共查询到20条相似文献，搜索用时 15 毫秒
1.
P. HUBRAL 《Geophysical Prospecting》1976,24(3):478-491
Various Dix-type formulae are derived, which are useful to approximate travel time functions that can be observed while modeling the common depth point (CDP) technique for 3-D isovelocity layers of varying dip and strike. All formulae can be used to compute interval velocities and recover the depth model from surface measurements. They are established by making use of the concept of wavefront curvature. Many similarities with known formulae valid for the 2-D plane isovelocity layer case exist. 相似文献
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3.
Igor Ravve 《Geophysical Prospecting》2016,64(3):517-542
We suggest a new method to determine the piecewise‐continuous vertical distribution of instantaneous velocities within sediment layers, using different order time‐domain effective velocities on their top and bottom points. We demonstrate our method using a synthetic model that consists of different compacted sediment layers characterized by monotonously increasing velocity, combined with hard rock layers, such as salt or basalt, characterized by constant fast velocities, and low velocity layers, such as gas pockets. We first show that, by using only the root‐mean‐square velocities and the corresponding vertical travel times (computed from the original instantaneous velocity in depth) as input for a Dix‐type inversion, many different vertical distributions of the instantaneous velocities can be obtained (inverted). Some geological constraints, such as limiting the values of the inverted vertical velocity gradients, should be applied in order to obtain more geologically plausible velocity profiles. In order to limit the non‐uniqueness of the inverted velocities, additional information should be added. We have derived three different inversion solutions that yield the correct instantaneous velocity, avoiding any a priori geological constraints. The additional data at the interface points contain either the average velocities (or depths) or the fourth‐order average velocities, or both. Practically, average velocities can be obtained from nearby wells, whereas the fourth‐order average velocity can be estimated from the quartic moveout term during velocity analysis. Along with the three different types of input, we consider two types of vertical velocity models within each interval: distribution with a constant velocity gradient and an exponential asymptotically bounded velocity model, which is in particular important for modelling thick layers. It has been shown that, in the case of thin intervals, both models lead to similar results. The method allows us to establish the instantaneous velocities at the top and bottom interfaces, where the velocity profile inside the intervals is given by either the linear or the exponential asymptotically bounded velocity models. Since the velocity parameters of each interval are independently inverted, discontinuities of the instantaneous velocity at the interfaces occur naturally. The improved accuracy of the inverted instantaneous velocities is particularly important for accurate time‐to‐depth conversion. 相似文献
4.
D. PATELLA 《Geophysical Prospecting》1977,25(4):699-729
The electrical potential generated by a point source of current on the ground surface is studied for a multi-layered earth formed by layers alternatively characterized by a constant conductivity value and by conductivity varying linearly with depth. The problem is accounted for by solving a Laplace's differential equation for the uniform layers and a Poisson's differential equation for the transitional layers. Then, by a simple algorithm and by the introduction of a suitable kernel function, the general expression of the apparent resistivity for a Schlumberger array placed on the surface is obtained. Moreover some details are given for the solution of particular cases as 1) the presence of a infinitely resistive basement, 2) the absence of any one or more uniform layers, and 3) the absence of any one or more transitional layers. The new theory proves to be rather general, as it includes that for uniform layers with sharp boundaries as a particular case. Some mathematical properties of the kernel function are studied in view of the application of a direct system of quantitative interpretation. Two steps are considered for the solution of the direct problem: (i) The determination of the kernel function from the field measurements of the apparent resistivity. Owing to the identical mathematical formalism of the old with this new resistivity theory, the procedures there developed for the execution of the first step are here as well applicable without any change. Thus, some graphical and numerical procedures, already published, are recalled. (ii) The determination of the layer distribution from the kernel function. A recurrent procedure is proposed and studied in detail. This recurrent procedure follows the principle of the reduction to a lower boundary plane, as originally suggested by Koefoed for the old geoelectrical theory. Here the method differs mainly for the presence of reduction coefficients, which must be calculated each time when passing to a reduced earth section. 相似文献
5.
