改进的模拟退火－单纯形综合反演方法

实际中的大量地球物理反演是一个多参数、非线性优化问题,所采用的目标函数,即度量由参数化的理论模型得出的预测值与观测值的吻合程度,往往具有多个局部极值．针对这类问题,本文综合全局反演方法具有的全域搜索能力强、局部方法收敛速度快和“均匀设计”布点效率高的特点,提出了模拟退火－单纯性综合反演方法,并通过一维声波非线性反演验证了这种综合方法的搜索能力和效率．     

改进的模拟退火－单纯形综合反演方法

实际中的大量地球物理反演是一个多参数、非线性优化问题,所采用的目标函数,即度量由参数化的理论模型得出的预测值与观测值的吻合程度,往往具有多个局部极值．针对这类问题,本文综合全局反演方法具有的全域搜索能力强、局部方法收敛速度快和“均匀设计”布点效率高的特点,提出了模拟退火－单纯性综合反演方法,并通过一维声波非线性反演验证了这种综合方法的搜索能力和效率．     

2D多尺度非线性地震速度成像

将遗传算法和单纯形算法相结合,得到了一种高效、健全的2D混合地震走时反演方法.把速度场划分为不同的空间尺度,定义网格节点上的速度作为待反演参数,采用双三次样条函数模型参数化,正问题采用有限差分走时计算方法,反问题采用多尺度混合反演方法.首先在较大的空间尺度内反演,然后减小空间尺度,将大尺度的反演结果作为次一级尺度反问题的初始模型,再进行混合反演,如此类推逐次逼近全局最优解.一个低速度异常体的数值模拟试验和抗走时扰动试验表明该方法是有效和健全的.我们将该方法应用到青藏高原东北缘阿尼玛卿缝合带东段上部地壳速度结构研究中,并与前人的成果进行了对比.     

布谷鸟马尔科夫链蒙特卡洛混合高斯地质统计学随机反演

地质统计学随机反演可以获得比常规反演更高分辨率的结果,目前已成为储层高分辨率预测的主流方法.地下不同岩相储层参数存在明显差异,本文在地质统计学反演框架下构建了岩相和储层参数同步反演目标函数,实现不同岩相条件下储层参数分布精细描述.在求解该高维数据多参数同步反演问题时,本文将可以动态调节搜索步长的布谷鸟算法与马尔科夫链蒙特卡洛方法融合,采用多条马尔科夫链进行Levy飞行产生新解的策略扩大解的空间范围,通过适应度最佳选择输出最优解实现全局优化迭代,有效提升了反演方法的稳定性和全局最优性,避免了传统马尔科夫链蒙特卡洛方法因抽样随机性而陷入局部最优的问题.通过含噪声模型和实际数据分析验证了本文方法的有效性.     

2D多尺度混合优化地球物理反演方法及其应用(英文)

局部优化和全局优化方法广泛应用到地球物理反演,但是两者各有其优缺点。将两类方法结合起来可以取长补短。将退火遗传算法（SAGA）和单纯形算法相结合,得到了一种高效、健全的2D非线性混合地震走时反演方法。首先,利用SAGA进行大范围的全局搜索,然后由单纯形方法进行快速局部搜索。为了降低层析成像的多解性,我们采用了多尺度逐次逼近的技巧。把速度场划分为不同的空间尺度,定义网格节点上的速度作为待反演参数,采用双三次样条函数模型参数化,正问题采用有限差分走时计算方法,反问题采用多尺度混合反演方法。一个低速度异常体的数值模拟试验和抗走时扰动试验表明该方法是有效和健全的。我们将该方法应用到青藏高原东北缘阿尼玛卿rlet,Meyer,Marr,缝合带东段上部地壳速度结构研究中。数字模型试验和实际资料的应用表明了方法的有效性和健全性。     

小生境遗传算法求解多峰问题在反演中应用

基于反演问题的不确定性和目标函数的多峰性，引入改进的小生境遗传算法，求解出目标函数的若干个局部峰（或全局峰），然后利用先验知识，判定得到满意解，并利用褶积模型进行层速度反演，通过理论速度与反演速度的比较，验证了进行多峰优化的有效性。     

