基于MCMC的叠前地震反演方法研究

马尔科夫链蒙特卡洛方法(MCMC)是一种启发式的全局寻优算法[1].它在贝叶斯框架下,利用已有资料进行约束,既可使最优解满足参数的统计特性,又通过融入的先验信息,提高解的精度;寻优过程可跳出局部最优,得到全局最优解.利用MCMC方法,可以得到大量来自于后验概率分布的样本,不仅可以得到每个未知参数的估计值,而且可以得到与...     

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.     

基于L1范数的瞬变电磁非线性反演

瞬变电磁反演存在高度的非线性特征,常用的最小二乘等线性反演方法往往对初始模型高度依赖,并且极易陷入局部最优解.本文基于观测数据与模拟数据的L1范数建立目标函数,采用模拟退火非线性全局最优化方法实现瞬变电磁一维反演.初始模型完全随机产生,通过指数函数退温机制模拟系统能量最小实现迭代,通过接收概率函数评价当前模型,实现局部最优解的跳出,最终实现全局最优化求解.通过数值算例发现,无论给定的反演层数等于还是大于设计模型,都可以获得较好的反演效果,因而可以在反演初始就设计较多的层数,实现反演模型的自动拟合;同时,利用含噪声数据反演进一步验证算法的稳定性.最后,对实测数据进行了反演测试,结果与钻孔编录基本一致,表明提出的基于L1范数的模拟退火反演可用于实测数据处理.     

快速模拟退火地震反演

讨论了用模拟退火方法进行地震资料的参数反演，利用快速的降温方式实现模拟退火反演，从而形成了快速模拟退火算法。模拟退火反演的优点是可以突破反演过程中局部最优的限制，获得全局最优解。因此，ＳＡ方法适于解决地震反演中的非凸性目标函数的最优化问题。     

改进蜂群算法及其在面波频散曲线反演中的应用

应用改进蜂群算法反演面波频散曲线以获得近地表横波速度剖面.蜂群算法属于群智能算法中的一种,灵感来源于蜜蜂群体特定的觅食行为,在该算法的基础上结合粒子群算法中的全局最优解引导思想,同时引入遗传算法中交叉运算操作,即采用基于交叉操作的全局人工蜂群算法对面波频散曲线进行反演研究.改进蜂群算法在继承传统算法精于探索特性的同时,针对其疏于开发的缺陷着重加强了算法对全局的探索能力.使用理论和实测瑞雷波数据,本文研究了改进蜂群算法在推导近地表横波速度分布的有效性和适用性.在反演中,目标函数的收敛性好,改进算法在迭代的过程中能够快速收敛到全局最优;模型参数的概率分布高,即在寻找到全局最优解的同时,能够确保解中每个参数同时达到最优,保证了反演的结果可靠度,使其能有效地应用于瑞雷波频散曲线的反演和解释中.     

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.     

波阻抗反演正则参数估计

为了解决用正则化方法能够将波阻抗反演的病态问题转为良态问题,通过统计方法合理地选择正则参数的初值,在反演过程中用极大似然（ML）方法实时进行正则参数值估计,提高反演收敛速度,改善反演结果。同时,在具体反演中将正则化方法与快速模拟退火算法相结合,充分发挥正则参数作用,可以获得全局最优解,取得了好的实际应用效果。     

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.     

大地电磁的人工鱼群最优化约束反演

大地电磁的反演问题是非线性,如果采用线性反演方法容易陷入局部极小,使得反演结果非唯一性严重.本文将人工鱼群算法引入到地球物理反演之中,提出了非线性的大地电磁人工鱼群最优化反演.该方法不需要进行偏导数的求取,可以对反演的范围进行约束,以减小反演结果的非唯一性.同时我们对搜索步长进行了改进,给出适用于大地电磁反演的人工鱼群参数.大量的理论数据试算表明,人工鱼群反演算法能够较好地寻找到全局最优解.实测数据的处理结果表明,该方法可以用来处理实际资料,并且能够取得很好的应用效果.     