V. N. Zyryanov 《Water Resources》2009,36(4):396-405
The effect of the formation of reverse slope of water level in stratified reservoirs and the appearance of current velocity peak within the water body are described. Velocity profiles with a peak within the flow have been recorded in experiments at relatively small vertical density gradients; therefore, the stratification alone is not enough to cause such effect. The wind as a cause of this effect is also ruled out. An important part in this problem is shown to belong to the effect of reservoir morphometry on the interrelated behavior of the free surface and the interfaces between layers. It is shown that, at a constant transit flow, the free surface in a stratified reservoir may be a nonmonotonic function decreasing in the general direction of transit flow and inversions in the level curve can appear, i.e., an inverse level course with an inverse slope of the free surface may form. Velocity profiles with an inflection point and a peak in underlying layers form in such cases. 相似文献
6.
S. BOISSE 《Geophysical Prospecting》1978,26(1):163-174
It is not possible to determine accurate geological velocities from seismic velocity analysis for thin layers or complex structural features, especially under an unconformity. Instead, we can approach the problem of interval velocity with seismic amplitudes analysis and compute the reflection coefficient along the unconformity surface. An error estimation has been made on a model to test the possibility of such a method and to choose the best parameters to be used. The method has been applied on an actual case: the computed interval velocities show good correlation with the values obtained by a sonic log. 相似文献
7.
S. M. DEREGOWSKI 《Geophysical Prospecting》1982,30(3):318-322
Application of dip-moveout attempts to correct pre-stack data in such a way that they stack correctly, however far the reflector geometry departs from an ideal plane horizontal interface. Even for plane dipping reflectors under a constant velocity overburden a common mid-point gather contains reflections distributed over a finite segment of the reflector. It is shown that under these conditions application of dip-moveout moves dipping energy on common offset gathers in such a manner that common mid-point gathers become true common depth point gathers. 相似文献
8.
R. CHANDER 《Geophysical Prospecting》1977,25(1):120-124
A polygonal ray path connects the seismic source and detector positions when the intervening medium consists solely of constant velocity layers with plane interfaces which may have arbitrary orientation. The coordinates of the ray vertices satisfy a system of coupled equations resulting from the requirement that Fermat's principle be satisfied along the ray path. Solving the system of equations is equivalent to tracing the ray numerically. A notable feature of this approach is that a ray which is critically refracted over a segment of its path requires no special handling. 相似文献
9.
In this paper, closed-form analytic expressions for the frequency-wave number domain Fourier amplitudes of the displacement field at the free surface of a layered, anelastic half-space are established. The displacement field is caused by a seismic source described by a shear dislocation propagating with constant velocity over a rectangular fault (Haskell's model). Three-dimensional plane wave propagation is considered in the layered half-space using a propagator-based formalism. The wave radiation from the source is decoupled into P-SV and SH motions and the two problems are treated separately. First, analytic expressions are calculated for the displacement field at the free surface due to unidirectional unit impulses. Then, these expressions are used to compute solutions for the displacement field due to effective point sources associated with a pure strike slip and a pure dip slip. Finally, these solutions are combined and integrated over the rectangular fault area to establish closed-form analytic expressions of the total displacement field at the free surface. 相似文献
10.
Bed load transport by bed form migration 总被引：1，自引：1，他引：0
A theoretically-based methodology is presented for the determination of bed load transport from high-resolution measurements of bed surface elevations for steady-state or developing dunes. The methodology is based on the general form of the Exner equation for sediment continuity and requires information on the distribution of sediment volume concentration as well as the migration velocity of bed layers. In order to determine layer speeds, a new method based on cross-correlation analysis of elevation slices is proposed. The methodology is tested using artificially-created data as well as data from a physical model and from a flume study of developing bed forms. The analyses show the applicability of the method to determine bed load transport without the need to introduce assumptions about the form of the migrating surface. It is shown that predicted transport rates match measured or theoretical transport rates for steadily moving bed forms of an arbitrary shape. The method can also be used to predict transport rates over deforming bed forms, with the reasons for potential deviations between predicted and measured or theoretical transport rates for deforming bed forms identified and discussed. It is further shown that a simplified bulk-surface approach, that is relatively straightforward to apply and in which it is assumed that bed-layer velocity is constant with depth, gives results that are comparable to analyses based on determined bed-layer velocity variation with depth. 相似文献
11.
