共查询到20条相似文献，搜索用时 31 毫秒
1.
R.-G. FERBER 《Geophysical Prospecting》1988,36(8):857-877
A new time-domain method is introduced for the calculation of theoretical seismograms which include frequency dependent effects like absorption. To incorporate these effects the reflection and transmission coefficients become convolutionary operators. The method is based on the communication theory approach and is applicable to non-normal incidence plane waves in flat layered elastic media. Wave propagation is simulated by tracking the wave amplitudes through a storage vector inside the computer memory representing a Goupillaud earth model discretized by equal vertical transit times. Arbitrary numbers of sources and receivers can be placed at arbitrary depth positions, while the computational effort is independent of that number. Therefore, the computation of a whole plane-wave vertical seismic profile is possible with no extra effort compared to the computation of the surface seismogram. The new method can be used as an aid to the interpretation of plane-wave decomposed reflection data where the whole synthetic vertical seismic profile readily gives the interpreter the correct depth position of reflection events. 相似文献
2.
E. A. ROBINSON 《Geophysical Prospecting》1975,23(4):779-797
Dynamic predictive deconvolution makes use of an entire seismic trace including all primary and multiple reflections to yield an approximation to the subsurface structure. We consider plane-wave motion at normal incidence in an horizontally layered system sandwiched between the air and the basement rock. Energy degradation effects are neglected so that the layered system represents a lossless system in which energy is lost only by net transmission downward into the basement or net reflection upward into the air; there is no internal loss of energy by absorption within the layers. The layered system is frequency selective in that the energy from a surface input is divided between that energy which is accepted over time by net transmission downward into the basement and the remaining energy that is rejected over time by net reflection upward into the air. Thus the energy from a downgoing unit spike at the surface as input is divided between the wave transmitted by the layered system into the basement and the wave reflected by the layered system into the air. This reflected wave is the observed seismic trace resulting from the unit spike input. From surface measurements we can compute both the input energy spectrum, which by assumption is unity, and the reflection energy spectrum, which is the energy spectrum of the trace. But, by the conservation of energy, the input energy spectrum is equal to the sum of the reflection energy spectrum and the transmission energy spectrum. Thus we can compute the transmission energy spectrum as the difference of the input energy spectrum and the reflection energy spectrum. Furthermore, we know that the layered system acts as a pure feedback system in producing the transmitted wave, from which it follows that the transmitted wave is minimum-delay. Hence from the computed energy spectrum of the transmitted wave we can compute the prediction-error operator that contracts the transmitted wave to a spike. We also know that the layered system acts as a system with both a feedback component and a feed-forward component in producing the reflected wave, that is, the observed seismic trace. Moreover, this feedback component is identical to the pure feedback system that produces the transmitted wave. Thus, we can deconvolve the observed seismic trace by the prediction-error operator computed above; the result of the deconvolution is the wave-form due to the feedforward component alone. Now the feedforward component represents the wanted dynamic structure of the layered system whereas the feedback component represents the unwanted reverberatory effects of the layered system. Because this deconvolution process yields the wanted dynamic structure and destroys the unwanted reverberatory effects, we call the process dynamic predictive deconvolution. The resulting feedforward waveform in itself represents an approximation to the subsurface structure; a further decomposition yields the reflection coefficients of the interfaces separating the layers. In this work we do not make the assumption as is commonly done that the surface as a perfect reflector; that is, we do not assume that the surface reflection coefficient has magnitude unity. 相似文献
3.
Fredy A.V. Artola Ricardo Leiderman Sergio A.B. Fontoura 《Geophysical Prospecting》2005,53(5):717-721
The existence of non‐zero reflectivity for zero‐offset PS waves in horizontally layered media is discussed. Field measurements have suggested the occurrence of this phenomenon. We show that, in some cases, if anisotropy is considered in the problem, this reflectivity can be predicted. By using an approximated formulation to determine the coefficient of reflection in arbitrarily anisotropic media, it is clear that, for some elastic arrangements of the subsurface, reflected energy is associated with the converted wave resulting from normal P‐wave incidence. 相似文献
4.
