基于Remez迭代算法求解差分系数的双相介质自适应有限差分正演模拟

利用传统有限差分方法对基于Biot理论的双相介质波动方程进行数值求解时,由于慢纵波的存在,数值频散效应较为明显,影响模拟精度.相对于声学近似方程及普通弹性波方程,Biot双相介质波动方程在同等数值求解算法和精度要求条件下,其地震波场正演模拟需要更多的计算时间.本文针对Biot一阶速度-应力方程组发展了一种变阶数优化有限差分数值模拟方法,旨在同时提高其正演模拟的精度和效率.首先结合交错网格差分格式推导Biot方程的数值频散关系式.然后基于Remez迭代算法求取一阶空间偏导数的优化差分系数,并用于Biot方程的交错网格有限差分数值模拟.在此基础上把三类波的平均频散误差参数限制在给定的频散误差阈值和频率范围内,此时优化有限差分算子的长度就能自适应非均匀双相介质模型中的不同速度区间.数值频散曲线分析表明:基于Remez迭代算法的优化有限差分方法相较传统泰勒级数展开方法在大波数范围对频散误差的压制效果更明显;可变阶数的优化有限差分方法能取得与固定阶数优化有限差分方法相近的模拟精度.在均匀介质和河道模型的数值模拟实验中将本文变阶数优化有限差分算法与传统泰勒展开算法、最小二乘优化算法进行比较,进一步证明其在复杂地下介质中的有效性和适用性.     

加权总体最小二乘在重心化Bursa模型中的应用

研究了基于加权总体最小二乘的重心化布尔沙模型的坐标转换算法,针对坐标转换中原始坐标和目标坐标均存在误差的问题,根据误差的影响程度不同而给予不同的权值,利用加权总体最小二乘方法求解转换参数。坐标重心化的方法可以解决布尔沙模型在局部地区容易出现病态的问题,将两种方法结合可以很好地提高坐标转换的精度,通过实例验证了该方法的优越性。     

地壳形变分析的抗差最小二乘配置迭代解法

利用最小二乘配置进行地壳形变分析,其结果的合理性关键在于经验协方差函数的拟合.考虑到观测数据存在粗差的情况,提出基于观测值中位数初值的抗差最小二乘配置方法和基于中位参数法的抗差最小二乘配置方法.两种方法首先分别利用观测值中位数给出观测值初始权阵以及利用中位参数法给出最小二乘配置初始解,然后均在给定协方差函数参数初始值的情况下,应用合适的等价权进行抗差估计并通过迭代计算,最终获得稳健的协方差函数参数估值及最小二乘配置解.利用本文提出的两种方法以及传统方法分别对庐山地震的GPS垂直位移数据和意大利L'Aquila地震的InSAR同震位移数据进行处理分析.结果表明:相对传统方法,基于观测值中位数初值的抗差最小二乘配置方法效果更好,更具稳健性.     

基于热点参考系的板块绝对运动模型

本文在最新一代板块相对运动模型(MORVEL模型)的基础上,通过最小二乘反演观测热点方向数据建立板块绝对运动模型.经过对前人用于约束板块绝对运动模型的所有热点数据与MORVEL模型的一致性作系统的统计学检验,发现存在离群数据.相应地,提出两种系统剔除离群数据的新方法:逐一剔除法和全局搜索法.结合对总残差的卡方检验和对残差频率分布的正态检验,逐步筛选最优模型,最终得到一个基于热点参考系的板块绝对运动新模型(T87模型).该模型能够合理拟合全球分布的87个热点方向数据,而模型预测的板块绝对运动速率比观测热点火山的迁移速率系统偏小,最大偏差达到4 cm·a~(-1).这样的偏差可由观测热点速率的系统误差或地幔返回流造成的热点间运动解释.不论是哪种解释成立,本文结果表明热点方向数据能够独立、有效地定义全球热点参考系.这样定义的热点参考系可方便地应用于板块绝对运动、地幔对流及真极移的研究.     

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.     

含偏心点声源的随钻测井声场模拟和地层各向异性反演研究

地层横波波速测量以及各向异性评价是目前随钻声波测井应用及方法研究的难题之一.针对这些问题,本文试图从钻铤上的偏心点声源在各向异性地层中的响应出发,寻求和探讨解决方案.我们基于三维有限差分模拟的随钻测井信号,研究了偏心点声源在水平横向各向同性(HTI)慢速地层井孔中激发声波传播规律,研究结果表明:在HTI地层中偏心点声源能够同时激发出快、慢两种波形,并且此两种波形中主要分别包含快、慢弯曲波,由于与钻铤波的耦合作用,其速度总是分别小于地层快、慢横波波速,所以无法直接用于地层横波波速的测量.但根据进一步的灵敏度分析可知当在3kHz以上时,它们的相速度分别对地层参数水平和垂直剪切模量(c66和c44)最为敏感.基于此特性,本文提出一种基于解析近似解的最小二乘拟合法,能够通过快、慢波频散曲线反演地层横波波速,所测值误差小于3%,并且具有很好的容错率和稳定性;进而由横波速度反演值评价地层各向异性大小.最后,地层快横波偏振方位可以利用垂直于偏心声源方向的偶极采集的信号能量变化曲线来获取.     