利用遗传算法和最小二乘联合反演共和地震位错参数

中国地震局第二地形变监测中心已监测到与1990年4月26日青海共和7.0级地震有关的大幅度隆起垂直形变资料．基于这些形变资料,本研究首先利用全局搜索性能优良的遗传算法和弹性半空间单一矩形均匀滑动模型,对该地震的震源位错参数进行了初步反演;然后以遗传算法的反演结果为初始值,利用拟牛顿阻尼最小二乘方法对该地震的震源位错参数进行了更精细的反演．结果表明,共和7.0级地震的发震断层为一走向NW60左右、倾向SW、倾角37左右的右旋走滑逆冲断层,同震断层破裂长度约37 km,宽度约6 km,错动幅度约2.7 m．反演结果还同时表明,遗传算法与最小二乘方法相结合是一种行之有效的联合反演方法,它既可以保证实现全局最优解,防止最小二乘方法的局部极值解问题,又可以有效地解决遗传算法达到全局最优解区域后收敛速度过慢的问题．      

基于Metropolis优化的叠前全局迭代地质统计学反演方法

叠前地质统计学反演将随机模拟与叠前反演相结合,不仅可以反演各种储层弹性参数,还提高了反演结果的分辨率.基于联合概率分布的直接序贯协模拟方法可以在原始数据域对数据进行模拟,不需要对数据进行高斯变换,拓展了地质统计学反演的应用范围;而联合概率分布的应用确保了反演参数之间相关性,提高了反演的精度.本文将基于联合概率分布的直接序贯协模拟方法与蒙特卡洛抽样算法相结合,参考全局随机反演策略,提出了基于蒙特卡洛优化算法的全局迭代地质统计学反演方法.为了提高反演的稳定性,我们修改了局部相关系数的计算公式,提出了一种新的基于目标函数的优化局部相关系数计算公式并应用到协模拟之中.模型测试及实际数据应用表明,该方法可以很好的应用于叠前反演之中.     

基于改进全变差正则化的GPR多尺度全波形双参数同步反演

针对探地雷达（GPR）双参数全波形反演中电导率反演精度差、双参数存在串扰现象、反演计算量大、易陷入局部极值等问题.作者将具有多参数调节功能的L-BFGS算法引入到GPR时间域全波形反演中,它避免了对Hessian矩阵的直接存储与精确求解,减小了存储量和计算量.结合参数调节因子的选取,有效减小了同步反演时介电常数与电导率的串扰影响,在不降低介电常数反演精度的前提下,提高电导率参数的反演精度.通过在反演目标函数中加载改进全变差正则化方法,提高了反演的稳定性,使目标体边缘轮廓更加清晰.首先以简单模型为例,对比了单尺度反演与多尺度串行反演策略的优劣,说明多尺度串行反演有利于逐步搜索全局最优解;而开展参数调节因子的选取实验,说明合适的参数调节因子可以有效改善介质电导率的反演精度;测试了不同正则化的反演效果,表明改进全变差正则化能提高反演稳定性,显著降低模型重构误差.最后,分别对含噪合成数据和实测数据进行了反演测试,说明本文提出的多尺度、双参数反演具有较强的鲁棒性,能提供更丰富的信息约束,重构图像界面清晰、反演效果好.     