本文对地震逆散射的研究，旨在于为抑制层间多次波和地震波场多重散射对一次反射干扰效应提供理论依据.这对薄互层地层滤波的高频恢复、保幅弹性反演、衍射地震勘探及海洋地震勘探中的干扰消除皆具重要意义.本文基于上下行波分解及弹性波互易定理，导出横向变速介质条件下线性预测算子的表达式和反射数据的广义谱分解方程. 文中先由上覆地层广义反射透射矩阵的元素定义线性预测算子，并将其表示成一系列单程波算子的线性组合,之后将横向变速介质条件下线性预测方程表达为反射数据与线性预测算子及其逆的乘积. 对该方程的求解可获得上覆地层的线性预测算子，从而可借以求出相应的反射透射算子. 本文先将水平层状介质条件下垂直入射的一维线性预测方程推广到斜入射的情况，以此为参照，导出横向非均匀介质条件下反射数据的地震逆散射广义谱分解方程.文中也揭示了单程波地震逆散射算子、反射透射算子的性态.本文还针对水平层状介质条件，给出斜入射的数值结果. 相似文献
5.
The analysis of frequency-dependent characteristics for fluid detection: a physical model experiment 总被引：1，自引：0，他引：1
According to the Chapman multi-scale rock physical model, the seismic response characteristics vary for different fluid-saturated reservoirs. For class I AVO reservoirs and gas-saturation, the seismic response is a high-frequency bright spot as the amplitude energy shifts. However, it is a low-frequency shadow for the Class III AVO reservoirs saturated with hydrocarbons. In this paper, we verified the high-frequency bright spot results of Chapman for the Class I AVO response using the frequency-dependent analysis of a physical model dataset. The physical model is designed as inter-bedded thin sand and shale based on real field geology parameters. We observed two datasets using fixed offset and 2D geometry with different fluidsaturated conditions. Spectral and time-frequency analyses methods are applied to the seismic datasets to describe the response characteristics for gas-, water-, and oil-saturation. The results of physical model dataset processing and analysis indicate that reflection wave tuning and fluid-related dispersion are the main seismic response characteristic mechanisms. Additionally, the gas saturation model can be distinguished from water and oil saturation for Class I AVO utilizing the frequency-dependent abnormal characteristic. The frequency-dependent characteristic analysis of the physical model dataset verified the different spectral response characteristics corresponding to the different fluid-saturated models. Therefore, by careful analysis of real field seismic data, we can obtain the abnormal spectral characteristics induced by the fluid variation and implement fluid detection using seismic data directly. 相似文献
6.
F. SCHERBAUM 《Geophysical Prospecting》1987,35(7):787-802
The Kunetz-Claerbout equation for the acoustic transmission problem in a layered medium in its original form establishes the relation between the transmission and the reflec tion response for P-waves in an horizontally layered medium and with vertical incidence. It states that the reflection seismogram due to an impulsive source at the surface, is one side of the autocorrelation of the seismogram due to an impulsive source at depth and a surface receiver. By adapting Claerbout's formulation to the transmission of SH-waves, the Kunetz-Claerbout equation also holds for reflection and transmission coefficients dependent on the incident angle. Thus, earthquake geometry SH-transmission seismograms can be used to caculate corresponding pseudoreflection seismograms which, in turn, can be inverted for the impedance structure using the Levinson algorithm. If the average incidence angle is known, a geometrical correction on the resulting impedance model can improve the resolution of layer thicknesses. In contrast to the inversion of reflection seismograms, the Levinson algorithm is shown to yield stable results for the inversion of transmission seismograms even in the presence of additive noise. This noise stabilization is inherent to the Kunetz-Claerbout equation. Results of inverted SH-wave microearthquake seismograms from the Swabian Jura, SW Germany, seismic zone obtained at recording site Hausen im Tal have been compared with sonic-log data from nearby exploration drilling at Trochtelfingen. The agreement of the main structural elements is fair to a depth of several hundred metres. 相似文献
7.
