低应变下变阻抗薄壁管桩动力响应频域解析解

管桩低应变完整性检测时,桩顶一点受到瞬态集中荷载的作用,其动力响应问题是一个三维波动问题。基于三维波动理论,建立了任意段变阻抗薄壁管桩动力响应的计算模型和波动方程,结合初边值条件,采用Laplace变换法求得了该波动方程的频域解析解,采用Fourier逆变换求得了时域响应。将计算结果与三维有限元结果进行了对比分析,解析解的计算结果和三维有限元结果较为接近,两者在入射波峰、缺陷反射峰和桩底反射峰处都较为吻合,两种方法位移响应曲线基本相同。给出了桩顶不同点的动力响应,并探讨了高频干扰问题。对变截面桩和变模量桩的动力响应特性进行了分析。     

基于能量变化率法自动拾取场地剪切波速

提出了一种提高单孔法剪切波速测量精度的新方法--能量变化率的自回归曲线法。首先把剪切波的时程曲线变换为能量变化率时程曲线;然后对能量变化率时程曲线进行长短平均处理,拾取各测点P波和S波的大致初至;最后提出采用一种二次方自回归模型对初至附近的能量变化率曲线进行二次方自回归处理,精确拾取出各测点P波和S波的精确到时。采用此方法、互相关函数法和人工拾取法对某场地的剪切波速进行了对比分析。分析结果表明：此方法相比互相关函数法,具有更好的噪声抑制能力,不仅能精确地自动拾取出各测点的S波的到时差,也能更准确地自动拾取出各测点的P波的到时差。以人工拾取结果为参考,此方法在实际测试中具有很高的准确率和稳定性。此方法丰富了场地剪切波速分析方法。基于此方法、互相关函数法和人工拾取法,设计了一套剪切波波速的测试系统,此系统能自动分析出各测点的剪切波速和形成完整的报告。     

侧装式弯曲元测量软黏土剪切波速的试验研究

判断剪切波到达时间并计算相应的剪切波速是弯曲元试验的关键问题之一。受到试验仪器差异和研究者波速判断主观性的影响,很难客观地、准确地获得土体的剪切波速。针对该问题,提出采用侧装式弯曲元测试系统测量剪切波传播时间和土体的剪切波速,利用上海典型的淤泥质黏土进行试验,分别采用初达波法、特征值法和互相关法计算土体的剪切波速。试验结果表明,（1）初达波法在信号判定过程主观性较大,土体剪切波速受发射信号频率的影响明显;（2）采用第二峰值点（特征点法）得到的试验结果波动性较小;（3）在满足相似性的前提下,互相关法在一定频率范围内（20～30 kHz）提高了确定剪切波速的客观性,降低了因试验者或激发频率的不同对试验结果产生较大影响的可能性。     

无线电磁波随钻测量系统姿态精度的影响因素分析

煤矿井下采用水力钻进方式进行碎软煤层瓦斯抽采时,容易出现塌孔、孔壁失稳,电磁波随钻测量系统适用于气体钻进,在碎软煤层瓦斯抽采中逐步得到应用。钻孔轨迹的准确性是影响碎软煤层瓦斯抽采效果的关键,电磁波随钻测量系统使用中,出现轨迹测量精度不够、误差大的现象。为解决这一问题,分析测量系统从设计到应用全过程中影响姿态精度的因素,列举因素产生的原因及解决方案,重点针对钻进现场出现的电磁波系统精度问题进行分析。通过现场采集数据、分析曲线趋势规律,确定造成误差大的原因为测量短节与外无磁钻杆不同轴,设计现场自校准方法和流程要求。提出查表补偿法和拟合函数法2种校准方式,对2种方法的原理、方法选择以及相关参数计算给出了说明。最后采用拟合函数法对实测数据进行了校准修正,修正后的姿态数据精度达到0.2°,解决了无线电磁波随钻测量系统在使用中的姿态精度不高问题,满足碎软煤层瓦斯抽采轨迹测量精度要求。      

用遗传算法进行瑞利波反演

瑞利波反演属于非线性最优化问题,已有的局部线性化方法(如阻尼最小二乘法)常使解估计陷入目标函数的局部极小值之中,且严重地依赖初始模型.另外,目前被广泛应用的一些简单的瑞利波反演方法也存在明显的缺陷.全局优化法-遗传算法大大放松了对初始模型选择的要求,且不易陷入局部最优解中.本文用已有的简单宜行的反演解释方法获取初始模型,从而确定模型参数的搜索范围,再用遗传算法反演得到最终的介质模型,效果非常理想.     