华北地区三维地壳上地幔结构 总被引：40，自引：7，他引：33
本文用均等显示滤波频时分析方法分析了长周期瑞利面波资料,获得了路经中国大陆及邻区的238条混合路径的面波群速度频散,其周期范围为10.5-113s.用改进的分格反演方法从混合路径频散中提取出位于华北地区的12个4°×4°网格单元的纯路径频散并反演其地壳上地幔结构.所得结果表明,华北地区地壳上地幔结构横向变化显著;从东向西地壳逐渐变厚;位于华北东部的分格在地壳中20km深处普遍存在低速层,整个华北地区上地幔低速层埋藏较浅,一般为55-100km之间.各个网格上地幔低速层的速度不尽相同. 相似文献
12.
目前完全弹性介质中面波频散特征的研究已较为完善,多道面波分析技术(MASW)在近地表勘探领域也取得了较好的效果,但黏弹介质中面波的频散特征研究依然较少.本文基于解析函数零点求解技术,给出了完全弹性、常Q黏弹和Kelvin-Voigt黏弹层状介质中勒夫波频散特征方程的统一求解方法.对于每个待计算频率,首先根据传递矩阵理论得到勒夫波复频散函数及其偏导的解析递推式,然后在复相速度平面上利用矩形围道积分和牛顿恒等式将勒夫波频散特征复数方程的求根问题转化为等价的连带多项式求解问题,最后通过求解该连带多项式的零点得到多模式勒夫波频散曲线与衰减系数曲线.总结了地层速度随深度递增和夹低速层条件下勒夫波频散特征根在复相速度平面上的运动规律和差异.证明了频散曲线交叉现象在复相速度平面上表现为:随频率增加,某个模式特征根的移动轨迹跨越了另一个模式特征根所在的圆,并给出了这个圆的解析表达式.研究还表明,常Q黏弹地层中的基阶模式勒夫波衰减程度随频率近似线性增加,而Kelvin-Voigt黏弹地层中的基阶模式勒夫波衰减程度随频率近似指数增加,且所有模式总体衰减程度强于常Q黏弹地层中的情况. 相似文献
13.
The electrical potential due to a point source of current placed on the ground surface is studied for a multi-layered earth consisting of homogeneous overburden of constant conductivity over a stack of transition layers where conductivity varies with depth according to power and exponential laws in even and odd layers, respectively. The general recursion relations are derived and are used to obtain expressions for the apparent resistivities for Schlumberger and Wenner electrode arrays. Their asymptotic behavior has been studied. The solutions for some particular cases are given: (i) odd layers with conductivities exponentially varying with depth while all even layers (and the first) have constant conductivities; (ii) even layer conductivities varying as a power law while odd number layers are of constant conductivity; and (iii) any two successive layers as transition layers and all others having constant conductivities. Further it is shown that Patella's theory is a particular case of the present study. It is concluded, therefore, that the present treatment is more general as all earlier models consisting of trasition layers can be derived from this study. 相似文献
14.
Hua-You Chai Kok-Kwang Phoon Chang-Fu Wei Ying-Fa Lu 《Journal of Applied Geophysics》2011,73(1):49-58
In the wave field induced by active sources, the observed phase velocity of surface waves is influenced by both mode incompatibility (i.e. non-planar spread of surface waves is idealized as plane waves) and body waves. Effects of sources are usually investigated based on numerical simulations and physical models. Several methods have been proposed to mitigate the effects. In application, however, these methods may also have difficulties since the energy of the body waves depends on soil stratification and parameters. There are multiple modes of surface waves in layered media, among which the higher modes dominate the wave field for soils with the irregular shear velocity profiles. Considering the mode incompatibility and the higher modes, we derive analytical expressions for the effective phase velocity of the surface waves based on the thin layer stiffness method, and investigate the effects of the body waves on the observed phase velocity through the phase analysis of the vibrations of both the surface waves and the body waves. The results indicate that the effective phase velocity of the surface waves in layered media varies with the frequency and the spread distance, and is underestimated compared to that of the plane surface waves in the spread range less than about one wavelength. The oscillations that appeared in the observed phase velocity are due to the involvement of the body waves. The mode incompatibility can be ignored in the range beyond one wavelength, while the influence range of the body waves is far beyond one wavelength. The body waves have a significant influence on the observed phase velocity of the surface waves in soils with a soft layer trapped between the first and the second layers because of strong reflections. 相似文献
15.