Soil moisture estimation using tomographic ground penetrating radar in a MCMC–Bayesian framework

In this study, we focus on a hydrogeological inverse problem specifically targeting monitoring soil moisture variations using tomographic ground penetrating radar (GPR) travel time data. Technical challenges exist in the inversion of GPR tomographic data for handling non-uniqueness, nonlinearity and high-dimensionality of unknowns. We have developed a new method for estimating soil moisture fields from crosshole GPR data. It uses a pilot-point method to provide a low-dimensional representation of the relative dielectric permittivity field of the soil, which is the primary object of inference: the field can be converted to soil moisture using a petrophysical model. We integrate a multi-chain Markov chain Monte Carlo (MCMC)–Bayesian inversion framework with the pilot point concept, a curved-ray GPR travel time model, and a sequential Gaussian simulation algorithm, for estimating the dielectric permittivity at pilot point locations distributed within the tomogram, as well as the corresponding geostatistical parameters (i.e., spatial correlation range). We infer the dielectric permittivity as a probability density function, thus capturing the uncertainty in the inference. The multi-chain MCMC enables addressing high-dimensional inverse problems as required in the inversion setup. The method is scalable in terms of number of chains and processors, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. The proposed inversion approach can successfully approximate the posterior density distributions of the pilot points, and capture the true values. The computational efficiency, accuracy, and convergence behaviors of the inversion approach were also systematically evaluated, by comparing the inversion results obtained with different levels of noises in the observations, increased observational data, as well as increased number of pilot points.     

Fast and accurate earthquake location within complex medium using a hybrid globallocal inversion approach

A novel hybrid approach for earthquake location is proposed which uses a combined coarse global search and fine local inversion with a minimum search routine, plus an examination of the root mean squares (RMS) error distribution. The method exploits the advantages of network ray tracing and robust formulation of the Fréchet derivatives to simultaneously update all possible initial source parameters around most local minima (including the global minimum) in the solution space, and finally to determine the likely global solution. Several synthetic examples involving a 3-D complex velocity model and a challenging source-receiver layout are used to demonstrate the capability of the newly-developed method. This new global-local hybrid solution technique not only incorporates the significant benefits of our recently published hypocenter determination procedure for multiple earthquake parameters, but also offers the attractive features of global optimal searching in the RMS travel time error distribution. Unlike the traditional global search method, for example, the Monte Carlo approach, where millions of tests have to be done to find the final global solution, the new method only conducts a matrix inversion type local search but does it multiple times simultaneously throughout the model volume to seek a global solution. The search is aided by inspection of the RMS error distribution. Benchmark tests against two popular approaches, the direct grid search method and the oct-tree important sampling method, indicate that the hybrid global-local inversion yields comparable location accuracy and is not sensitive to modest level of noise data, but more importantly it offers two-order of magnitude speed-up in computational effort. Such an improvement, combined with high accuracy, make it a promising hypocenter determination scheme in earthquake early warning, tsunami early warning, rapid hazard assessment and emergency response after strong earthquake occurrence.     

三维复杂速度模型中地震的快速精确定位

讨论了全局选择震源初始位置下的矩阵反演求取全局解的问题．与流行的全局优化搜寻直接定位方法相比,该反演算法是一种行之有效的定位方法,具有定位精度高、计算时间少以及对噪声数据不敏感等特点．其突出的优点是在不增加计算难度和计算时间的前提下,用矩阵反演的方法确保得到全局最小值解,可适应于地震早期预警,海啸早期预警,以及大震速报等实际工作．      

基于不等式约束的三维电阻率探测混合反演方法

三维电阻率探测的线性反演和非线性反演中均存在着多解性的固有难题.电阻率线性反演方法的效率较高,但反演结果对初始模型的依赖性较强,易陷入局部极小;而非线性反演方法不依赖初始模型,但搜索效率极低,尚未见到关于三维电阻率非线性反演的文献.针对上述问题,融合线性与非线性反演方法的互补优势,提出了最小二乘法(线性方法)与改进遗传算法(非线性方法)相结合的混合反演方法的概念和思想.首先,提出了将介质电阻率变化范围作为不等式约束引入反演方程的思路,以实现压制多解性、提高可靠性的目标.提出了宽松不等式约束和基于钻孔推断的局部严格不等式约束的获取及定义方法.在此基础上,分别提出了基于不等式约束的最小二乘线性反演方法和遗传算法非线性反演方法.其次,对于遗传算法在变异搜索方向控制、初始群体产生等方面进行了改进,优化了其搜索方向和初始群体多样性.然后,提出了混合反演方法及其实现方案,利用改进遗传算法进行第一阶段反演,发挥其对初始模型的依赖程度低的优势,搜索到最优解附近的空间,输出当前最优个体;利用最小二乘法进行第二阶段反演,将遗传算法得到的当前最优个体作为初始模型,在最优解附近空间执行高效率的局部线性搜索,最终实现地电结构的三维成像.最后,开展了合成数据与实际工程算例验证,与传统最小二乘方法进行了对比,发现混合反演方法在压制多解性、摆脱初始模型依赖和提高反演效果方面有较好效果.     

