Stochastic simulations of ocean waves: An uncertainty quantification study

The primary objective of this study is to introduce a stochastic framework based on generalized polynomial chaos (gPC) for uncertainty quantification in numerical ocean wave simulations. The techniques we present can be easily extended to other numerical ocean simulation applications. We perform stochastic simulations using a relatively new numerical method to simulate the HISWA (Hindcasting Shallow Water Waves) laboratory experiment for directional near-shore wave propagation and induced currents in a shallow-water wave basin. We solve the phased-averaged equation with hybrid discretization based on discontinuous Galerkin projections, spectral elements, and Fourier expansions. We first validate the deterministic solver by comparing our simulation results against the HISWA experimental data as well as against the numerical model SWAN (Simulating Waves Nearshore). We then perform sensitivity analysis to assess the effects of the parametrized source terms, current field, and boundary conditions. We employ an efficient sparse-grid stochastic collocation method that can treat many uncertain parameters simultaneously. We find that the depth-induced wave-breaking coefficient is the most important parameter compared to other tunable parameters in the source terms. The current field is modeled as random process with large variation but it does not seem to have a significant effect. Uncertainty in the source terms does not influence significantly the region before the submerged breaker whereas uncertainty in the incoming boundary conditions does. Considering simultaneously the uncertainties from the source terms and boundary conditions, we obtain numerical error bars that contain almost all experimental data, hence identifying the proper range of parameters in the action balance equation.     

基于稀疏表达的OBS去噪方法

海底地震仪（OBS）采集数据的去噪处理是开展OBS震相分析及后续处理反演的基础.本文结合曲波（Curvelet）变换及压缩感知提出一种稀疏化表达的OBS去噪方法,并通过与小波变化对比等探讨去噪效果.曲波变换具有抛物尺度及识别线性异常的优点,可以稀疏地表示OBS数据,再结合压缩感知思想对稀疏表达OBS数据进行去噪处理和重构.通过对变换后的系数进行基于L₁范数的冷却阈值迭代滤波,获得最优的变换系数,本文指出基于曲波变换的冷却阈值迭代法能够很好地对OBS数据去噪.对比小波和曲波两种变换在相同迭代次数下对理论模型数据进行去噪处理,表明曲波变换得到的结果信噪比更高.利用本文方法对渤海地区采集的OBS数据进行去噪处理获得了更加清晰连续的震相,噪声压制效果更明显,为震相拾取及后续速度模型反演奠定了良好的基础.     

页岩微米孔隙结构重构的非光滑正则化及快速梯度优化算法

页岩微观结构认识是页岩气勘探开发的基础.传统的探测手段是基于表面的有损观测方法.本文应用上海光源同步辐射技术对页岩结构进行无损探测获取投影数据,该技术可以避免X射线硬化.我们利用X射线计算机断层成像技术进行图像恢复,提出了L1模+TV(全变差)非光滑正则化方法抑制噪声影响,提高图像对比度.实验证明,该方法是准确重建页岩微观结构的有效方法.     

基于压缩感知的加权MCA地震数据重构方法

地震数据规则化重构是地震资料处理十分重要的基础性工作.压缩感知理论打破了香农采样定理的制约,利用信号在某个变换域的稀疏特性重构出完整的信号,在地震数据重构领域得到了很好的应用.深反射地震剖面大都布置在地质构造比较复杂的区段,复杂的地质构造使深反射地震剖面上的波阻特征复杂,采用单一稀疏变换不能最有效地表征数据的内部结构特征.MCA(形态成分分析)方法将信号分解为几种形态特征区别明显的分量来逼近数据的内部复杂结构,但是对各成分简单的叠加仍然无法有效地描述复杂构造数据的各种特征.结合两种方法的优点,本文提出了一种新的基于压缩感知的重构算法框架,在MCA方法的基础上对各稀疏字典进行加权,在迭代中不断更新各个稀疏字典的权值系数,对信号内部的各种特征进行最优描述,从而实现对信号的高质量重构.模型测试和实际资料处理结果表明:基于压缩感知的加权MCA方法不仅可以对地质构造复杂的地震数据进行高效的插值重建,而且可以很好的消除空间假频.     

Probabilistic outlier detection for sparse multivariate geotechnical site investigation data using Bayesian learning