Seismic amplitude variations with offset contain information about the elastic parameters. Prestack amplitude analysis seeks to extract this information by using the variations of the reflection coefficients as functions of angle of incidence. Normally, an approximate formula is used for the reflection coefficients, and variations with offset of the geometrical spreading and the anelastic attenuation are often ignored. Using angle of incidence as the dependent variable is also computationally inefficient since the data are recorded as a function of offset. Improved approximations have been derived for the elastic reflection and transmission coefficients, the geometrical spreading and the complex travel-time (including anelastic attenuation). For a 1 D medium, these approximations are combined to produce seismic reflection amplitudes (P-wave, S-wave or converted wave) as a Taylor series in the offset coordinate. The coefficients of the Taylor series are computed directly from the parameters of the medium, without using the ray parameter. For primary reflected P-waves, dynamic ray tracing has been used to compute the offset variations of the transmission coefficients, the reflection coefficient, the geometrical spreading and the anelastic attenuation. The offset variation of the transmission factor is small, while the variations in the geometrical spreading, absorption and reflection coefficient are all significant. The new approximations have been used for seismic modelling without ray tracing. The amplitude was approximated by a fourth-order polynomial in offset, the traveltime by the normal square-root approximation and the absorption factor by a similar expression. This approximate modelling was compared to dynamic ray tracing, and the results are the same for zero offset and very close for offsets less than the reflector depth. 相似文献
8.
转换波和非转换波与射线参数p的关系 总被引：1，自引：1，他引：1
本文对Aki固体-固体分界面的反射和透射公式进行适当变换,使之成为一组适合不同坐标系下,固体、液体、气体和真空之间所有可能形成的分界面上,入射P、SV和SH波所形成的反射和透射公式,从而把不同边界条件的反射和透射方程统一起来,并且阐明了转换波和非转换波动力学特征的差异.指出:在不同弹性介质分界面上入射平面弹性波,转换波的反射系数和透射系数是射线参数p的奇函数;非转换波的反射系数和透射系数是射线参数p的偶函数.根据奇函数和偶函数的性质可见:垂直入射时不存在转换波.同时也为简化Zoeppricz方程,开展AVO分析打开新思路. 相似文献
9.
Consider the mathematical model of a horizontally layered system subject to an initial downgoing source pulse in the upper layer and to the condition that no upgoing waveforms enter the layered system from below the deepest interface. The downgoing waveform (as measured from its first arrival) in each layer is necessarily minimum-phase. The net downgoing energy in any layer, defined as the difference of the energy spectrum of the downgoing wave minus the energy spectrum of the upgoing wave, is itself in the form of an energy spectrum, that is, it is non-negative for all frequencies. The z-transform of the autocorrelation function corresponding to the net downgoing energy spectrum is called the net downgoing spectral function for the layer in question. The net downgoing spectral functions of any two layers A and B are related as follows: the product of the net downgoing spectral function of layer A times the overall transmission coefficient from A to B equals the product of the net downgoing spectral function of layer B times the overall transmission coefficient from B to A. The net downgoing spectral function for the upper layer is called simply the spectral function of the system. In the case of a marine seismogram, the autocorrelation function corresponding to the spectral function can be used to recursively generate prediction error operators of successively increasing lengths, and at the same time the reflection coefficients at successively increasing depths. This recursive method is mathematically equivalent to that used in solving the normal equations in the case of Toeplitz forms. The upgoing wave-form in any given layer multiplied by the direct transmission coefficient from that layer to the surface is equal to the convolution of the corresponding prediction error operator with the surface seismogram. The downgoing waveform in this given layer multiplied by the direct transmission coefficient from that layer to the surface is equal to the convolution of the corresponding hindsight error operator (i.e., the time reverse of the prediction error operator) with the surface seismogram. 相似文献
10.
本文研究了纵波垂直入射情况下两种介质分界面处的纵波反射和透射系数的频散特性,分界面上下两侧分别为层状双孔页岩介质和层状双孔砂岩介质.当纵波沿垂直于分界面的方向传播至分界面处时,会在上层双孔介质中产生三类反射纵波,在下层双孔介质中产生三类透射纵波.基于层状双孔介质的特性,给出了分界面处的六个边界条件.根据层状双孔介质的波动方程,利用平面波分析得到了纵波的反射和透射系数.结果表明：当多孔介质中存在流体时,纵波的反射和透射系数与频率相关,即存在频散现象.波致流体流动是造成纵波反射和透射系数频散的主要原因.此外,结果还表明局部流体流动引起地震频带内反射和透射系数的频散,宏观Biot流引起超声频带内反射和透射系数的频散.本文同时对岩石参数对反射和透射系数频散曲线的影响进行了研究. 相似文献
11.