爆破荷载应力波在无限弹性介质中传播的特征线法解

双指数爆破荷载的应力时程关系是爆破工程的数值分析常用的动力输入。其在弹性岩石中传播衰减的特征线法解是工程爆破数值分析中弹性以及弹塑性分析的重要参照,也是动力学数值分析算法开发的重要高阶校准工具。应用统一弹性波的特征线法解求解源自圆形孔洞的双指数爆破荷载在理想介质中的传播。介绍了源自圆形孔洞的双指数爆破荷载在周围弹性介质传播过程中的径向应力、周向应力、位移以及速度波的特征线法解的具体过程,在MATLAB中进行了4种波的特征线法解的数值实施。对径向应力、周向应力、位移以及速度波的特征线法解的结果进行了多方面讨论。结果表明,特征线法是求解双曲型偏微分方程的一种有效方法,双指数爆破荷载在弹性岩石中传播衰减的特征线法解可为爆破工程数值分析以及动力学数值分析算法开发提供重要的支撑。     

Comparing the Gradual Deformation with the Probability Perturbation Method for Solving Inverse Problems

Inverse problems are ubiquitous in the Earth Sciences. Many such problems are ill-posed in the sense that multiple solutions can be found that match the data to be inverted. To impose restrictions on these solutions, a prior distribution of the model parameters is required. In a spatial context this prior model can be as simple as a Multi-Gaussian law with prior covariance matrix, or could come in the form of a complex training image describing the prior statistics of the model parameters. In this paper, two methods for generating inverse solutions constrained to such prior model are compared. The gradual deformation method treats the problem of finding inverse solution as an optimization problem. Using a perturbation mechanism, the gradual deformation method searches (optimizes) in the prior model space for those solutions that match the data to be inverted. The perturbation mechanism guarantees that the prior model statistics are honored. However, it is shown with a simple example that this perturbation method does not necessarily draw accurately samples from a given posterior distribution when the inverse problem is framed within a Bayesian context. On the other hand, the probability perturbation method approaches the inverse problem as a data integration problem. This method explicitly deals with the problem of combining prior probabilities with pre-posterior probabilities derived from the data. It is shown that the sampling properties of the probability perturbation method approach the accuracy of well-known Markov chain Monte Carlo samplers such as the rejection sampler. The paper uses simple examples to illustrate the clear differences between these two methods     

Optimal difference schemes for Maxwell’s equations in solving forward problems of electromagnetic soundings

In this paper, the solution of two-dimensional Maxwell’s equations is considered using the Laguerre transform. Optimal parameters of the difference schemes for the equations are obtained and presented. Numerical values of these optimal parameters are given. Second-order difference schemes with the optimal parameters provide an accuracy of the solution of the equations that is comparable to the accuracy of the solution using fourth-order schemes. It is shown that, when using the Laguerre transform, the number of optimal parameters can be reduced compared to the Fourier transform. This reduction leads to a simplification of the difference scheme and a reduction in the amount of computation, i.e., to efficiency of the algorithm.     

Fast automatic solution of the inverse resistivity problem

The paper presents a fast automatic approach to solve the inverse resistivity problem, assisted by optimization, which is a non-linear model-fitting technique. The selected inverse problems are ill-posed and the inverse solution is defined by ‘best fit’ in the sense of least-squares. Formulations are presented in a systematic manner for Newton’s method, least squares method and Marquardt’s modification (ridge regression) method based on local linearization of non-linear problem. The convergence of least-squares method and Marquardt’s method, to provide a robust solution, are first tested on a theoretical model and effectiveness of Marquardt’s method is demonstrated, and then two-field apparent resistivity curves from Banda district, India are interpreted and discussed.     

