INMOD—TWO DIMENSIONAL INVERSE MODELING ALGORITHM BASED ON RAY THEORY*

Two dimensional inverse modeling, a process to be applied after standard processing and interpretation, uses interfaces picked by the user. These interfaces are transformed into an approximate subsurface model. The subsurface model is represented by curved interfaces and interval velocities. The interfaces have to be unique functions of the line coordinate. Otherwise they may be arbitrarily curved and may begin or terminate anywhere along the section, e.g., at faults, pinchouts, salt domes and the like. Interval velocities may vary laterally along the section. The inverse modeling algorithm then modifies the model until traveltimes calculated from this model match the traveltimes observed as closely as possible in a least squares sense. The traveltimes corresponding to the model are obtained through ray tracing taking exact account of refraction. The traveltimes observed are the arrival times of single impulses before stacking contributing to the interfaces. These traveltimes are provided by ANAKON, a continuous interface analysis system. The comparison of INMOD results with those of well measurements and those of classical interval velocity computation from seismic data shows the accuracy of the method. Deviations of INMOD derived interface depths are within 2% of well data.     

A discontinuous Galerkin method for seismic wave propagation in coupled elastic and poroelastic media

Numerical simulation in coupled elastic and poroelastic media is important in oil and gas exploration. However, the interface between elastic and poroelastic media is a challenge to handle. In order to deal with the coupled model, the first-order velocity–stress wave equations are used to unify the elastic and poroelastic wave equations. In addition, an arbitrary high-order discontinuous Galerkin method is used to simulate the wave propagation in coupled elastic–poroelastic media, which achieves same order accuracy in time and space domain simultaneously. The interfaces between the two media are explicitly tackled by the Godunov numerical flux. The proposed forms of numerical flux can be used efficiently and conveniently to simulate the wave propagation at the interfaces of the coupled model and handle the absorbing boundary conditions properly. Numerical results on coupled elastic–poroelastic media with straight and curved interfaces are compared with those from a software that is based on finite element method and the interfaces are handled by boundary conditions, demonstrating the feasibility of the proposed scheme in dealing with coupled elastic–poroelastic media. In addition, the proposed method is used to simulate a more complex coupled model. The numerical results show that the proposed method is feasible to simulate the wave propagation in such a media and is easy to implement.     

Seismic wavefront evolution of multiply reflected, transmitted, and converted phases in 2D/3D triangular cell model

Conventionally grid-cell-based schemes for simulating seismic wavefront propagation, such as the finite difference eikonal equation solver or the shortest-path method, usually adopt regular grids or cells in model parameterization to obtaining (but not exclusively) first arrivals only. However, later arrivals, which often result from the velocity interfaces or discontinuities, can be prevalent and significant (sometimes of large amplitude), making them potentially important additional information to use in practical applications. To better approximate the data acquisition geometry and the irregular interfaces, we exploit a triangular shortest-path method (TSPM; that is to use triangular cells in model parameterization) to simulate seismic wavefront evolution, comprising any kind of transmissions, reflections (or refractions), mode conversions, and combinations thereof, in 2D/3D heterogeneous media. A practical procedure, known as the multistage scheme, was incorporated with the TSPM to propagate seismic wavefronts from one interface (or subsurface in 3D) to the next. By treating each separate layer that the wavefront enters as an independent computational domain, one can simulate wavefront transmission and mode conversion by reinitializing it in the adjacent layer and wavefront reflection (and/or conversion) by reinitializing it in the incident layer. To further improve the computational accuracy, a second level of forward star scheme, previously defined in the grid model, is introduced into the triangular cell model. Several examples (including the Marmousi model) are used to demonstrate the viability and versatility of the multistage TSPM in heterogeneous media, even in the presence of high-velocity contrasts involving interfaces of relatively high curvature. With the introduction of the second level of forward star scheme, the total numbers of nodes are reduced sufficiently, and hereafter the computer memory is less required. Most important is that the computing accuracy with the second-level forward star scheme can be largely improved over those with the first level of forward star scheme applied in the multistage TSPM scheme.     