Various uncertainties arising during acquisition process of geoscience data may result in anomalous data instances(i.e.,outliers)that do not conform with the expected pattern of regular data instances.With sparse multivariate data obtained from geotechnical site investigation,it is impossible to identify outliers with certainty due to the distortion of statistics of geotechnical parameters caused by outliers and their associated statistical uncertainty resulted from data sparsity.This paper develops a probabilistic outlier detection method for sparse multivariate data obtained from geotechnical site investigation.The proposed approach quantifies the outlying probability of each data instance based on Mahalanobis distance and determines outliers as those data instances with outlying probabilities greater than 0.5.It tackles the distortion issue of statistics estimated from the dataset with outliers by a re-sampling technique and accounts,rationally,for the statistical uncertainty by Bayesian machine learning.Moreover,the proposed approach also suggests an exclusive method to determine outlying components of each outlier.The proposed approach is illustrated and verified using simulated and real-life dataset.It showed that the proposed approach properly identifies outliers among sparse multivariate data and their corresponding outlying components in a probabilistic manner.It can significantly reduce the masking effect(i.e.,missing some actual outliers due to the distortion of statistics by the outliers and statistical uncertainty).It also found that outliers among sparse multivariate data instances affect significantly the construction of multivariate distribution of geotechnical parameters for uncertainty quantification.This emphasizes the necessity of data cleaning process(e.g.,outlier detection)for uncertainty quantification based on geoscience data.     

A sampling approach to estimate the log determinant used in spatial likelihood problems

Likelihood-based methods for modeling multivariate Gaussian spatial data have desirable statistical characteristics, but the practicality of these methods for massive georeferenced data sets is often questioned. A sampling algorithm is proposed that exploits a relationship involving log-pivots arising from matrix decompositions used to compute the log determinant term that appears in the model likelihood. We demonstrate that the method can be used to successfully estimate log-determinants for large numbers of observations. Specifically, we produce an log-determinant estimate for a 3,954,400 by 3,954,400 matrix in less than two minutes on a desktop computer. The proposed method involves computations that are independent, making it amenable to out-of-core computation as well as to coarse-grained parallel or distributed processing. The proposed technique yields an estimated log-determinant and associated confidence interval.

全球环流系统关联性的时空演化特征研究

利用NCEP/NCAR全球高度场和地面气压资料,运用矩阵理论,研究了全球高度场和地面气压序列关联性的时空演变特征.结果表明,各层次高度场的关联性在中低纬度区域较好,并向中高纬度地区逐步递减,呈准带状分布;垂直方向上,低层的关联性较弱,随着高度升高关联性逐渐增强;北太平洋区域从低层至高层大气中均存在一个较强的负关联中心,...     

Constraining Navigation by Matching Swath Bathymetry and Gravity Measurements at Ship Track Crossovers

A method which utilizes the lateral offset information obtained by comparing swath bathymetric data at track crossover points as a further constraint on the navigation is presented. The method, based on generalized least squares inversion theory, derives a new navigational solution that minimizes the overall misfit between the pairs of topography at crossovers while trying to remain smooth and close to the starting model. To achieve a high numerical efficiency during inversions of large matrices, we employed sparse matrix algorithms. The inversion scheme was applied to a set of Sea Beam data collected over the East Pacific Rise near 9° 30' N in early 1988 at the time when the Global Positioning System had limited coverage. The starting model was constructed by taking evenly spaced samples of positions along the tracklines. For each one of the 361 crossovers, we gridded the bathymetric data around the crossover point compared the gridded maps, and calculated the offset and uncertainty associated with this estimation. A suite of inversion solutions were obtained depending on the choice of three free parameters (that is, the a priori model variance, the correlation interval of a priori model, and the trade-off coefficient between fitting the data and remaining close to the a priori model). The best solution was chosen as one that minimizes both the Sea Beam topography and free-air gravity anomaly differences at crossovers. The improvement was significant; the initial rms mismatch between the tracks and free-air gravity anomalies at crossovers was reduced from 610m to 75m and from 2.5mGal to 1.9mGal, respectively.     

Spectral sparse Bayesian learning reflectivity inversion

A spectral sparse Bayesian learning reflectivity inversion method, combining spectral reflectivity inversion with sparse Bayesian learning, is presented in this paper. The method retrieves a sparse reflectivity series by sequentially adding, deleting or re‐estimating hyper‐parameters, without pre‐setting the number of non‐zero reflectivity spikes. The spikes with the largest amplitude are usually the first to be resolved. The method is tested on a series of data sets, including synthetic data, physical modelling data and field data sets. The results show that the method can identify thin beds below tuning thickness and highlight stratigraphic boundaries. Moreover, the reflectivity series, which is inverted trace‐by‐trace, preserves the lateral continuity of layers.     

Effect of field plot location on estimating tropical forest above-ground biomass in Nepal using airborne laser scanning data

The prediction of tropical forest attributes using airborne laser scanning (ALS) is becoming attractive as an alternative to traditional field measurements. Area-based ALS inventories require a set of representative field plots from the study area, which may be difficult to obtain in tropical forests with limited accessibility. This study investigates the effect of sample-plot selection in Nepal, based on two accessibility factors: distance to road and degree of slope. The sparse Bayesian method was employed in the model to estimate above-ground biomass (AGB) with an independent validation dataset for model validation. Study findings showed that the sample plot distance and slope had a considerable effect on the accuracy of the AGB estimation, because the forest structure varied according to the level of accessibility. Thus, the field sample plots that are used in model construction should cover the full range of sample plot distances and slopes occurring within the area.