The surface motion during an earthquake is different from point to point depending on the propagation properties of the seismic waves. Rocking and torsion are thus present in the free field, in proportion to the spatial derivatives of the surface motion with respect to a given direction. These derivatives are inversely proportional to the apparent wave velocity in that direction, so the smaller the wave apparent velocity, the more important its contribution to the rotations. In this respect, a marked contribution to surface rotations from surface waves is expected. A mathematical model is presented, based on a detailed representation of soil impedance, an approximate identification of surface waves and a deconvolution of body waves in P and SV contributions. Through this model the surface motion obtained from the records of strong-motion accelerometers can be expressed as a superposition of plane waves of known wavelengths. Rocking response spectra are computed and results are compared with previously published spectra. A sensitivity analysis is performed on some parameters of the model. 相似文献
16.
将起伏曲面B上的位场向下延拓至曲面最低点的平面A的插值-迭代法步骤是：1）将曲面B上的场值放置在水平面A上具有相同水平坐标的点上,作为A上的初值;2）用若干水平面切割B,从A的初值,用快速傅里叶变换法(FFT)向上延拓出这些平面的场值,用插值的方法从这些平面的场值计算曲面B的场值;3）根据B上的实测值与计算值的差值,对A上的值进行加权改正;4）重复步骤2）和3）,直到B上的差值小到可以忽略.这种插值-迭代法具有高的计算速度,比通常的FFT法延拓得更深,可以超过10倍点距.文中给出计算实例. 相似文献
17.
Anisotropy in subsurface geological models is primarily caused by two factors: sedimentation in shale/sand layers and fractures. The sedimentation factor is mainly modelled by vertical transverse isotropy (VTI), whereas the fractures are modelled by a horizontal transversely isotropic medium (HTI). In this paper we study hyperbolic and non‐hyperbolic normal reflection moveout for a package of HTI/VTI layers, considering arbitrary azimuthal orientation of the symmetry axis at each HTI layer. We consider a local 1D medium, whose properties change vertically, with flat interfaces between the layers. In this case, the horizontal slowness is preserved; thus, the azimuth of the phase velocity is the same for all layers of the package. In general, however, the azimuth of the ray velocity differs from the azimuth of the phase velocity. The ray azimuth depends on the layer properties and may be different for each layer. In this case, the use of the Dix equation requires projection of the moveout velocity of each layer on the phase plane. We derive an accurate equation for hyperbolic and high‐order terms of the normal moveout, relating the traveltime to the surface offset, or alternatively, to the subsurface reflection angle. We relate the azimuth of the surface offset to its magnitude (or to the reflection angle), considering short and long offsets. We compare the derived approximations with analytical ray tracing. 相似文献
18.
在我国西北地区的柴达木盆地东部和甘肃地区,在距离炮点40互100公里处,能够接收到不少能量较强的地壳深界面反射波。另外还发现一种与一般反射波性质不同的波,其视速度特大,视速度随距离的变化不大,而且有较明显的终点;其吋距曲线与一般深界面反射波的时距曲线相交。根据它的特征可以判断地壳中存在具有速度梯度的高速夹层.求得的夹层参数为: 甘肃地区柴达木盆地东部覆盖层厚度 18.8公里 30.5公里覆盖层平均速度 5.5公里/秒 5.3公里/秒夹层厚度 6.0公里 3.2公里夹层速度 7.5-8.5公里/秒 7.5-8.0公里/秒夹层的上下界面均为强反射面,可以产生多次反射波。分別利用相邻两个反射波可以求得各层参数,并能避免射线折射的影响。甘肃地区和柴达木盆地东部的地壳厚度分別为51和52公里。地壳中有高速夹层的存在,可以更好地说明P~*速度分散的原因,而且也能够解释Lg波的传播机制。 相似文献
19.
