Large-offset approximation to seismic reflection traveltimes

Conventional approximations of reflection traveltimes assume a small offset-to-depth ratio, and their accuracy decreases with increasing offset-to-depth ratio. Hence, they are not suitable for velocity analysis and stacking of long-offset reflection seismic data. Assuming that the offset is large, rather than small, we present a new traveltime approximation which is exact at infinite offset and has a decreasing accuracy with decreasing offset-to-depth ratio. This approximation has the form of a series containing powers of the offset from 1 to −∞. It is particularly accurate in the presence of a thin high-velocity layer above the reflector, i.e. in a situation where the accuracy of the Taner and Koehler series is poor. This new series can be used to gain insight into the velocity information contained in reflection traveltimes at large offsets, and possibly to improve velocity analysis and stacking of long-offset reflection seismic data.     

Internal structure of an alpine rock glacier based on crosshole georadar traveltimes and amplitudes

Rapid melting of permafrost in many alpine areas has increased the probability of catastrophic rock slides. In an attempt to provide critical structural information needed for the design and implementation of suitable mitigation procedures, we have acquired low frequency (22 MHz) cross‐hole radar data from within a fast‐moving rock glacier, an important form of alpine permafrost. Since the ice, rock and pockets of water and air found in the underground of high alpine areas have very different dielectric permittivities and electrical conductivities, the radar method was well‐suited for investigating the structure and state of the rock glacier. Our interpretation of the radar velocities and attenuations was constrained by geomorphological observations, borehole lithological logs and the results of a surface seismic survey. The radar data revealed the existence of a discontinuous 7–11 m thick ice‐rich zone distinguished by high velocities (0.14–0.17 m/ns) and low attenuations (0.04–0.09 m^?1) and a thin underlying ice‐free zone characterized by moderate velocities (0.11–0.12 m/ns) and low attenuations (0.04–0.09 m^?1). Beneath these two zones, we observed a prominent band of high velocities (0.14–0.17 m/ns) and moderately high attenuations (0.10–0.20 m^?1) associated with unconsolidated glacial sediments and numerous large air‐filled voids, which in the past were probably filled with ice. At greater depths, the variably dry to water‐saturated sediments were represented by generally lower velocities (0.08–0.10 m/ns) and higher attenuations (0.16–0.24 m^?1). The bedrock surface was represented by an abrupt ～0.03 m/ns velocity increase. We speculate that the disappearance of ice, both laterally and with depth, occurred during the past one to two decades.     

基于初至波走时层析成像的Tikhonov正则化与梯度优化算法

初至波走时层析成像是利用地震初至波走时和其传播的射线路径来反演地下介质速度的技术.该问题本质上是一个不适定问题,需要使用正则化方法并辅之以适当的最优化技巧.本文从数值优化的角度介绍了初至波走时层析成像的反演原理,建立了Tikhonov正则化层析成像反演模型并提出求解极小化问题的加权修正步长的梯度下降算法.该方法可以从速度模型的可行域中迭代找到一个最优解.数值试验表明,该方法是可行和有应用前景的.     

Efficient and accurate edge‐preserving smoothing for 3D hexagonally sampled seismic data

The automatic detection of geological features such as faults and channels is a challenging problem in today's seismic exploration industry. Edge detection filters are generally applied to locate features. It is desirable to reduce noise in the data before edge detection. The application of smoothing or low‐pass filters results in noise suppression, but this causes edge blurring as well. Edge‐preserving smoothing is a technique that results in simultaneous edge preservation and noise suppression. Until now, edge‐preserving smoothing has been carried out on rectangular sampled seismic data. In this paper, an attempt has been made to detect edges by applying edge‐preserving smoothing as a pre‐processing step in the hexagonally sampled seismic‐data spatial domain. A hexagonal approach is an efficient method of sampling and has greater symmetry than a rectangular approach. Here, spiral architecture has been employed to handle the hexagonally sampled seismic data. A comparison of edge‐preserving smoothing on both rectangular and hexagonally sampled seismic data is carried out. The data used were provided by Saudi Aramco. It is shown that hexagonal processing results in well‐defined edges with fewer computations.     

