层状半无限空间中波动问题的数值模拟

本文对波动方程首先进行富里叶—贝赛尔积分变换,在波数k域内构成(z,t)的有限差分隐格式进行迭代,由此计算出纵向非均匀的层状模型的合成地震图。对含有低速层和高速薄层的几种模型做了对比计算,通过时间场与空间场的波动分析,揭示了几种主要震相的传播与形成过程。计算结果表明,无论高速层的厚薄如何。反射波始终很强烈。但初至首波在薄层构造中不清晰,一种属转换型的续至薄层首波震相值得注意;低速层的顶界面难以形成能量较强的上行波,因此在推断低速层埋深上存在不确定性。     

Interpretation of first arrival travel times in seismic refraction work

The necessary condition for the seismic refraction method to succeed is that the refracted first arrivals from each layer in a multilayered earth system should be detected on a seismogram as first arrivals, and this is possible only when velocities of all underlying layers are successively greater. The usual procedure to interpret the refraction travel times is to fit such a data set with several intersecting straight lines by employing a visual technique which may lead to errors of subjective judgment, as the velocity model depends on the selection of various line segments through the data. To remove the visual fit we propose here a layer stripping method based on minimum intercept time, apparent velocity, rms residual, and maximum data points by least-squares fitting to yield several intersecting straight lines. Once data are segmented out, the conventional equations can be used to determine the velocity structure.     

Use of traveltime skips in refraction analysis to delineate velocity inversion1

First arrival refraction data does not normally provide any indication of the velocity inversion problem. However, under certain favourable circumstances, when the low-velocity layer (LVL) is considerably thicker than the overlying higher-velocity layer (HVL), the velocity inversion can be seen in the form of a traveltime skip. Model Studies show that in such cases the length of the HVL traveltime branch can be used to determine the thickness of the HVL and the magnitude of the traveltime skip in order to determine the thickness of the LVL. This is also applicable in the case of field data.     

来自海底高速层径向波的理论地震图研究

本文利用各向异性反射率技术计算理论地震图,提出海底高速薄层会产生沿高速层水平传播的波（简称径向波）,这种波在水层中作为P波,在固液界面激发下行横波,该均匀横波以临界角入射高速薄层,在层内作为超临界角的非均匀横波水平传播,再以临界角转换为上行传播的均匀横波,最终在固液界面上行透射转换为水层中P波.高速薄层传播的径向波不同于界面折射波,也不同于具有频散的面波和通道波.理论地震图的研究表明,径向波具有线性时距,能与海底强反射具有同等振幅水平;径向波有其振幅、时距位置和斜率这些观测记录参数,分别对应高速层的厚度、深度和近似的横波速度;径向波可以克服折射波解释中遇到的振幅强弱和高速层速度等困难.径向波可作为探测海底高速薄层的有力工具,对于研究高速层屏蔽、海底反射类型的多样性和相应的资料处理解释有重要意义.     

地震波在垂向不均匀介质中传播问题的某些探讨

本文计算了含有高速夹层介质中首波的理论地震图。通过分析得到,当高速夹层薄到一定程度时,就会产生干涉型首波,从而从一个侧面证明了射线理论的局限性。通过对地震波反射—折射系数能量守恒关系的分析,探讨了反射—折射系数大于1的可能性。最后,介绍了一种计算垂向不均匀介质中拉梅问题理论地震图的数值方法——有限差分法。     

HIDDEN LAYER PROBLEM IN SEISMIC REFRACTION WORK*

The hidden layer problem in seismic refraction work has been studied for three velocity configurations – the intermediate layer having (a) lower, (b) intermediate and (c) higher velocity than the underlying and overlying beds. It has been shown that conventional methods fail to locate the presence of the intermediate layer for the cases (a) and (c) and lead to errors in calculating the depth to the bedrock. For the case (b), it is possible to interpret the first arrival travel time analytically as an alternative to Green's graphical approach. It has been suggested that the hidden layer may be detected in all the three cases if converted S waves are also recorded in the seismogram.     

The study and analysis of floating datum selection for rugged terrain

We analyze the characteristics of different floating datums for static corrections and discuss the methods for determining them. The effect of different floating datum corrections was studied using theoretical model experiments, resulting in the conclusion that the velocity obtained after the floating datum correction with the minimum static correction errors depends on the velocity of the layer below the low velocity layer （LVL） lower boundary and is not related to topographic relief and LVL structure. For the real data processing case, wave equation numerical model experiments were conducted which resulted in a new method for calculating objective functions based on the waveform and modifications to the calculation equation for minimum static correction errors to make the method suitable for real data static correction processing using inhomogeneous velocity models with lower velocity boundary relief. Real data processing results demonstrate the method＇s superiority.     