Mariarosaria Manzo Yuri Fialko Francesco Casu Antonio Pepe Riccardo Lanari 《Pure and Applied Geophysics》2012,169(8):1463-1482
We investigate the capabilities and limitations of the Differential Interferometric Synthetic Aperture Radar (DInSAR) techniques, in particular of the Small BAseline Subset (SBAS) approach, to measure surface deformation in active seismogenetic areas. The DInSAR analysis of low-amplitude, long-wavelength deformation, such as that due to interseismic strain accumulation, is limited by intrinsic trade-offs between deformation signals and orbital uncertainties of SAR platforms in their contributions to the interferometric phases, the latter being typically well approximated by phase ramps. Such trade-offs can be substantially reduced by employing auxiliary measurements of the long-wavelength velocity field. We use continuous Global Positioning System (GPS) measurements from a properly distributed set of stations to perform a pre-filtering operation of the available DInSAR interferograms. In particular, the GPS measurements are used to estimate the secular velocity signal, approximated by a spatial ramp within the azimuth-range radar imaging plane; the phase ramps derived from the GPS data are then subtracted from the available set of DInSAR interferograms. This pre-filtering step allows us to compensate for the major component of the long-wavelength range change that, within the SBAS procedure, might be wrongly interpreted and filtered out as orbital phase ramps. With this correction, the final results are obtained by simply adding the pre-filtered long-wavelength deformation signal to the SBAS retrieved time series. The proposed approach has been applied to a set of ERS-1/2 SAR data acquired during the 1992–2006 time interval over a 200?×?200?km area around the Coachella Valley section of the San Andreas Fault in Southern California, USA. We present results of the comparison between the SBAS and the Line Of Sight (LOS)—projected GPS time series of the USGC/PBO network, as well as the mean LOS velocity fields derived using SBAS, GPS and stacking techniques. Our analysis demonstrates the effectiveness of the presented approach and provides a quantitative assessment of the accuracy of DInSAR measurements of interseismic deformation in a tectonically active area. 相似文献
20.
Despite the complexity of wave propagation in anisotropic media, reflection moveout on conventional common-midpoint (CMP) spreads is usually well described by the normal-moveout (NMO) velocity defined in the zero-offset limit. In their recent work, Grechka and Tsvankin showed that the azimuthal variation of NMO velocity around a fixed CMP location generally has an elliptical form (i.e. plotting the NMO velocity in each azimuthal direction produces an ellipse) and is determined by the spatial derivatives of the slowness vector evaluated at the CMP location. This formalism is used here to develop exact solutions for the NMO velocity in anisotropic media of arbitrary symmetry. For the model of a single homogeneous layer above a dipping reflector, we obtain an explicit NMO expression valid for all pure modes and any orientation of the CMP line with respect to the reflector strike. The contribution of anisotropy to NMO velocity is contained in the slowness components of the zero-offset ray (along with the derivatives of the vertical slowness with respect to the horizontal slownesses) — quantities that can be found in a straightforward way from the Christoffel equation. If the medium above a dipping reflector is horizontally stratified, the effective NMO velocity is determined through a Dix-type average of the matrices responsible for the ‘interval’ NMO ellipses in the individual layers. This generalized Dix equation provides an analytic basis for moveout inversion in vertically inhomogeneous, arbitrarily anisotropic media. For models with a throughgoing vertical symmetry plane (i.e. if the dip plane of the reflector coincides with a symmetry plane of the overburden), the semi-axes of the NMO ellipse are found by the more conventional rms averaging of the interval NMO velocities in the dip and strike directions. Modelling of normal moveout in general heterogeneous anisotropic media requires dynamic ray tracing of only one (zero-offset) ray. Remarkably, the expressions for geometrical spreading along the zero-offset ray contain all the components necessary to build the NMO ellipse. This method is orders of magnitude faster than multi-azimuth, multi-offset ray tracing and, therefore, can be used efficiently in traveltime inversion and in devising fast dip-moveout (DMO) processing algorithms for anisotropic media. This technique becomes especially efficient if the model consists of homogeneous layers or blocks separated by smooth interfaces. The high accuracy of our NMO expressions is illustrated by comparison with ray-traced reflection traveltimes in piecewise-homogeneous, azimuthally anisotropic models. We also apply the generalized Dix equation to field data collected over a fractured reservoir and show that P-wave moveout can be used to find the depth-dependent fracture orientation and to evaluate the magnitude of azimuthal anisotropy. 相似文献