横观各向同性层状地基动应力响应的求解与分析

动力响应问题的求解对于地基在外荷载作用下引起的弹性波动问题研究有重要的意义。本文提出了一种求解横观各向同性层状地基在施加时间简谐荷载作用下任意点的应力响应的算法。此算法利用傅里叶变换将广义平面应变问题频率-空间域的动力方程转化到频率-波数域内,结合对偶变量的引入,利用高精度的精细积分算法对状态方程进行求解,在得到频率-波数域内的位移响应的基础上,利用傅里叶逆变换得到任意点的动应力响应。简谐荷载不仅可以施加在地基表面,而且可以施加在地基内部。对比算例验证了本文算法的准确性,同时对地基各向异性特性、激励频率和阻尼比对动应力响应的影响进行了参数分析,为工程实际提供可靠的数值依据。     

A Frequency Matching Method: Solving Inverse Problems by Use of Geologically Realistic Prior Information

The frequency matching method defines a closed form expression for a complex prior that quantifies the higher order statistics of a proposed solution model to an inverse problem. While existing solution methods to inverse problems are capable of sampling the solution space while taking into account arbitrarily complex a priori information defined by sample algorithms, it is not possible to directly compute the maximum a posteriori model, as the prior probability of a solution model cannot be expressed. We demonstrate how the frequency matching method enables us to compute the maximum a posteriori solution model to an inverse problem by using a priori information based on multiple point statistics learned from training images. We demonstrate the applicability of the suggested method on a synthetic tomographic crosshole inverse problem.     

3D dynamic response of a transversely isotropic multilayered medium subjected to a moving load

The dynamic problem of a transversely isotropic multilayered medium is reducible to quasi‐static problem by introducing a moving system that travels synchronously with the load. Based on the governing equations in the moving system, the ordinary differential equations in the Fourier transformed domain are deduced. An extended precise integration method is adopted to solve the ordinary differential equations, and the solution in the physical domain is recovered by the inverse Fourier transform. Numerical examples are performed to verify the accuracy of the presented method and to analyze the influence of material properties and the load characteristic.     

Crustal structure of the Barents Sea from seismic data

In 1976, the Institute of Physics of the Earth and the Institute of Oceanology, the U.S.S.R. Academy of Sciences, carried out deep seismic soundings in the Barents Sea along a profile 700 km long northeast of Murmansk. A system of reversed and overlapping traveltime curves from 200 to 400 km long has been obtained. The wave correlation was effected by several independent approaches, which identified on the records the refracted and reflected waves from boundaries in the Earth's crust and the upper mantle. Different methods were applied for the solution of the inverse problem: the isochrone method, the intercept-time method, and the iteration method.The use of these different methods gives an indication of the general applicability of the interpretation and of the most reliable elements in the seismic model.All the interpretations and representations of the section positively establish an essentially horizontal inhomogeneity of the Earth's crust in the Barents Sea. On the whole the structure is similar to that of deep sedimentary basins of the East European platform. The thickness of the sedimentary layer varies from 8 to 17 km, the average crustal thickness is about 35–40 km; the velocities in the upper part of the consolidated crust are 5.8–6.4 km/s; in the lower crust they are 6.8–7.0 km/s and higher.     

The application of an innovative inverse model for understanding and predicting landslide movements (Salazie cirque landslides,Reunion Island)

The prediction of landslide movement acceleration is a complex problem, among others identified for deep-seated landslides, and represents a crucial step for risk assessment. Within the scope of this problem, the objective of this paper is to explore a modelling method that enables the study of landslide function and facilitates displacement predictions based on a limited data set. An inverse modelling approach is proposed for predicting the temporal evolution of landslide movement based on rainfall and displacement velocities. Initially, the hydrogeology of the studied landslides was conceptualised based on correlative analyses. Subsequently, we applied an inverse model with a Gaussian-exponential transfer function to reproduce the displacements. This method was tested on the Grand Ilet (GI) and Mare-à-Poule-d’Eau (HB) landslides on Reunion Island in the Indian Ocean. We show that the behaviour of landslides can be modelled by inverse models with a bimodal transfer function using a Gaussian-exponential impulse response. The cumulative displacements over 7 years of modelling (2 years of calibration period for GI, and 4 years for HB) were reproduced with an RMSE above 0.9. The characteristics of the bimodal transfer function are directly related to the hydrogeological functioning demonstrated by the correlative analyses: the rapid reaction of a landslide can be associated with the effect of a preferential flow path on groundwater level variations. Thus, this study shows that the inverse model using a Gaussian-exponential transfer function is a powerful tool for predicting deep-seated landslide movements and for studying how they function. Beyond modelling displacements, our approach effectively demonstrates its ability to contribute relevant data for conceptualising the sliding mechanisms and hydrogeology of landslides.     