Velocity imaging by tau–p transformation of refracted seismic traveltimes

We present a new method for producing a ‘brute’ velocity image rapidly and automatically from traveltimes picked from densely sampled refraction data. The procedure involves imaging by data transformation from the time–offset domain into the tau–p (intercept–slope) domain, and does not include conventional modelling steps. Differences in apparent velocity and tau along reciprocal paths in the up- and downdip directions allow the estimation of the true velocity and geometrical position of the ray turning points. The tau–velocity–turningpoint (τ–ν–x) map distributes phases automatically on the basis of geometry and velocity to give a two-dimensional representation of subsurface structure. This map may be converted simply to depth and two-way-time images. Such images have potential for direct geological interpretation, for use as a starting model for seismic inversion, for superimposition on to conventional reflection images, or for input into prestack depth migration and other processing routines.     

A new direction for shallow refraction seismology: integrating amplitudes and traveltimes with the refraction convolution section

The refraction convolution section (RCS) is a new method for imaging shallow seismic refraction data. It is a simple and efficient approach to full‐trace processing which generates a time cross‐section similar to the familiar reflection cross‐section. The RCS advances the interpretation of shallow seismic refraction data through the inclusion of time structure and amplitudes within a single presentation. The RCS is generated by the convolution of forward and reverse shot records. The convolution operation effectively adds the first‐arrival traveltimes of each pair of forward and reverse traces and produces a measure of the depth to the refracting interface in units of time which is equivalent to the time‐depth function of the generalized reciprocal method (GRM). Convolution also multiplies the amplitudes of first‐arrival signals. To a good approximation, this operation compensates for the large effects of geometrical spreading, with the result that the convolved amplitude is essentially proportional to the square of the head coefficient. The signal‐to‐noise (S/N) ratios of the RCS show much less variation than those on the original shot records. The head coefficient is approximately proportional to the ratio of the specific acoustic impedances in the upper layer and in the refractor. The convolved amplitudes or the equivalent shot amplitude products can be useful in resolving ambiguities in the determination of wave speeds. The RCS can also include a separation between each pair of forward and reverse traces in order to accommodate the offset distance in a manner similar to the XY spacing of the GRM. The use of finite XY values improves the resolution of lateral variations in both amplitudes and time‐depths. The use of amplitudes with 3D data effectively improves the spatial resolution of wave speeds by almost an order of magnitude. Amplitudes provide a measure of refractor wave speeds at each detector, whereas the analysis of traveltimes provides a measure over several detectors, commonly a minimum of six. The ratio of amplitudes obtained with different shot azimuths provides a detailed qualitative measure of azimuthal anisotropy and, in turn, of rock fabric. The RCS facilitates the stacking of refraction data in a manner similar to the common‐midpoint methods of reflection seismology. It can significantly improve S/N ratios.Most of the data processing with the RCS, as with the GRM, is carried out in the time domain, rather than in the depth domain. This is a significant advantage because the realities of undetected layers, incomplete sampling of the detected layers and inappropriate sampling in the horizontal rather than the vertical direction result in traveltime data that are neither a complete, an accurate nor a representative portrayal of the wave‐speed stratification. The RCS facilitates the advancement of shallow refraction seismology through the application of current seismic reflection acquisition, processing and interpretation technology.     

地震几何属性的快速算法实现

地震几何属性被广泛用于提取地震数据中的几何结构特征,从而辅助解释相关的地质沉积和构造过程.本文提出基于多种递归滤波和构造导向滤波的地震几何属性快速算法,能显著提高地震相干和体曲率的计算效率和分辨率.递归滤波的计算效率远高于传统的加权求和计算,且其计算成本与平均窗口的大小无关;同时,利用高维滤波的可分离特性可以将其分解为多个一维滤波来进一步提升计算效率并有利于多线程并行运算.此外,使用构造导向滤波实现相干计算,可以有效地消除倾斜构造对结果的影响而无需传统方法中耗时的插值运算.三维实际地震数据的应用结果表明,本文提出的快速算法能将传统的相干和曲率属性计算速度提高10~30倍且对断层的刻画更加完整和连续.