瞬变电磁测深资料的ABC算法反演研究

目前瞬变电磁测深资料的反演基本局限于一维,且多数是基于最小二乘法,实际上是将非线性问题做线性化处理,再利用迭代的方法逐步逼近最优解,所以在一定程度上会丢失许多细节信息,同时极度依赖初始模型,易陷入局部最优解,而非全局最优解.为提高瞬变电磁测深法的反演解释精度,本文以瞬变电磁测深的一维正演理论为基础,同时针对野外实测资料的特点,建立非线性反演问题的目标函数,考虑到现有非线性反演算法存在的易陷入局部优化和过学习等问题,首次引入了一种当前优化领域的十分新颖且性能优良的智能优化算法——ABC(人工蜂群)算法,来求解反演问题.ABC算法对求解多极值非线性问题优势明显,它不需要了解待求解问题特殊信息,只需要对问题进行优劣的比较,通过单独人工蜂的局部寻优的行为,最终将全局最优值突显出来,具有很快的收敛速度.通过在Matlab平台下对算法参数的详细试算研究,最终确定了一套最佳反演参数,并以二、三、四层的地电模型为例进行了验证.在野外实测资料的反演解释中,经过与实地钻孔资料及其他反演方法的对比分析,表明利用ABC算法建立的瞬变电磁测深一维反演系统具有明显的理论优势和实用价值.     

用一种混杂的全局搜索算法测定震源参数

混杂的全局最优化算法是一种模拟退火法和下坡的单纯形法相结合的方法，该法用来反演远震体波求解震源参数，在时间域对震源时间函数加约束，反演双力偶参数而不是反演矩张互通主考虑多重震源导致非线性和多重模型问题，在这些问题中，目标函数包括许多局部极小值。     

二维波动方程参数反演的微分进化算法

利用微分进化算法进行二维波动方程参数反演的研究.微分进化算法属于全局最优化算法,具有鲁棒性强、收敛速度快、计算精度高的优点.把参数反演问题转化为非线性优化问题,通过保持在解空间不同区域中各个点的搜索,以最大的概率找到问题的全局最优解.同时还进行了数值模拟,结果令人满意.     

基于局部优化粒子群算法的背景噪声反演

从背景噪声中提取瑞雷波频散曲线并通过反演获得地下横波速度结构已被广泛应用于大尺度的地下结构探测和小尺度的工程勘探中.基于频散函数的反演目标函数可以有效解决多阶模频散曲线联合反演的模式误判问题,然而其广泛分布的局部极值导致更为严重的多解性,在大范围的参数搜索空间下很难获得最优解,需要搭配全局搜索性能强的优化算法.本文提出局部优化粒子群算法(PSOG),通过粒子迭代过程中引入局部优化方法提高种群多样性,避免陷入局部极值并加快收敛速度.为验证新算法的有效性,结合基于久期函数的目标函数对理论合成数据进行反演,结果表明,局部优化粒子群算法比传统算法的稳定性与准确性都有显著提高.处理了上海苏州河地区的背景噪声数据,成功地对古河道切割造成的软弱层进行成像.PSOG算法与新型反演目标函数的结合在背景噪声勘探的工程应用上具有巨大潜力.     

大地电磁阻尼粒子群优化反演法研究

粒子群优化算法（PSO）是模仿鸟群寻找食物的社会行为的一种全局最优化算法,在多维空间函数寻优、动态目标寻优等方面有着收敛速度快、解质量高且需要设置的参数较少等优点.本文在研究常规粒子群优化算法的基础上,对常规的粒子群算法进行了改进,提出了一种新的惯性权重ω参数振荡递减策略,加快了PSO算法的收敛速度,构造的新算法称为阻尼粒子群优化算法.在MATLAB 6.5 编程环境中对阻尼PSO算法进行了数值实验,并对大地电磁测深的理论模型和实测数据进行了反演试算,结果表明,阻尼PSO算法不依赖于初始模型、能够搜索到全局极值,不易陷入局部极值,是一种快速有效的地球物理反演方法.     