UK 1-D regional velocity models by analysis of variance of P-wave travel times from local earthquakes

A method is presented for deriving 1-D velocity depth models from earthquake bulletin data. The models can be used as initial models for more advanced modelling techniques such as tomographic inversion. The method is useful when there is little or no refraction and long-range reflection survey data. The bulletin travel times are subjected to an analysis of variance, where they are separated into source, distance, and receiving station terms. The distance terms describe the variation of travel time with distance, and the associated trend lines allow 1-D velocity models for the crustal layers to be determined. The velocity models provide an average crustal model for the region derived from local data. This does not include superficial layers which are necessarily poorly determined. Earthquake bulletin P-wave data from propagation paths across three different regions of the UK are employed to illustrate the use of the technique.     

复杂地层构造的地震模拟

复杂地层构造的地震模拟,是地震勘探理论的重要问题。本文提出了一个模拟系统:用有限元素表示复杂地层构造,在此基础上应用射线轨迹法计算二维合成记录,从而得到复杂地层构造的理论剖面。这个系统可以用来模拟构造和岩性,为解释人员提供理论依据。 作者研制了适用于任意复杂地层构造计算的通用程序,并用以计算了某测线的一批模型,所得合成剖面由电视加以显示,最后对结果作了简单的分析讨论。     

Modelling of local velocity anomalies: a cookbook

The determination of small-scale velocity anomalies (from tens to a few hundreds of metres) is a major problem in seismic exploration. The impact of such anomalies on a structural interpretation can be dramatic and conventional techniques such as tomographic inversion or migration velocity analysis are powerless to resolve the ambiguity between structural and velocity origins of anomalies. We propose an alternative approach based on stochastic modelling of numerous anomalies until a set of models is found which can explain the real data. This technique attempts to include as much a priori geological information as possible. It aims at providing the interpreter with a set of velocity anomalies which could possibly be responsible for the structural response. The interpreter can then choose one or several preferred models and pursue a more sophisticated analysis. The class of retained models are all equivalent in terms of data and therefore represent the uncertainty in the model space. The procedure emulates the real processing sequence using a simplified scheme. Essentially, the technique consists of five steps: 1 Interpretation of a structural anomaly in terms of a velocity anomaly with its possible variations in terms of position, size and amplitude. 2 Drawing a model by choosing the parameters of the anomaly within the acceptable range. 3 Modelling the traveltimes in this model and producing the imaging of the reflected interface. 4 Comparing the synthetic data with the real data and keeping the model if it lies within the data uncertainty range. 5 Iterate from step 2. In order to avoid the high computational cost inherent in using statistical determinations, simplistic assumptions have been made: ? The anomaly is embedded in a homogeneous medium: we assume that the refraction and the time shift due to the anomaly have a first-order effect compared with ray bending in the intermediate layers. ? We model only the zero-offset rays and therefore we restrict ourselves to structural problems. ? We simulate time migration and so address only models of limited structural complexity. These approximations are justified in a synthetic model which includes strong lateral velocity variations, by comparing the result of a full processing sequence (prestack modelling, stack and depth migration) with the simplified processing. This model is then used in a blind test on the inversion scheme.     

SEISMIC REFRACTION AND SCREENING BY THIN HIGH-VELOCITY LAYERS *

The screening effect of thin, relatively shallow high-velocity layers often presents considerable problems in seismic exploration. Such layers prevent the greater part of the seismic energy from travelling to greater depths and introduce additional refraction arrivals, confusing the seismogram still further. In order to investigate both the screening and refractive properties of high-velocity layers, scale-model experiments have been made over a wide range of layer-thickness/ wavelength ratios (0.05 < d/λ < 2) for suitably chosen material contrasts. The results may be summarised as follows. Refraction arrivals from thin layers in the field may be recognised by their relatively rapid amplitude decay. Furthermore, the “echeloning”-effect observed for refraction first arrivals may be due to the presence of a (thin) layered structure. Since the apparent refraction velocity varies with d/λ when d/λ < 1, differences between vertical well-log velocities and velocities observed along the surface may be expected, making time/depth conversion using surface velocity data inaccurate. Transmission of elastic energy may be expected, if anywhere, only near the shotpoint, at small geophone offset, and for relatively thin screens (d/λ < 0.1). The transmitted signal shape is then independent of the layer thickness. This transmitted energy may be registered either in a reflection set-up with geophones near the shotpoint, or in long-distance refraction work. Three possibilities are offered for overcoming the screening effect of thin high-velocity layers: Use longer-wavelength signals Apply short-spread reflection shooting Apply long-distance refraction shooting The experimental results obtained in scale-model arrangements of such set-ups confirm the potentialities of these methods.     