—An algorithm has been developed to compute the dispersive and dissipative seismic response using FUTTERMAN’S (1962) third attenuation-dispersion relationship. In the computation, frequency-dependent velocity and quality factor Q have been used but in the case of the nondispersive synthetic seismogram, frequency-independent velocity has been used. The model’s parameters are density, phase velocity, quality factors and thicknesses of the layers. Dispersive and nondispersive synthetic seismograms have been computed with and without absorption for a layered earth geological model. Fast Fourier transform (FFT) technique has been adopted for converting the frequency domain response into the time domain. The frequency spacing, Δf = 0.976?Hz, has been considered to avoid the aliasing effect. The results have revealed changes in the reflected waveforms in the frequency domain as well as in the time domain for absorption and dispersion cases. It is also concluded that dispersion reduces the arrival time and this effect is increasing with the travel time. The effect of constant Q on the seismic response has also been studied. 相似文献
12.
S. Mohapatra 《地球物理与天体物理流体动力学》2013,107(5):347-374
Scattering of oblique incident waves by small bottom undulation in a two-layer fluid, where the upper layer has a thin ice-cover while the lower one has the undulation, is investigated within the framework of linearized water wave theory. The ice-cover is being modeled as an elastic plate of very small thickness. There exist two modes of time-harmonic waves–one with lower wave number propagating along the ice-cover (ice-cover mode) and the other with higher wave number along the interface (interfacial mode). A perturbation analysis is employed to solve the corresponding boundary value problem governed by modified Helmholtz equation and thereby evaluating the reflection and transmission coefficients approximately up to first order for both modes. A patch of sinusoidal ripples, having two different wave numbers over two consecutive stretches, is considered as an example and the related coefficients are determined. It is observed that when the wave is incident on the ice-cover surface we always find energy transfer to the interface, but for interfacial incident waves there are parameter ranges for which no energy transfer to the ice-cover surface is possible. Also it is observed that for small angles of incidence, the reflected energy is more as compared to the other angles of incidence. These results are demonstrated in graphical form. From the derived results, the solutions for problems with free surface can be obtained as particular cases. 相似文献
13.
Reflection and transmission of inhomogeneous waves in a composite porous solid saturated by two immiscible fluids 
下载免费PDF全文
下载免费PDF全文 This paper is concerned with reflection and transmission of a plane, elastic, and inhomogeneous wave striking obliquely at some discontinuity inside a porous medium composed of two distinct solids and saturated by two immiscible fluids. It is found that four P‐ and two SV‐waves are reflected, whereas four P‐ and two SV‐waves are transmitted at the interface. All reflected and transmitted waves are inhomogeneous in nature and specified with different directions of propagation and attenuation vectors. An expression for the Umov–Poynting energy flux vector is derived for the system. Continuity of energy flux along normal to the interface gives 12 required boundary conditions. Expressions of amplitude and energy ratios of various reflected and transmitted waves are derived. Variations in amplitude and energy coefficients of reflected and transmitted waves with angle of incidence are numerically studied for a porous matrix composed of shaley sandstone and clay, saturated with water and oil. The effects of change in oil saturation and volume fraction of clay are also observed on amplitude ratios. Numerical simulation reveals that the change in sign in the difference of capillary pressure across the interface causes jump in the values of amplitude ratios of all waves. 相似文献
14.
This paper is directed at modeling layered media. We extend the plane-wave normal-incidence state-space model developed by Mendel, Nahi and Chan in 1979, to the non-normal incidence case. To do this we introduce a shifting principle, a zero-offset wavefront, and zero-offset travel times for different layers. We also develop an algorithm for obtaining a synthetic line source reflection seismogram. In this algorithm non-normal incidence plane-wave seismograms are summed over a range of incident angles. The algorithm is based on a modified version of Sommerfield's (1896) theorem. Simulations of acoustic and elastic media are included which illustrate the applicability of our plane-wave and line source seismograms for both elastic and acoustic cases. 相似文献
15.
16.
