Research Note: A workaround for the corner problem in numerically exact non-reflecting boundary conditions

Simulations of wave propagation in the Earth usually require truncation of a larger domain to the region of interest to keep computational cost acceptable. This introduces artificial boundaries that should not generate reflected waves. Most existing boundary conditions are not able to completely suppress all the reflected energy, but suffice in practice except when modelling subtle events such as interbed multiples. Exact boundary conditions promise better performance but are usually formulated in terms of the governing wave equation and, after discretization, still may produce unwanted artefacts. Numerically exact non-reflecting boundary conditions are instead formulated in terms of the discretized wave equation. They have the property that the numerical solution computed on a given domain is the same as one on a domain enlarged to the extent that waves reflected from the boundary do not have the time to reach the original truncated domain. With a second- or higher-order finite-difference scheme for the one-dimensional wave equation, these boundary conditions follow from a recurrence relation. In its generalization to two or three dimensions, a recurrence relation was only found for a single non-reflecting boundary on one side of the domain or two of them at opposing ends. The other boundaries should then be zero Dirichlet or Neumann. If two non-reflecting boundaries meet at a corner, translation invariance is lost and a simple recurrence relation could not be found. Here, a workaround is presented that restores translation invariance by imposing classic, approximately non-reflecting boundary conditions on the other sides and numerically exact ones on the two opposing sides that otherwise would create the strongest reflected waves with the classic condition. The exact ones can also be applied independently. As a proof of principle, the method is applied to the two-dimensional acoustic wave equation, discretized on a rectangular domain with a second-order finite-difference scheme and first-order Enquist–Majda boundary conditions as approximate ones. The method is computationally costly but has the advantage that it can be reused on a sequence of problems as long as the time step and the sound speed values next to the boundary are kept fixed.     

Estimation of a non-stationary prior covariance from seismic data

Non-stationarity in statistical properties of the subsurface is often ignored. In a classical linear Bayesian inversion setting of seismic data, the prior distribution of physical parameters is often assumed to be stationary. Here we propose a new method of handling non-stationarity in the variance of physical parameters in seismic data. We propose to infer the model variance prior to inversion using maximum likelihood estimators in a sliding window approach. A traditional, and a localized shrinkage estimator is defined for inferring the prior model variance. The estimators are assessed in a synthetic base case with heterogeneous variance of the acoustic impedance in a zero-offset seismic cross section. Subsequently, this data is inverted for acoustic impedance using a non-stationary model set up with the inferred variances. Results indicate that prediction as well as posterior resolution is greatly improved using the non-stationary model compared with a common prior model with stationary variance. The localized shrinkage predictor is shown to be slightly more robust than the traditional estimator in terms of amplitude differences in the variance of acoustic impedance and size of local neighbourhood. Finally, we apply the methodology to a real data set from the North Sea basin. Inversion results show a more realistic posterior model than using a conventional approach with stationary variance.     

太湖梅梁湾沉积岩芯元素地球化学记录的多元统计分析

通过沉积岩芯元素含量垂直分布和富集因子分析,结合多元统计方法如系统聚类和模糊聚类分析,研究了太湖梅梁湾沉积岩芯元素地球化学记录的湖泊环境演化过程.以系统聚类分析和模糊聚类分析为基础,将梅梁湾地球化学记录的环境过程划分为如下几个层段:0-6cm为人类活动强烈干扰的阶段,25-50cm和55-72cm层段都是自然过程的表现,反映了流域物源的影响,而两层段元素记录的差异反映了不同自然作用驱动下的湖泊环境变化;6-25cm和50-55cm层段则是不同环境特征的过渡阶段,因此,综合应用多元统计方法可以更直观更精确地量化影响湖泊环境的因素,有助于恢复湖泊环境历史演化过程.     