二阶精度广义非线性全局最优的偏移速度反演方法(英文)

如何快速、精确地利用叠前深度偏移进行偏移速度分析是勘探地震学的一项重要研究内容,针对该问题,本文提出一种二阶精度广义非线性全局最优的偏移速度反演方法。我们将首先去掉速度模型修正量与成象深度差呈线性关系的假设,推导出具有二阶精度的速度模型修正量计算公式,使每一次迭代得到的速度模型尽可能地接近实际模型;然后采用广义非线性反演方法反演获得对所有道集的全局最优的速度模型修正量,不仅极大地加快了收敛速度,而且反演过程中陷入局部极小的可能性也减小了。理论模型和Marmousi模型的处理结果表明:本方法精度高、处理速度快,提高了偏移速度分析方法的实用性和对复杂构造成像的准确性。     

Solutions of the inherent problem of the equivalence in direct current resistivity and electromagnetic methods through global optimization and joint inversion by successive refinement of model space

The problem of equivalence in direct current (DC) resistivity and electromagnetic methods for a thin resistive and conducting layer is well‐known. Attempts have been made in the past to resolve this problem through joint inversion. However, equivalence still remains an unresolved problem. In the present study, an effort is made to reduce non‐uniqueness due to equivalence using global optimization and joint inversion by successive refinement of the model space. A number of solutions derived for DC resistivity data using very fast simulated annealing global inversion that fits the observations equally well, follow the equivalence principle and show a definite trend. For a thin conductive layer, the quotient between resistivity and thickness is constant, while for a resistive one, the product between these magnitudes is constant. Three approaches to obtain very fast simulated annealing solutions are tested. In the first one, layer resistivities and thicknesses are optimized in a linear domain. In the second, layer resistivities are optimized in the logarithmic domain and thicknesses in the linear domain. Lastly, both layer resistivities and thicknesses are optimized in the logarithmic domain. Only model data from the mean models, corresponding to very fast simulated annealing solutions obtained for approach three, always fit the observations. The mean model defined by multiple very fast simulated annealing solutions shows extremely large uncertainty (almost 100%) in the final solution after inversion of individual DC resistivity or electromagnetic (EM) data sets. Uncertainty associated with the intermediate resistive and conducting layers after global optimization and joint inversion is still large. In order to reduce the large uncertainty associated with the intermediate layer, global optimization is performed over several iterations by reducing and redefining the search limits of model parameters according to the uncertainty in the solution. The new minimum and maximum limits are obtained from the uncertainty in the previous iteration. Though the misfit error reduces in the solution after successive refinement of the model space in individual inversion, it is observed that the mean model drifts away from the actual model. However, successive refinement of the model space using global optimization and joint inversion reduces uncertainty to a very low level in 4–5 iterations. This approach works very well in resolving the problem of equivalence for resistive as well as for conducting layers. The efficacy of the approach has been demonstrated using DC resistivity and EM data, however, it can be applied to any geophysical data to solve the inherent ambiguities in the interpretations.     

单相介质AVO反演的精度分析

振幅随偏移距变化（AVO）反演是一个非线性的组合最优化过程，理论上可先将该非线性问题线性化，然后求解线性问题；或者直接利用非线性的模拟退火、遗传算法等方法求解.但无论哪种反演思路，实际中影响其精度的因素很多，因此分析AVO反演中的误差来源对提高反演精度和评价反演方法的可靠性非常重要.本文对能造成反演误差的主要因素，噪音、薄层调谐、地震数据处理中的误差、入射角范围等进行了分析，讨论了这些因素可能对反演结果造成的影响，发现在AVO反演过程中可以从优化参数选择和针对性处理方面来减小这些误差，提高反演精度.     