基于网格走时计算的弯曲界面下菲涅尔体研究

为了研究弯曲界面曲率变化对分辨率的影响,首先推导了垂直入射下来自弯曲界面的反射波和透射波界面菲涅尔带近似的解析公式,证明了公式中曲率为零恰好对应已经被推导的平界面菲涅尔带的解析公式,然后给出了利用网格走时计算方法计算弯曲界面下反射波和透射波菲涅尔体的数值实现策略,这一实现策略同时保证了网格走时计算的精度和菲涅尔体计算的精度,最后对比了不同弯曲界面（不同曲率）下的菲涅尔体相对于平界面（曲率为零）下菲涅尔体的变化.研究结果表明,界面下高速时,向斜弯曲造成菲涅尔体在界面附近变宽,使得分辨率降低;背斜弯曲造成菲涅尔体在界面附近变窄,使得分辨率提高.并且向斜弯曲对分辨率的影响程度要明显大于背斜弯曲.而界面下低速时,结论正好相反.     

Equivalent series system to model a multiple friction pendulum system with numerous sliding interfaces for seismic analyses

Current structural analysis software programs offer few if any applicable device-specifi c hysteresis rules or nonlinear elements to simulate the precise mechanical behavior of a multiple friction pendulum system(MFPS) with numerous sliding interfaces.Based on the concept of subsystems,an equivalent series system that adopts existing nonlinear elements with parameters systematically calculated and mathematically proven through rigorous derivations is proposed.The aim is to simulate the characteristics of sliding motions for an MFPS isolation system with numerous concave sliding interfaces without prior knowledge of detailed information on the mobilized forces at various sliding stages.An MFPS with numerous concave sliding interfaces and one articulated or rigid slider located between these interfaces is divided into two subsystems: the fi rst represents the concave sliding interfaces above the slider,and the second represents those below the slider.The equivalent series system for the entire system is then obtained by connecting those for each subsystem in series.The equivalent series system is validated by comparing numerical results for an MFPS with four sliding interfaces obtained from the proposed method with those from a previous study by Fenz and Constantinou.Furthermore,these numerical results demonstrate that an MFPS isolator with numerous concave sliding interfaces,which may have any number of sliding interfaces,is a good isolation device to protect structures from earthquake damage through appropriate designs with controllable mechanisms.     

TIME MIGRATION—SOME RAY THEORETICAL ASPECTS*

Using an elementary theory of migration one can consider a reflecting horizon as a continuum of scattering centres for seismic waves. Reflections arising at interfaces can thus be looked upon as the sum of energy scattered by interface points. The energy from one point is distributed among signals upon its reflection time surface. This surface is usually well approximated by a hyperboloid in the vicinity of its apex. Migration aims at focusing the scattered energy of each depth point into an image point upon the reflection time surface. To ensure a complete migration the image must be vertical above the depth point. This is difficult to achieve for subsurface interfaces which fall below laterally in-homogeneous velocity media. Migration is hence frequently performed for these interfaces as well by the Kirchhoff summation method which systematically sums signals into the apex of the approximation hyperboloid even though the Kirchhoff integral is in this case not strictly valid. For a multilayered subsurface isovelocity layer model with interfaces of a generally curved nature this can only provide a complete migration for the uppermost interface. Still there are various advantages gained by having a process which sums signals consistently into the minimum of the reflection time surface. The position of the time surface minimum is the place where a ray from the depth point emerges vertically to the surface. The Kirchhoff migration, if applied to media with laterally inhomogeneous velocity, must necessarily be followed by a further time-to-depth migration if the true depth structure is to be recovered. Primary normal reflections and their respective migrated reflections have a complementary relationship to each other. Normal reflections relate to rays normal to the reflector and migrated reflections relate to rays normal to the free surface. Ray modeling is performed to indicate a new approach for simulating seismic reflections. Commonly occuring situations are investigated from which lessons can be learned which are of immediate value for those concerned with interpreting time migrated reflections. The concept of the ‘image ray’ is introduced.     