     

The effect of inertial coupling on seismic reflection amplitudes

A problem of reflection and transmission of elastic waves at a plane interface between a uniform elastic solid half-space and a porous elastic half-space containing two immiscible fluids is investigated. The theory developed by Lo, Sposito and Majer for porous media containing two immiscible fluids is employed to find out the reflection and transmission coefficients. The incident wave is assumed to propagate through the uniform elastic half-space and two cases are considered. In the first case, a beam of plane longitudinal wave is assumed to be incident and in the second case, a beam of transverse wave is assumed to be incident at the interface. By taking granite as impervious elastic medium and columbia fine sandy loam containing air-water mixture as porous medium, reflection and transmission coefficients are obtained. By neglecting the inertial coupling coefficients, these coefficients are reduced to those obtained by Tomar and Arora using the theory of Tuncay and Corapcioglu. It is found that the inertial coupling parameters significantly affect the phase speeds and the amplitude ratios of the transmitted waves.     

Effect of station conditions on amplitudes and periods of seismic waves

Summary Station corrections for Prhonice, relating to Praha, were determined for body and surface waves using observations of Kirnos seismographs. The time stability of the station corrections was investigated and the possible causes of observed instabilities were discussed. A systematic difference in periods recorded at the stations was found.Dedicated to Academician Alois Zátopek on His 65th Birthday     

A new scheme for fast calculation of seismic traveltimes and ray paths in heterogeneous media

IntroductionBoth traveltimes and ray paths are vital information for seismic theoretical research and practice such as stack migration, traveltime inverse, calculation of covering time and so on (Xu, et al,1992). At present, they are obtained usually by either ray shooting (Liu, el al, 1986) or finite difference solution of the eikonal equation (Vidale, 1988; Zhang, et al, 1996). The ray shootingmethod can be understood and programmed easily. However, it is difficult for the method to treatc…     

非均匀介质中地震波走时与射线路径快速计算技术

介绍了一种基于惠更斯原理和费马原理求取地震波走时及其反射波射线路径的新方法 .该方法具有原理简单、易于实现、能适应较为复杂地质模型以及易于将其推广到各向异性介质等优点 .为了克服基本算法速度较慢的缺陷 ,提出了一种地震波走时和反射波射线路径计算的改进方法 .在保证精度的条件下 ,该改进算法的计算速度显著提高 .     

Dependence of amplitudes of seismic body waves on the distance

Резюме Нзменение амплитуд объемных волн с расстоянием было изучено на основании б аемлетрясений, регистрированных 30 сейсмическими станциями в эпицентральных расстояниях<30°. Из рисунков видно, что амплитуды продолных и поперечных волн меняются в изучаемых расстояниях подобным образом, но минимум и максимум кривой (A ^*, Δ) для волнSH подвинуты к ббльшим эпицентральным расстояниям чем в случае воумPH.

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Address: Boční II, Praha 13-Spořilov.     

针对复杂地形的三种地震波走时算法及对比

复杂地形条件下地震波走时算法对于研究复杂地形地区的成像问题有着重要的意义.为了得到精度高且适应于复杂地形的走时算法,首先提出阶梯网格迎风差分法.然后将该方法与不等距网格有限差分法和混合网格线性插值法进行对比研究,得出如下结论:混合网格线性插值法的计算精度最高,但其计算效率最低;阶梯网格迎风差分法的计算精度最低,但其计算效率最高;不等距网格有限差分法的计算精度和计算效率均居中;而究竟选取哪种算法作为给定复杂地形模型的地震波走时算法,应该综合考虑地形的特点、所研究问题对计算精度及计算效率的要求等因素.最后通过一个计算实例验证了三种算法在面对复杂地形、近地表及地下复杂介质等复杂地质条件时均有很好的适应性和稳定性.     