Determining flow patterns and emplacement dynamics from tsunami deposits with no visible sedimentary structure

In the absence of eyewitness reports or clear sedimentary structures, it can be difficult to interpret tsunami deposits or reconstruct tsunami inundation patterns. The emplacement dynamics of two historical tsunami deposits were investigated at seven transects in Okains Bay, New Zealand, using a combined geospatial, geomagnetic and sedimentological approach. The tsunami deposits are present as layers of sand and silt intercalated between soils and become finer and thinner with distance inland. The deposits are attributed to the 1960 and possibly the 1868 tsunamis, based on radiometric dating and correlation with historical records. Measurements of Magnetic Fabric (MF: Anisotropy of Magnetic Susceptibility) and particle size were used to reconstruct the evolution of flow dynamics laterally and vertically. A combination of statistical methods, including spatial autocorrelation testing, Spearman's rank order correlation, Principal Component Analysis (PCA) and K‐means cluster analysis, was applied to examine relationships between MF parameters and sediment texture, and infer depositional hydrodynamics. Flow patterns deduced from MF show the estuary channel acted as a conduit for inundation, with flow commonly aligned sub‐perpendicular to the estuary bed. MF and sediment data suggest deposition occurred from settling during laminar flow. Evidence of both uprush and backwash deposition, as well as wave reflection from infrastructure, was found. Statistical analysis of data showed significant relationships between grain size parameters and MF parameters associated with flow speed and magnetic fabric type. PCA and cluster analysis differentiated samples into two primary hydrodynamic groups: (1) samples deposited from laminar flow; and (2) samples deposited close to the limit of inundation, which includes samples deposited further inland, those affected by flow convergence, and those in the upper part of tsunami deposits. This approach has potential as a tool for reconstructing hydrodynamic conditions for palaeotsunamis and by combining spatial and statistical analyses, large‐scale investigations can be more easily performed. Copyright © 2016 John Wiley & Sons, Ltd.     

Inter-annual Arcellinida (testate lobose amoebae) assemblage dynamics within lacustrine environments

Arcellinida (testate lobose amoebae) were examined from 22 surface-sediment samples collected from homogenous environments in eastern Canadian lakes (Lac du Castor Blanc, SW Quebec; Oromocto Lake, SW New Brunswick) to: 1) evaluate the faunal consistency of assemblages within the targeted environments; and, 2) assess the Arcellinida assemblage response evident in samples collected from Oromocto Lake in 2010 CE (n = 10) and 2012 CE (n = 6) to inter-annual changes in environmental conditions. Cluster analysis and detrended correspondence analysis (DCA), redundancy analysis (RDA), and Bray-Curtis Dissimilarity Matrix (BCDM) were used to identify the dominant arcellinidan assemblages, determine physicochemical controls over the Arcellinida distribution, and assess the assemblages’ faunal homogeneity, respectively. Cluster analysis, DCA, and BCDM results revealed two distinct and relatively homogenous arcellinidan assemblages: 1) Lac du Castor Blanc Assemblage; and 2) Oromocto Lake Assemblage, which could further be subdivided into Oromocto Lake 2010 CE (OL10), and 2012 CE (OL12) sub-assemblages. RDA results showed that 65.6% of the variance in the arcellinidan distribution could be attributed to four significant parameters; sand size fraction (32.1%), calcium (29.2%), manganese (2.7%), and organic content (1.5%). The OL10 and OL12 sub-assemblages aligned well with the respective sample collection dates of 2010 CE and 2012 CE, with proportions of the healthy-lake-indicating Diffluggiid taxa being higher in OL12, likely due to a concurrent slight increase in substrate organic content in the 2012 CE sediments. Our results confirm the faunal homogeneity of assemblages in limnologically similar environments, and demonstrate the rapid response of Arcellinida assemblages to changes in lake conditions at inter-annual time scales.     

The magnetotelluric impedance tensor through Clifford algebras: part II — a constrained stochastic heuristic method for recovering the magnetotelluric regional impedance tensor in 2D/3D case

A method for obtaining the galvanic distortion matrix is presented so that the regional impedance tensor (free of distortion) is recovered. The method is a constrained stochastic heuristic method, which consists in randomly exploring the space of the distortion parameters. Constraints are imposed on the shortest periods of the regional impedance tensor that, at these short periods, tends to be two dimensional (or one dimensional). Depending on the constraints used, two different methods to recover the regional impedance tensor in this 2D/3D case are presented. Method 1 needs to find the strike of the short periods and Method 2 applies to the measurement directions. Twist, shear and anisotropy parameters are obtained. Thus, the regional impedance tensor is recovered with the only exception being the vertical shift due to the gain, which is equal for all the components of the tensor. Examples with synthetic impedance tensors from 2D/3D models perturbed with galvanic distortion are presented to illustrate how the algorithm works. The presence of noise in data is considered and rules for proceeding are provided. The same examples perturbed by Gaussian noise together with experimental data illustrate the capabilities of the algorithm.     