Gully erosion spatial modelling: Role of machine learning algorithms in selection of the best controlling factors and modelling process

This investigation assessed the efficacy of 10 widely used machine learning algorithms (MLA) comprising the least absolute shrinkage and selection operator (LASSO), generalized linear model (GLM), stepwise generalized linear model (SGLM), elastic net (ENET), partial least square (PLS), ridge regression, support vector machine (SVM), classification and regression trees (CART), bagged CART, and random forest (RF) for gully erosion susceptibility mapping (GESM) in Iran. The location of 462 previously existing gully erosion sites were mapped through widespread field investigations, of which 70% (323) and 30% (139) of observations were arbitrarily divided for algorithm calibration and validation. Twelve controlling factors for gully erosion, namely, soil texture, annual mean rainfall, digital elevation model (DEM), drainage density, slope, lithology, topographic wetness index (TWI), distance from rivers, aspect, distance from roads, plan curvature, and profile curvature were ranked in terms of their importance using each MLA. The MLA were compared using a training dataset for gully erosion and statistical measures such as RMSE (root mean square error), MAE (mean absolute error), and R-squared. Based on the comparisons among MLA, the RF algorithm exhibited the minimum RMSE and MAE and the maximum value of R-squared, and was therefore selected as the best model. The variable importance evaluation using the RF model revealed that distance from rivers had the highest significance in influencing the occurrence of gully erosion whereas plan curvature had the least importance. According to the GESM generated using RF, most of the study area is predicted to have a low (53.72%) or moderate (29.65%) susceptibility to gully erosion, whereas only a small area is identified to have a high (12.56%) or very high (4.07%) susceptibility. The outcome generated by RF model is validated using the ROC (Receiver Operating Characteristics) curve approach, which returned an area under the curve (AUC) of 0.985, proving the excellent forecasting ability of the model. The GESM prepared using the RF algorithm can aid decision-makers in targeting remedial actions for minimizing the damage caused by gully erosion.     

King Canute muses in the South Seas: Why aren’t Pacific Islands transitioning to low carbon sea transport futures?

Transition to low carbon sea transport is a logical response to the extreme dependency of the Pacific Islands region on imported fossil fuel, its significant vulnerability to the effects of climate change and the critical shipping needs of Pacific Island countries (PICs). Building on previous work in low carbon sea transport in the Pacific, this paper further considers the barriers to achieving such transition by assessing, through a ‘post-Paris Agreement’ lens, the Intended Nationally Determined Contributions (INDCs) submitted by PICs and contrasting these to the near total lack of investment and planning for low carbon transition in the transport sector with the parallel occurrence in the electricity sector where ~USD 2 billion of donor investment is deployed or queued despite electricity using only ~20% of fossil fuel across the region. Consistent with recent international studies, inadequate and inappropriate financing and policy have been identified as dominant transition barriers for low carbon sea transport development in PICs. This paper further examines the regional level barriers to policy development, and finds them inhibited by the silo nature of the major regional actors. The implications that the Paris Agreement has for climate financing to support the essential research and capacity development needed to underpin a successful low carbon sea transport transition strategy at any useful scale and speed are also considered in this paper.     

Local gravity field modeling using spherical radial basis functions and a genetic algorithm

Spherical Radial Basis Functions (SRBFs) can express the local gravity field model of the Earth if they are parameterized optimally on or below the Bjerhammar sphere. This parameterization is generally defined as the shape of the base functions, their number, center locations, bandwidths, and scale coefficients. The number/location and bandwidths of the base functions are the most important parameters for accurately representing the gravity field; once they are determined, the scale coefficients can then be computed accordingly. In this study, the point-mass kernel, as the simplest shape of SRBFs, is chosen to evaluate the synthesized free-air gravity anomalies over the rough area in Auvergne and GNSS/Leveling points (synthetic height anomalies) are used to validate the results. A two-step automatic approach is proposed to determine the optimum distribution of the base functions. First, the location of the base functions and their bandwidths are found using the genetic algorithm; second, the conjugate gradient least squares method is employed to estimate the scale coefficients. The proposed methodology shows promising results. On the one hand, when using the genetic algorithm, the base functions do not need to be set to a regular grid and they can move according to the roughness of topography. In this way, the models meet the desired accuracy with a low number of base functions. On the other hand, the conjugate gradient method removes the bias between derived quasigeoid heights from the model and from the GNSS/leveling points; this means there is no need for a corrector surface. The numerical test on the area of interest revealed an RMS of 0.48 mGal for the differences between predicted and observed gravity anomalies, and a corresponding 9 cm for the differences in GNSS/leveling points.     

平均入射角道集PP波与PS波联合反演

在界面两侧地层的弹性参数弱反差的假设难以成立的情况下,本文提出用平均入射角道集进行PP波与PS波的联合反演.首先,在PP波与PS波AVA(amplitude versus angle,振幅随入射角变化)道集的基础上,分别选择小入射角范围与大入射角范围的AVA道集进行局部加权叠加,以获得由两个角度组成的平均入射角道集,并作为后续反演的输入数据.然后,再通过最小二乘原理建立了PP波与PS波联合反演目标函数,推导了模型修改量的向量公式,建立了平均入射角道集联合反演的流程.模型数据与实际数据的测试结果表明:在信噪比较低、地层弹性参数反差较大、层厚较薄的情况下,该反演方法的精度在很大程度上超过了基于近似反射系数的反演方法,为复杂油气藏勘探提供了新的思路.