When a porous layer is permeated by mesoscale fractures, wave-induced fluid flow between pores and fractures can cause significant attenuation and dispersion of velocities and anisotropy parameters in the seismic frequency band. This intrinsic dispersion due to fracturing can create frequency-dependent reflection coefficients in the layered medium. In this study, we derive the frequency-dependent PP and PS reflection coefficients versus incidence angle in the fractured medium. We consider a two-layer vertical transverse isotropy model constituted by an elastic shale layer and an anelastic sand layer. Using Chapman's theory, we introduce the intrinsic dispersion due to fracturing in the sand layer. Based on the series coefficients that control the behaviour of velocity and anisotropy parameters in the fractured medium at low frequencies, we extend the conventional amplitude-versus-offset equations into frequency domain and derive frequency-dependent amplitude-versus-offset equations at the elastic–anelastic surface. Increase in fracture length or fracture density can enlarge the frequency dependence of amplitude-versus-offset attributes of PP and PS waves. Also, the frequency dependence of magnitude and phase angle of PP and PS reflection coefficients increases as fracture length or fracture density increases. Amplitude-versus-offset type of PP and PS reflection varies with fracture parameters and frequency. What is more, fracture length shows little impact on the frequency-dependent critical phase angle, while the frequency dependence of the critical phase angle increases with fracture density. 相似文献
17.
Kianoosh Hatami 《Soil Dynamics and Earthquake Engineering》1997,16(7-8):407-415
The absorption of hydrodynamic pressure waves at the reservoir bottom has dominant effects on the structural response of the dam when subjected to ground motion. In the present study, a model is proposed for the absorption effects of the reservoir bottom in the earthquake analysis of dams. The model utilizes the wave reflection coefficient approach and is based on the solution of the wave equation in a sediment layer of viscoelastic material with a constant thickness overlying an elastic, semi-infinite foundation. Numerical studies were conducted to evaluate the effect of the sediment layer thickness and material properties as well as the effect of reflection of waves from the underlying rock. It is shown that the current approach of assuming the wave reflection coefficient at the reservoir bottom based on the characteristics of the sediment material and excluding the effect of the reflected waves from the underlying rock, may significantly underestimate the seismic response of the dam. 相似文献
18.
WILLIAM J. VETTER 《Geophysical Prospecting》1981,29(3):363-373
A forward solution for the reflection response of a parallel stratified lossless medium characterized by discrete reflection coefficients and unequal layer delays, for a normally incident pressure source signal, is presented. The notation, which details the reflection history of each wavelet in a response record, facilitates systematic enumeration of all terms in the reflection impulse response model, the determination of compact closed form expressions for amplitudes and delays of multiply reflected wavelets, and the aggregation of dynamic analog groups. An equal delay time constraint on layer thicknesses leads then to the reflection sequence or synthetic seismogram structure as an infinite sum of wavelets by their order of reflection. 相似文献
19.
光滑处理使得单界面成为非均匀薄层,界面反射转变为层反射.为了探讨光滑处理的影响,以平面波作为入射波场,首先利用过渡层反射系数推导了反射信号的理论公式,然后就非均匀薄层下反射系数的计算问题,给出了具体的实现算法,并通过与经典Epstein过渡层反射系数解析结果的对比说明了算法的精度.最后在单界面及其被光滑后界面的对比分析中,得出了几点重要结论：随着光滑次数的增加,反射信号的到时基本保持不变,而反射信号的主频与能量呈减少趋势,其中信号能量在低光滑次数的衰减速率明显大于高光滑次数. 相似文献
20.
孔隙介质弹性波传播理论在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用.而孔隙介质中的弹性波受孔隙度、渗透率、流体黏滞系数等参数的影响,因此研究波场的传播特征将有助于分析和提取这些信息.本文在Biot理论的基础上,针对三维层状孔隙介质模型,利用在合成理论地震图的研究中已经被证实具有稳定、高效且适用范围较广的Luco-Apsel-Chen（LAC）广义反透射方法,给出了弹性波场的一种积分形式的半解析解,可通过数值方法高效、准确地计算层状孔隙介质中的理论波场,所以该积分形式的半解析解可为三维层状孔隙介质波场传播特征的理论数值模拟研究提供一种新的途径和手段. 相似文献