noise) performs best. However, the problems inherent to single-trace deconvolution techniques, for example the problem of generating spurious events, remain. For practical application, a greater problem is that only the main, well-separated events are properly resolved. 相似文献
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In this paper, we derive analytical expressions for one‐way and two‐way kinematical parameters in elliptical tilted transverse isotropy media. We show that the homogeneous elliptical tilted transverse isotropy models result in hyperbolic moveout with a reflection point sideslip x0, which can be considered as an additional traveltime parameter for one‐way wave propagation. For homogeneous elliptical tilted transverse isotropy models we show that the inversion of one‐way traveltime parameters suffers from the ambiguity for large tilts. It is shown that the accuracy of the inversion is sensitive to the error in x0. We also derive and invert the traveltime parameters for a vertically heterogeneous elliptical tilted transverse isotropy model with a tilt gradually changing with depth. The a priori knowledge of parameter δ is very important for inversion. The wrong choise of this parameter results in significant errors in inverted model parameters. 相似文献
15.
A type of iterative deconvolution that extracts the source waveform and reflectivity from a seismogram through the use of zero memory, non-linear estimators of reflection coefficient amplitnde is developed. Here, we present a theory for iterative deconvolution that is based upon the specification of a stochastic model describing reflectivity. The resulting parametric algorithm deconvolves the seismogram by forcing a filtered version of the seismogram to resemble an estimated reflection coefficient sequence. This latter time series is itself obtained from the filtered seismogram, and so a degree of iteration is required. Algorithms utilizing zero memory non-linearities (ZNLs) converge to a family of processes, which we call Bussgang, of which any colored Gaussian process and any independent process are members. The direction of convergence is controlled by the choice of ZNL used in the algorithm. Synthetic and real data show that, generally, five to ten iterations are required for acceptable deconvolutions. 相似文献
16.
The azimuthally varying non‐hyperbolic moveout of P‐waves in orthorhombic media can provide valuable information for characterization of fractured reservoirs and seismic processing. Here, we present a technique to invert long‐spread, wide‐azimuth P‐wave data for the orientation of the vertical symmetry planes and five key moveout parameters: the symmetry‐plane NMO velocities, V(1)nmo and V(2)nmo , and the anellipticity parameters, η(1), η(2) and η(3) . The inversion algorithm is based on a coherence operator that computes the semblance for the full range of offsets and azimuths using a generalized version of the Alkhalifah–Tsvankin non‐hyperbolic moveout equation. The moveout equation provides a close approximation to the reflection traveltimes in layered anisotropic media with a uniform orientation of the vertical symmetry planes. Numerical tests on noise‐contaminated data for a single orthorhombic layer show that the best‐constrained parameters are the azimuth ? of one of the symmetry planes and the velocities V(1)nmo and V(2)nmo , while the resolution in η(1) and η(2) is somewhat compromised by the trade‐off between the quadratic and quartic moveout terms. The largest uncertainty is observed in the parameter η(3) , which influences only long‐spread moveout in off‐symmetry directions. For stratified orthorhombic models with depth‐dependent symmetry‐plane azimuths, the moveout equation has to be modified by allowing the orientation of the effective NMO ellipse to differ from the principal azimuthal direction of the effective quartic moveout term. The algorithm was successfully tested on wide‐azimuth P‐wave reflections recorded at the Weyburn Field in Canada. Taking azimuthal anisotropy into account increased the semblance values for most long‐offset reflection events in the overburden, which indicates that fracturing is not limited to the reservoir level. The inverted symmetry‐plane directions are close to the azimuths of the off‐trend fracture sets determined from borehole data and shear‐wave splitting analysis. The effective moveout parameters estimated by our algorithm provide input for P‐wave time imaging and geometrical‐spreading correction in layered orthorhombic media. 相似文献
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AVO investigations of shallow marine sediments 总被引：2，自引：0，他引：2
Amplitude‐variation‐with‐offset (AVO) analysis is based on the Zoeppritz equations, which enable the computation of reflection and transmission coefficients as a function of offset or angle of incidence. High‐frequency (up to 700 Hz) AVO studies, presented here, have been used to determine the physical properties of sediments in a shallow marine environment (20 m water depth). The properties that can be constrained are P‐ and S‐wave velocities, bulk density and acoustic attenuation. The use of higher frequencies requires special analysis including careful geometry and source and receiver directivity corrections. In the past, marine sediments have been modelled as elastic materials. However, viscoelastic models which include absorption are more realistic. At angles of incidence greater than 40°, AVO functions derived from viscoelastic models differ from those with purely elastic properties in the absence of a critical angle of incidence. The influence of S‐wave velocity on the reflection coefficient is small (especially for low S‐wave velocities encountered at the sea‐floor). Thus, it is difficult to extract the S‐wave parameter from AVO trends. On the other hand, P‐wave velocity and density show a considerably stronger effect. Attenuation (described by the quality factor Q) influences the reflection coefficient but could not be determined uniquely from the AVO functions. In order to measure the reflection coefficient in a seismogram, the amplitudes of the direct wave and the sea‐floor reflection in a common‐midpoint (CMP) gather are determined and corrected for spherical divergence as well as source and streamer directivity. At CMP locations showing the different AVO characteristics of a mud and a boulder clay, the sediment physical properties are determined by using a sequential‐quadratic‐programming (SQP) inversion technique. The inverted sediment physical properties for the mud are: P‐wave velocity α=1450±25 m/s, S‐wave velocity β=90±35 m/s, density ρ=1220±45 kg/m3, quality factor for P‐wave QP=15±200, quality factor for S‐wave QS=10±30. The inverted sediment physical properties for the boulder clay are: α=1620±45 m/s,β=360±200 m/s,ρ=1380±85 kg/m3,QP=790±660,QS=25±10. 相似文献
18.
In order to perform a good pulse compression, the conventional spike deconvolution method requires that the wavelet is stationary. However, this requirement is never reached since the seismic wave always suffers high‐frequency attenuation and dispersion as it propagates in real materials. Due to this issue, the data need to pass through some kind of inverse‐Q filter. Most methods attempt to correct the attenuation effect by applying greater gains for high‐frequency components of the signal. The problem with this procedure is that it generally boosts high‐frequency noise. In order to deal with this problem, we present a new inversion method designed to estimate the reflectivity function in attenuating media. The key feature of the proposed method is the use of the least absolute error (L1 norm) to define both the data and model error in the objective functional. The L1 norm is more immune to noise when compared to the usual L2 one, especially when the data are contaminated by discrepant sample values. It also favours sparse reflectivity when used to define the model error in regularization of the inverse problem and also increases the resolution, since an efficient pulse compression is attained. Tests on synthetic and real data demonstrate the efficacy of the method in raising the resolution of the seismic signal without boosting its noise component. 相似文献
19.
K.-P. SENGPIEL 《Geophysical Prospecting》1988,36(4):446-459
A complex transfer function c (or generalized skin depth) can be derived from data for the secondary magnetic field measured by a dipole system with small coil spacing at height h above the ground. This function has a useful property: For a uniform or layered ground, the real part of c yields the‘ centroid depth’z* of the in-phase current system as a function of frequency. This parameter can be combined with the apparent resistivity ρa derived by conventional methods. The function ρa(z*), if known over a broad frequency range, yields a smoothed approximation of the true distribution ρ(z) without an initial model. The relations between ρa(z*) and ρ(z) are studied for a number of multilayer models. An example of the application of the ρa*) algorithm to data from a groundwater survey is given. 相似文献