界面二次源波前扩展法全局最小走时射线追踪技术

以Moser方法为代表的最短路径射线追踪算法可以快速稳定地获得整个追踪区域的全局最小走时和路径,但它存在两个缺陷：一是射线大多由折线呈锯齿状相连,长度和位置偏离真实射线路径;二是在低变速区容易出现射线路径多值现象．本文提出的界面二次源波前扩展法全局最小走时射线追踪技术（以下简称界面源法）旨在解决上述两个问题．不同于Moser方法,界面源法只在物性分界面上设置子波源点,子波出射射线可以到达任何不穿越物性界面而直接到达的空间点和界面离散点,在均匀块体内或层内地震波以精确的射线路径传播．显然,界面源法的子波出射方向数远远大于传统方法,算法的追踪误差主要由界面离散引起的,因此,界面源法很好地解决了Moser法存在的问题,大大提高了追踪的精度．同时,由于界面源法的子波源点数远远小于Moser法,因而效率也很高．模型实算证实了该算法的高效性．     

三维分块倾斜界面的反演及其应用

介绍了利用反射波走时反演介质层速度和包含直立断层的三维界面的计算方法．对各层界面利用多个倾斜或平界面方程来描述．给出了数值计算实例．结果表明，反演解与真模型很接近，说明计算方法是有效的．利用该方法处理了唐山地震区的ＰｍＰ反射波资料，获得了该区域莫霍界面的三维分块形态．唐山附近莫霍界面错断与该区域１９７６年唐山地震及一系列余震的发生有密切的联系．     

无网格局部Petrov-Galerkin法大地电磁场二维正演模拟

有限差分法和有限单元法在大地电磁场数值模拟中已经得到了广泛的应用,但其数值结果的精度在很大程度上依赖于网格的离散程度.当模拟起伏地形、弯曲界面等复杂地电模型大地电磁场响应时,常常需要花费大量的时间以便得到较合理的离散网格.无网格局部Petrov-Galerkin法(MLPG)不同于有限差分法和有限元法,其形函数和权函数脱离了网格的束缚.本文详细推导了二维大地电磁场边值问题的弱式形式,并将其离散为局部积分域内的表达形式.通过模拟二维海洋地电模型大地电磁场响应,并与结构网格有限元结果进行对比,验证了本文算法和程序的正确性及精度.设计了一个含有弯曲界面的二维地电模型,讨论了不同离散网格对MLPG无网格法模拟结果的影响,并与结构有限元法结果进行了比较,结果表明MLPG无网格法模拟结果受离散网格影响较小.最后利用MLPG无网格法计算了两个海洋起伏地形模型的大地电磁响应,讨论了海底起伏地形对大地电磁响应的影响.     

基于Hinge损失函数的垂向全变差约束全波形反演

全波形反演可以为叠前深度偏移成像提供更高精度的速度模型,但该方法具有较强的非线性,对初始速度模型的依赖性较强,尤其是在实际应用中,地质条件复杂多变,速度变化不连续,增加了反演非线性程度,常常使反演陷入局部极小值,影响反演的精度.全变差约束在图像去噪领域应用广泛,属于非光滑约束,在去噪过程中能有效的保留图像的不连续界面和边缘信息.本文提出基于Hinge损失函数的垂向全变差约束全波形反演方法,在全变差约束的基础上,利用Hinge损失函数控制模型的更新方向,并使用原-对偶混合梯度算法进行求解,给出这一优化问题的迭代格式,有效提高了对地下不连续界面的重构精度,同时也降低反演对初始速度模型的依赖程度.数值算例证明：与常规全波形反演方法相比,基于全变差约束的全波形反演方法可以有效的重构速度模型中的不连续界面,尤其对高速体边缘的重构效果更明显,但该方法对初始速度模型的依赖性仍然较强;基于Hinge损失函数的垂向全变差约束全波形反演方法降低了对初始速度模型的依赖程度,可以从一个较差的初始模型通过循环迭代的方式最终得到同样精确的速度模型,较好的重构了高速体边缘和不连续界面.     