Mechanical hysteresis in rocks at low strain amplitudes and seismic frequencies

A sensitive capacitance displacement transducer has been used to record hysteresis loops in the stress-strain diagrams of laboratory samples of granite, basalt, sandstone and concrete subjected to cyclic axial strains with amplitudes of order 10^?5 and periods of 10–300 sec. The ends of the loops are always cusped, whether the load cycle is sinusoidal or not, and at low strain amplitudes the loop shape becomes symmetrical and appears to be independent of amplitude. Thermal relaxation influences the observed loop shapes, so that the strain cycles represent a compromise between adiabatic and isothermal compressions. However, this does not affect the conclusion that stress-strain loops are always cusped. This observation does not appear to be consistent with linear theories of damping of acoustic and seismic waves, which indicate elliptical loops.     

The influence of sea water velocity variation on seismic traveltimes, ray paths, and amplitude

The main factors affecting seismic exploration is the propagation velocity of seismic waves in the medium. In the past, during marine seismic data processing, the propagation velocity of sea water was generally taken as a constant 1500 m/s. However, for deep water exploration, the sound velocity varies with the season, time, location, water depth, ocean currents, and etc.. It also results in a layered velocity distribution, so there is a difference of seismic traveltime, ray paths, and amplitude, which affect the migration imaging results if sea water propagation velocity is still taken as constant for the propagation wavefield. In this paper, we will start from an empirical equation of seismic wave velocity in seawater with changes of temperature, salinity, and depth, consider the variation of their values, build a seawater velocity model, and quantitatively analyze the impact of seawater velocity variation on seismic traveltime, ray paths, and amplitude in the seawater velocity model.     

Dependence of seismic wave amplitudes on the size of shot-hole explosions

Summary The paper presents relations experimentally determined between seismic wave amplitudes and the charge size in the immediate vicinity of the shotpoint ( 800 m), on the one hand, and at a more distant station ( 22.5 km), on the other hand. Whereas close to the shotpoint the amplitudes observed sometimes display a considerably degree of scatter, as well as a change in character of the P-wave record due mainly to the change in position of the holes in the area of the shotpoint, this effect was not observed at the more distant station. Since the charge size was changed in the course of the measurements, the observed amplitudes will be reduced to a unified charge size of Q=1,200 kg, according to Eq. (8), in which the exponent n has the following values: n_Pg=0.77, n_Sg=0.92 and n_Lm=1.51. The values of the exponent n for P-waves are very close to the values given in [4–9].     

Fast accurate computation of shelf waves for arbitrary depth profiles

A simple fast and straightforward, accurate numerical method is proposed for calculating barotropic non-divergent continental shelf waves, above general shelf profiles. The problem is reduced to a linear eigenvalue problem for the along-stream wavenumber k, that can be solved directly with exponential accuracy, using any standard linear eigenvalue package.     

Second-order interpolation of later-arrival traveltimes

The performance of a 3D prestack migration of the Kirchhoff type can be significantly enhanced if the computation of the required stacking surface is replaced by an efficient and accurate method for the interpolation of diffraction traveltimes. Thus, input traveltimes need only be computed and stored on coarse grids, leading to considerable savings in CPU time and computer storage. However, interpolation methods based on a local approximation of the traveltime functions fail in the presence of triplications of the wavefront or later arrivals. This paper suggests a strategy to overcome this problem by employing the coefficients of a hyperbolic traveltime expansion to locate triplications and correct for the resulting errors in the interpolated traveltime tables of first and later arrivals.     

Parallel computation of seismic analysis of high arch dam

Parallel computation programs are developed for three-dimensional meso-mechanics analysis of fully-graded dam concrete and seismic response analysis of high arch dams （ADs）, based on the Parallel Finite Element Program Generator （PFEPG）. The computational algorithms of the numerical simulation of the meso-structure of concrete specimens were studied. Taking into account damage evolution, static preload, strain rate effect, and the heterogeneity of the meso-structure of dam concrete, the fracture processes of damage evolution and configuration of the cracks can be directly simulated. In the seismic response analysis of ADs, all the following factors are involved, such as the nonlinear contact due to the opening and slipping of the contraction joints, energy dispersion of the far-field foundation, dynamic interactions of the dam-foundation- reservoir system, and the combining effects of seismic action with all static loads. The correctness, reliability and efficiency of the two parallel computational programs are verified with practical illustrations.