Characteristics of head wave in multi-layered half-space

Introduction Head wave is one of the main phases of local seismic arrivals, and it is important in the study of the crustal structure and the physical characteristics of the transition-zone between the crust and the mantle. So far, the kinetic characteristics of head wave such as arrival time have been widely used, while the dynamic characteristics of head wave like amplitude were usually ignored al-though it includes more information of the structure. In this article, we shall investigate the…     

基于三重震相拟合的华南地区上地幔P波与S波速度结构

利用中国数字测震台网（CDSN）记录到的台湾地区两个地震事件6°~30°震中距范围的三重震相波形资料,基于观测与理论波形拟合法,获到华南地区上地幔P波和S波的最佳波形拟合速度模型及其V_P/V_S比值.与AK135模型相比,华南地区410 km深度上方存在明显低速层：S波低速区厚度约为70 km,速度降为2%~5%;而P波低速区厚度为70~230 km,速度降为5%~6%.另外,410 km间断面整体表现为一个梯度层,厚度约为10~40 km,V_P跃增量为4.0%~5.4%,而V_S跃增量为2.6%~11.7%.研究区内,低速层的V_P和V_S异常值大小和410 km间断面速度跃变量由北向南逐步减小.结合以往的接收函数和地震层析成像结果,华南地区410 km间断面上方的低速区可能与太平洋俯冲板块脱水有关.     

垂向非均匀介质中首波特征分析

利用合成理论地震图方法研究了存在高速层或低速层的地壳模型及壳-幔过渡带模型中首波等震相的动力学特征，指出首波的特征对于高速层的结构变化比较敏感．当高速层厚度与特征波长相比较小时，地震波的衍射现象明显，这种情况下高速层不能屏蔽在其下面一层的上界面传播的首波，且该首波震相的强度随高速层厚度或速度的增加而递减；当高速层厚度与特征波长相当时，高速层底面的反射波震相与首波震相到时接近，会因互相干涉而减弱；对于低速层，首波震相强度较弱且随低速层速度的减小而递减；在壳-幔间断处引入一定厚度和速度变化范围的过渡带，可以得到更加明显的视首波震相，强度随过渡带厚度或速度变化范围的增加而增大．      

Finite-Difference Modeling and Dispersion Analysis of High-Frequency Love Waves for Near-Surface Applications

Love-wave propagation has been a topic of interest to crustal, earthquake, and engineering seismologists for many years because it is independent of Poisson’s ratio and more sensitive to shear (S)-wave velocity changes and layer thickness changes than are Rayleigh waves. It is well known that Love-wave generation requires the existence of a low S-wave velocity layer in a multilayered earth model. In order to study numerically the propagation of Love waves in a layered earth model and dispersion characteristics for near-surface applications, we simulate high-frequency (>5 Hz) Love waves by the staggered-grid finite-difference (FD) method. The air–earth boundary (the shear stress above the free surface) is treated using the stress-imaging technique. We use a two-layer model to demonstrate the accuracy of the staggered-grid modeling scheme. We also simulate four-layer models including a low-velocity layer (LVL) or a high-velocity layer (HVL) to analyze dispersive energy characteristics for near-surface applications. Results demonstrate that: (1) the staggered-grid FD code and stress-imaging technique are suitable for treating the free-surface boundary conditions for Love-wave modeling, (2) Love-wave inversion should be treated with extra care when a LVL exists because of a lack of LVL information in dispersions aggravating uncertainties in the inversion procedure, and (3) energy of high modes in a low-frequency range is very weak, so that it is difficult to estimate the cutoff frequency accurately, and “mode-crossing” occurs between the second higher and third higher modes when a HVL exists.     

Seismogram Analysis of Indonesian Earthquakes at DAV Observation Station

The S-wave velocity across the earth structure under Indonesia for Indonesia earthquakes has been investigated through seismogram analysis, simultaneously in the time domain and three Cartesian components. The data were recorded at DAV observational station, the Philippines. The main data set is the seismogram comparison between the measured and synthetic seismogram, instead of travel time data, as commonly used in other seismological research. The synthetic seismogram is calculated using the GEMINI method, which is equivalent to Mode Summation. The above seismogram comparison shows that the global earth mantle of PREMAN gives a deviating synthetic seismogram and has earlier arrival times than those of the measurement. The gradient of β_h in the upper mantle layers is altered into a positive, rather than negative slope as stated in the PREMAN model, and negative corrections are imposed to the zero order of the polynomials coefficients in all earth mantle layers. The excellent fitting, as well as travel time or waveform, is obtained from the surface waves of Love and Rayleigh, surface wave to the S and SS mantle waves as well as the core reflected waves. This result expresses that part of the earth mantle, due to a collision between India and Asia tectonic released zones, has a negative anomaly in S-wave velocity and vertical anisotropy in all of the earth mantle layers.     