Joint parameter estimation from magnetic resonance and vertical electric soundings using a multi‐objective genetic algorithm

Magnetic resonance sounding (MRS) has increasingly become an important method in hydrogeophysics because it allows for estimations of essential hydraulic properties such as porosity and hydraulic conductivity. A resistivity model is required for magnetic resonance sounding modelling and inversion. Therefore, joint interpretation or inversion is favourable to reduce the ambiguities that arise in separate magnetic resonance sounding and vertical electrical sounding (VES) inversions. A new method is suggested for the joint inversion of magnetic resonance sounding and vertical electrical sounding data. A one‐dimensional blocky model with varying layer thicknesses is used for the subsurface discretization. Instead of conventional derivative‐based inversion schemes that are strongly dependent on initial models, a global multi‐objective optimization scheme (a genetic algorithm [GA] in this case) is preferred to examine a set of possible solutions in a predefined search space. Multi‐objective joint optimization avoids the domination of one objective over the other without applying a weighting scheme. The outcome is a group of non‐dominated optimal solutions referred to as the Pareto‐optimal set. Tests conducted using synthetic data show that the multi‐objective joint optimization approximates the joint model parameters within the experimental error level and illustrates the range of trade‐off solutions, which is useful for understanding the consistency and conflicts between two models and objectives. Overall, the Levenberg‐Marquardt inversion of field data measured during a survey on a North Sea island presents similar solutions. However, the multi‐objective genetic algorithm method presents an efficient method for exploring the search space by producing a set of non‐dominated solutions. Borehole data were used to provide a verification of the inversion outcomes and indicate that the suggested genetic algorithm method is complementary for derivative‐based inversions.     

地球物理资料群体智能反演(英文)

复杂地球物理资料的反演问题往往是一个求解多参数非线性多极值的最优解问题。而鸟和蚂蚁等群体觅食的过程,正好与寻找地球物理反演最优解的过程相似。基于自然界群体协调寻优的思想,本文提出了交叉学科的群体智能地球物理资料反演方法,并给出了其对应的数学模型。用一个有无限多个局部最优解的已知模型对该类方法进行了试验。然后,将它们应用到了不同的复杂地球物理反演问题中:(1)对噪声敏感的线性问题;(2)非线性和线性同步反演问题;(3)非线性问题。反演结果表明,群体智能反演是可行的。与常规遗传算法和模拟退火法相比,该类方法有收敛速度相对快、收敛精度相对高等优点;与拟牛顿法和列文伯格一马夸特法相比,该类方法有能跳出局部最优解等优点。     

正则参数控制下的波阻抗约束反演

通过势函数方式将波阻抗反演的病态问题转为良态问题，并且给出了边界保护势函数所具备的条件. 在反演过程中，通过改变正则参数数值以及合理地选择正则参数的初值，改善反演结果，提高反演收敛速度. 同时，在具体反演中使用快速模拟退火算法，可以克服目标函数局部极值的限制，从而获得全局最优解. 通过理论模型试算和实际资料处理，说明本文方法具有精度高、实用性强的特点.     

CDP mapping in tilted transversely isotropic (TTI) media. Part II: Velocity analysis by combining CDP mapping with a genetic algorithm

This paper presents a method for velocity analysis in tilted transversely isotropic (TTI) media by combining CDP mapping with a genetic algorithm. CDP mapping is a velocity analysis method for determining anisotropic velocity but has difficulties due to the following factors: (i) it involves a non-linear and multimodal objective function; (ii) it is prohibitively expensive in the evaluation of candidate solutions, which often involves the calculation of images in the depth domain; (iii) there is often a very large parameter space. Recognizing the global and multimodal nature of the problem, a genetic algorithm is employed to search for the optimal velocity model. The efficiency of the method contributes to two critical processes: rapid model evaluation, achieved by generating CDP mapping only in the neighbourhood of specific reflectors, and fast computation, based on Fermat's principle, of the CDP points and traveltimes in TTI media. The method produces subsurface structure images in the depth domain, and can also solve for Thomsen's anisotropic parameters (ɛ and δ), the vertical velocity and the dip of the symmetry axis in the model space, simultaneously.