Estimation of Salt Water Upconing Using a Steady‐State Solution for Partial Completion of a Pumped Well

A new steady‐state analytical solution to the two‐dimensional radial‐flow equation was developed for drawdown (head) conditions in an aquifer with constant transmissivity, no‐flow conditions at the top and bottom, constant head conditions at a known radial distance, and a partially completed pumping well. The solution was evaluated for accuracy by comparison to numerical simulations using MODFLOW. The solution was then used to estimate the rise of the salt water‐fresh water interface (upconing) that occurs under a pumping well, and to calculate the critical pumping rate at which the interface becomes unstable, allowing salt water to enter the pumping well. The analysis of salt water‐fresh water interface rise assumed no significant effect on upconing by recharge; this assumption was tested and supported using results from a new steady‐state analytical solution developed for recharge under two‐dimensional radial‐flow conditions. The upconing analysis results were evaluated for accuracy by comparison to those from numerical simulations using SEAWAT for salt water‐fresh water interface positions under mild pumping conditions. The results from the equation were also compared with those of a published numerical sharp‐interface model applied to a case on Cape Cod, Massachusetts. This comparison indicates that estimating the interface rise and maximum allowable pumping rate using the analytical method will likely be less conservative than the maximum allowable pumping rate and maximum stable interface rise from a numerical sharp‐interface model.     

台湾海峡大容量气枪震源海陆联测初探

本文利用在我国台湾海峡采用大容量气枪震源开展海陆联测获得的广角地震测线HX9, 采用二维射线追踪法反演得到了HX9剖面的地壳二维速度结构和地壳界面形态, 初步探明了福建—台湾海峡海陆过渡带的深部构造． 结果表明: HX9剖面的地壳内存在两个速度间断面, 即C界面和莫霍面, 其中: C界面为上、 下地壳的分界面, 是一个小的速度不连续面, 速度变化值达0.08—0.16 km/s; 而地壳底部的莫霍面则有较大的速度反差, 变化值达1.02—1.29 km/s, 莫霍面上、 下的速度分别为6.75—6.97 km/s和8.00—8.07 km/s． 沿剖面的地壳界面形态总体起伏不大, 陆域上、 下地壳的厚度和界面变化趋势均相似, 从陆域到海域呈微倾斜变化趋势, 表现为减薄陆壳的特征． 莫霍面陆域埋深约为31.6 km, 向福建东南沿海逐渐减薄至27.4 km左右．      

Slopes of an airborne electromagnetic resistivity model interpolated jointly with borehole data for 3D geological modelling

We investigate a novel way to introduce resistivity models deriving from airborne electromagnetic surveys into regional geological modelling. Standard geometrical geological modelling can be strengthened using geophysical data. Here, we propose to extract information contained in a resistivity model in the form of local slopes that constrain the modelling of geological interfaces. The proposed method is illustrated on an airborne electromagnetic survey conducted in the region of Courtenay in France. First, a resistivity contrast corresponding to the clay/chalk interface was interpreted confronting the electromagnetic soundings to boreholes. Slopes were then sampled on this geophysical model and jointly interpolated with the clay/chalk interface documented in boreholes using an implicit 3D potential‐field method. In order to evaluate this new joint geophysical–geological model, its accuracy was compared with that of both pure geological and pure geophysical models for various borehole configurations. The proposed joint modelling yields the most accurate clay/chalk interface whatever the number and location of boreholes taken into account for modelling and validation. Compared with standard geological modelling, the approach introduces in between boreholes geometrical information derived from geophysical results. Compared with conventional resistivity interpretation of the geophysical model, it reduces drift effects and honours the boreholes. The method therefore improves what is commonly obtained with geological or geophysical data separately, making it very attractive for robust 3D geological modelling of the subsurface.     

折射波地震记录叠加成像方法研究

多次覆盖折射波地震勘探是用来追踪反射波成像质量较差地区的地质构造或用于追踪深层基底形态及研究基岩面的一种勘探方法.基于折射波理论，用折射地震记录中的折射波对地下折射界面进行成像，应用共深度折射面元叠加成像理论方法，给出用共深度折射面元叠加成像技术对地下折射界面进行成像的速度分析与动校正计算方法，提出一种适用于折射波发育探区的共深度折射点叠加成像方法，最后以模型和实际例子说明方法的正确性和实用性.     