Dispersion Energy Analysis of Rayleigh and Love Waves in the Presence of Low-Velocity Layers in Near-Surface Seismic Surveys

High-frequency surface-wave analysis methods have been effectively and widely used to determine near-surface shear (S) wave velocity. To image the dispersion energy and identify different dispersive modes of surface waves accurately is one of key steps of using surface-wave methods. We analyzed the dispersion energy characteristics of Rayleigh and Love waves in near-surface layered models based on numerical simulations. It has been found that if there is a low-velocity layer (LVL) in the half-space, the dispersion energy of Rayleigh or Love waves is discontinuous and ‘‘jumping’’ appears from the fundamental mode to higher modes on dispersive images. We introduce the guided waves generated in an LVL (LVL-guided waves, a trapped wave mode) to clarify the complexity of the dispersion energy. We confirm the LVL-guided waves by analyzing the snapshots of SH and P–SV wavefield and comparing the dispersive energy with theoretical values of phase velocities. Results demonstrate that LVL-guided waves possess energy on dispersive images, which can interfere with the normal dispersion energy of Rayleigh or Love waves. Each mode of LVL-guided waves having lack of energy at the free surface in some high frequency range causes the discontinuity of dispersive energy on dispersive images, which is because shorter wavelengths (generally with lower phase velocities and higher frequencies) of LVL-guided waves cannot penetrate to the free surface. If the S wave velocity of the LVL is higher than that of the surface layer, the energy of LVL-guided waves only contaminates higher mode energy of surface waves and there is no interlacement with the fundamental mode of surface waves, while if the S wave velocity of the LVL is lower than that of the surface layer, the energy of LVL-guided waves may interlace with the fundamental mode of surface waves. Both of the interlacements with the fundamental mode or higher mode energy may cause misidentification for the dispersion curves of surface waves.     

ON THE POSSIBILITY OF SEISMIC EXPLORATION USING SURFACE TORQUE SOURCE AND RELATED TOPICS*

In this study we derive expressions for particle displacement or particle velocity anywhere inside a stratified earth and at its surface due to horizontal torque source located in the top layer. Equivalently, invoking Green's function reciprocity theorem, the solution applies also to the case of a surface or subsurface source when the resulting displacement or velocity is measured within the top layer. In order to evaluate the closed-form analytical solution economically and accurately it is advisable to introduce inelastic attenuation. Causal inelastic attenuation also lends the necessary realism to the computed seismic trace. To provide proof that the analytical solution is indeed correct and applicable to the multilayer case, a thick uniform overburden was assumed to consist of many thin layers. The correctness of the computed particle velocity response can be very simply verified by inspection. The computed response can also serve as a check on other less accurate methods of producing synthetic seismograms, such as the techniques of finite differences, finite elements, and various sophisticated ray-tracing techniques. It is not difficult to construct horizontal surface torque source. It appears that such source is well suited for seismic exploration in areas with a high-velocity surface layer. A realistic source function is analyzed in detail and normalized displacement response evaluated at different incidence angles in the near and the far fields. In an effort to distinguish the features of an SH torque seismogram from a pressure seismogram two models with identical layerings and layer parameters have been set up. As expected the torque seismogram is very different from the compressional seismogram. One desirable feature of a torque seismogram is the fast decay of multiples. Exact synthetic seismograms have many uses; some of them, such as the study of complex interference phenomena, phase change at wide angle reflection, channeling effects, dispersion (geometrical and material), absolute gain, and inelastic attenuation, can be carried out accurately and effortlessly. They can also be used to improve basic processing techniques such as deconvolution and velocity analysis. The numerical evaluation of the analytical solution of the wave equation as described in this paper has a long history. Most of the work leading to this paper was carried out by one of us (M. J. K.) in the years 1957 to 1968 at the Geophysical Research Corporation. However, the full testing of the various computer codes was carried out only very recently at the Phillips Petroleum Company.     

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.     

WAVEFRONT DIVERGENCE,MULTIPLES, AND CONVERTED WAVES IN SYNTHETIC SEISMOGRAMS*

Synthetic seismograms can be very useful in aiding understanding of wave propagation through models of real media, verification of geologic models derived from interpretation of field seismic data, and understanding the nature and complexity of wave phenomena. If meaningful results are to be obtained from synthetic seismograms, the method of their computation must, in general, include three-dimensional geometrical spreading of wavefronts associated with highly concentrated (i.e., point) sources. The method should also adequately represent the seismic response of solid-layered media by including enough primaries, multiples, and converted phases to accurately approximate the total wavefield. In addition to these features, it is also very helpful, although not always essential, if the method of seismogram computation provides for explicit identification of wave type and ray path for each arrival. Various seismograms, computed via asymptotic ray theory and an automatic ray generation scheme, are presented for a highly simplified North Sea velocity structure. This is done to illustrate the importance of the above features and to demonstrate the inadequacy of the plane-wave synthesis method of seismogram computation for point sources and the limitations of acoustic models of solid-layered media.