Markov chain Monte Carlo ground‐motion selection algorithms for conditional intensity measure targets

Two new algorithms are presented for efficiently selecting suites of ground motions that match a target multivariate distribution or conditional intensity measure target. The first algorithm is a Markov chain Monte Carlo (MCMC) approach in which records are sequentially added to a selected set such that the joint probability density function (PDF) of the target distribution is progressively approximated by the discrete distribution of the selected records. The second algorithm derives from the concept of the acceptance ratio within MCMC but does not involve any sampling. The first method takes advantage of MCMC's ability to efficiently explore a sampling distribution through the implementation of a traditional MCMC algorithm. This method is shown to enable very good matches to multivariate targets to be obtained when the numbers of records to be selected is relatively large. A weaker performance for fewer records can be circumvented by the second method that uses greedy optimisation to impose additional constraints upon properties of the target distribution. A preselection approach based upon values of the multivariate PDF is proposed that enables near‐optimal record sets to be identified with a very close match to the target. Both methods are applied for a number response analyses associated with different sizes of record sets and rupture scenarios. Comparisons are made throughout with the Generalised Conditional Intensity Measure (GCIM) approach. The first method provides similar results to GCIM but with slightly worse performance for small record sets, while the second method outperforms method 1 and GCIM for all considered cases.     

Time‐lapse seismic imaging using regularized full‐waveform inversion with a prior model: which strategy?

Full‐waveform inversion is an appealing technique for time‐lapse imaging, especially when prior model information is included into the inversion workflow. Once the baseline reconstruction is achieved, several strategies can be used to assess the physical parameter changes, such as parallel difference (two separate inversions of baseline and monitor data sets), sequential difference (inversion of the monitor data set starting from the recovered baseline model) and double‐difference (inversion of the difference data starting from the recovered baseline model) strategies. Using synthetic Marmousi data sets, we investigate which strategy should be adopted to obtain more robust and more accurate time‐lapse velocity changes in noise‐free and noisy environments. This synthetic application demonstrates that the double‐difference strategy provides the more robust time‐lapse result. In addition, we propose a target‐oriented time‐lapse imaging using regularized full‐waveform inversion including a prior model and model weighting, if the prior information exists on the location of expected variations. This scheme applies strong prior model constraints outside of the expected areas of time‐lapse changes and relatively less prior constraints in the time‐lapse target zones. In application of this process to the Marmousi model data set, the local resolution analysis performed with spike tests shows that the target‐oriented inversion prevents the occurrence of artefacts outside the target areas, which could contaminate and compromise the reconstruction of the effective time‐lapse changes, especially when using the sequential difference strategy. In a strongly noisy case, the target‐oriented prior model weighting ensures the same behaviour for both time‐lapse strategies, the double‐difference and the sequential difference strategies and leads to a more robust reconstruction of the weak time‐lapse changes. The double‐difference strategy can deliver more accurate time‐lapse variation since it can focus to invert the difference data. However, the double‐difference strategy requires a preprocessing step on data sets such as time‐lapse binning to have a similar source/receiver location between two surveys, while the sequential difference needs less this requirement. If we have prior information about the area of changes, the target‐oriented sequential difference strategy can be an alternative and can provide the same robust result as the double‐difference strategy.