Dynamic stiffness of foundation embedded in layered halfspace based on wave propagation in cones

An Erratum has been published for this article in Earthquake Engineering & Structural Dynamics 33(6) 2004, 793. The dynamic stiffness of a foundation embedded in a multiple‐layered halfspace is calculated postulating one‐dimensional wave propagation in cone segments. In this strength‐of‐materials approach the sectional property of the cone segment increases in the direction of wave propagation. Reflections and refractions with waves propagating in corresponding cone segments occur at layer interfaces. Compared to rigorous procedures the novel method based on cone segments is easy to apply, provides conceptual clarity and physical insight in the wave propagation mechanisms. This method postulating one‐dimensional wave propagation in cone segments with reflections and refractions at layer interfaces is evaluated, calculating the dynamic stiffness of a foundation embedded in a multiple‐layered halfspace. For sites resting on a flexible halfspace and fixed at the base, engineering accuracy (deviation of ±20%) is achieved for all degrees of freedom with a vast parameter variation. The behaviour below the cut‐off frequency in an undamped site fixed at its base is also reliably predicted. The accuracy is, in general, better than for the method based on cone frustums, which can lead to negative damping. Copyright © 2003 John Wiley & Sons, Ltd.     

基于面向对象的无监督分类的遥感影像自动分类方法

为了实现无任何先验知识的高分辨率遥感数据的自动分类,并进一步提高自动分类精度和效率,提出了一种基于面向对象的无监督分类方法(Object Oriented Unsupervised Classification).具体步骤如下:首先对遥感影像进行分割,得到一系列空间上相邻、同质性较好的分割单元,然后对分割单元进行特征提取,得到分割单元的对象特征(光谱特征、纹理特征等多特征信息),进而对分割单元进行基于对象特征马氏距离聚类.最后,通过分类后处理(类别合并、错分类别调整等)得到最终的分类结果.通过实验表明:本文提出的方法不仅能够利用影像中更多的特征信息进行聚类而且还可以有效地减少聚类对象的个数,从而使自动分类的精度和效率都得到较大的提升.     

Ray path of head waves with irregular interfaces

Head waves are usually considered to be the refracted waves propagating along flat interfaces with an underlying higher velocity. However, the path that the rays travel along in media with irregular interfaces is not clear. Here we study the problem by simulation using a new approach of the spectral-element method with some overlapped elements (SEMO) that can accurately evaluate waves traveling along an irregular interface. Consequently, the head waves are separated from interface waves by a time window. Thus, their energy and arrival time changes can be analyzed independently. These analyses demonstrate that, contrary to the case for head waves propagating along a flat interface, there are two mechanisms for head waves traveling along an irregular interface: a refraction mechanism and transmission mechanism. That is, the head waves may be refracted waves propagating along the interface or transmitted waves induced by the waves propagating in the higher-velocity media. Such knowledge will be helpful in constructing a more accurate inversion method, such as head wave travel-time tomography, and in obtaining a more accurate model of subsurface structure which is very important for understanding the formation mechanism of some special areas, such as the Tibetan Plateau.     

Wavefield features of teleseismic receiver function in laterally inhomogeneous media

IntroductionSince1980(s,theteleseismicreceiverfunctionhasbeenbroadlyappliedtoexploringthecrustalanduppermantlestructure.Thatthismethoddrawssomanyattentionsisnotonlybecauseitscheapercostandhighverticalresolution,butalsobecauseitcanbeusedforexploringthelateralvariationofthecrustalstructure.IntheUSnationalresearchprogramofthecontinentaldynamicsmuchemphasiswasgiventothereceiverfunctionmethod(Phinney,1989).Uptonow,the1-Dreceiverfunctioninversiontechniquehasbecomesophisticatedandmanypracticalresul…     

界面和速度反射联合成像──理论与方法

依据波逆行原理重新推导了由地震波反射走时资料反演界面深度的关系式──走时对界面偏导数关系，它不仅适用于反射波，也适用于透射波．还给出了任意多个复杂界面情况下走时对界面偏导数关系的离散形式．另外，正交算子投影法被推广用来解决速度与界面的同时成像问题．数值模拟的结果表明，本文的方法是有效的．