扩散波的时空反演与洪水实时预报技术

以扩散波方程描述天然河道中的洪水波运动规律。将数学物理反问题理论和离散反演算法与河道流量演算相结合提出了扩散波实时预报的方法。该法的特点是在求解流量场Ｑ（ｘ,ｔ）的同时反演计算扩散波波速Ｃ（ｘ,ｔ）和扩散系数Ｄ（ｘ,ｔ）,根据不断监测的新信息系列,直接利用原偏微分方程进行参数的实时校正和预报过程实时修正。     

瑞利波法检测地基压实度的探讨

在利用瑞利波法测试地基土的压实度时,由于瑞利波速度与压实度之间是一种非线性关系,因此,必须根据瑞利波速度采用非线性反演的方法来获得地基土的压实度。过去一般是采用回归分析的方法,现拟采用人工神经网络的方法,即根据瑞利波速度与神经网络工具反演获得压实度。根据神经网络预测结果与灌砂法测试结果的对比可知,神经网络预测结果的平均绝对误差为1.188 6%,平均相对误差为1.221 4%,其反演结果的精度比回归分析法更高。     

三维黏弹性人工边界地震波动输入方法研究

对三维黏弹性人工边界给出了一种实用的地震波动输入方法。用等效边界力法进行地震波动输入时,把入射地震波假设为竖直向上入射的平面波,使施加在人工边界上的总荷载可以由输入波位移和速度的关系式完全表达,使地震动输入更容易在有限元计算程序中实现。解决了三维黏弹性人工边界采用球面波进行地震波动输入会出现尚待确定的未知项,不易实现地震波动的输入的困难。数值算例表明,该地震波动输入方法是十分有效的。     

Modelling techniques for volumetric reconstruction of earth structures

Visualisation of seismic and tomographic results is a crucial point to properly understand the models provided by seismic methods. We consider several geostatistical methods (inverse distance weighting, point kriging and mathematical wavelets) to map surface wave tomography in a sparsely sampled study area, and to compare their accuracy and efficiency with proper raypath methodologies (inversion and projection onto convex sets). A large set of synthetic data is used to estimate seismic velocities before application to real data. The contour maps of prediction errors indicate that spatial prediction and inversion perform similarly.     

基于L—BFGS算法的全波形反演Q值方法研究

估计地层品质因子Q对描述地下构造分布和油气预测都有着重要的意义。考虑到地震波在介质中传播时的黏滞吸收作用,笔者选择2D黏滞性声波方程全波形反演,将观测波场与正演模拟计算得到的波场构建一个目标函数,引入L--BFGS算法反演出地层品质因子。将该方法应用于异常体模型和Marmousi模型测试,结果均表明反演的模型与理论模型的相对误差较小,计算精度高,反演效果好。     

基于最佳小波基的地震面波插值方法

在利用实际地震数据中的面波反演近地表横波速度的过程中,若道间距较大、空间采样率不足,则会产生空间假频现象,从而降低频率速度谱的信噪比,影响频散曲线提取的精度以及反演效果,因此需要针对面波进行插值处理。文中提出了一种基于最佳小波基的地震面波插值方法,通过理论分析和实验误差对比在地震数据处理常用的众多小波基中选出适用于插值处理的最佳小波基bior6.8,提高了插值精度。针对面波同向轴为线性且斜率较大的特点,文中首先采用线性动校正的方法对面波进行拉平处理,再进行小波变换插值,最后进行反线性动校正恢复面波。通过对理论模型与实际资料进行插值处理验证了本文方法的有效性,插值后的面波记录波形恢复较好,显著提高了频率速度谱的信噪比,有效解决了面波数据空间采样率不足引起的假频问题。