基于空间差异的黑河中游土地多功能利用研究

土地多功能利用是提高土地利用综合效率、协调用地矛盾的有效途径。选择人地关系较活跃的黑河中游为研究区,融合多源数据,采用集对分析、热点分析和空间自相关等方法,对2000-2014年土地多功能利用进行动态评价及空间关系揭示。结果表明：土地利用功能增加了近一倍,以社会功能和经济功能为主;各功能之间表现为协同或互斥关系：社会功能和经济功能、环境功能和文化功能之间均呈正相关关系,但社会功能和环境功能之间呈负相关关系;土地利用各功能均具有明显的空间聚集性特点,多功能利用集中在黑河水系形成的绿洲平原区、区县建成区和南部山区。研究结果对干旱区土地持续利用管理具有重要的借鉴意义。     

非洲沿海国家海洋渔业资源开发利用现状

根据联合国粮农组织提供的1950-2015年非洲渔获生产统计数据,结合Fishbase提供的相关鱼种营养级（Trophic level, TL）以及Sea Around Us Project Database提供的海洋无脊椎动物营养级,探讨了1950-2015年北非、东非、南非、中非和西非的沿海国家渔获物平均营养级（Mean trophic level, MTL）的变化情况,以此来判定非洲沿海国海洋渔业资源的开发利用现状。结果表明：非洲沿海国家的海洋渔业资源开采大致经历开发不足、快速开发、过度开发阶段,1984-1991年,北非地区的海洋渔业资源遭到一定程度的破坏,高营养级渔业资源渔获量减少了33.5%,MTL由3.44降低到3.25;东非地区渔获量较其他4个区域低,目前,大部分鱼类资源处于充分捕捞利用状态;南非地区在21世纪初发生“捕捞降低海洋食物网”现象,2004-2015年,MTL恢复小幅上升趋势,渔业均衡指数（Fishing-in-balance index, FIB）趋于平稳;2013-2015年,中非地区的MTL与FIB均呈下降趋势,说明产量的增加速度不足以弥补营养级的降低,生态系统结构功能开始遭到破坏;1950-2015年,西非地区的渔获量不断增加,从上世纪60年代开始,过度捕捞现象愈加严重,低营养级鱼类数量占比呈先减少后增加趋势,2001-2012年,MTL波动下降,FIB平稳变化,说明MTL的下降由产量的增加而抵消。21世纪以来,部分北非、南非与西非沿海国家加强了资源管理,渔业资源状况有所好转。研究认为：渔获物平均营养级的下降主要由过度捕捞引起,非洲国家的管理不力加重了过度捕捞现象,建议非洲各国尽快建立起基于渔获物统计的海洋渔业资源实时监测系统,以便掌握捕捞活动下的鱼类群落结构的变动情况。     

Computational reproducibility in geoscientific papers: Insights from a series of studies with geoscientists and a reproduction study

Reproducibility is a cornerstone of science and thus for geographic research as well. However, studies in other disciplines such as biology have shown that published work is rarely reproducible. To assess the state of reproducibility, specifically computational reproducibility (i.e. rerunning the analysis of a paper using the original code), in geographic research, we asked geoscientists about this topic using three methods: a survey (n = 146), interviews (n = 9), and a focus group (n = 5). We asked participants about their understanding of open reproducible research (ORR), how much it is practiced, and what obstacles hinder ORR. We found that participants had different understandings of ORR and that there are several obstacles for authors and readers (e.g. effort, lack of openness). Then, in order to complement the subjective feedback from the participants, we tried to reproduce the results of papers that use spatial statistics to address problems in the geosciences. We selected 41 open access papers from Copernicus and Journal of Statistical Software and executed the R code. In doing so, we identified several technical issues and specific issues with the reproduced figures depicting the results. Based on these findings, we propose guidelines for authors to overcome the issues around reproducibility in the computational geosciences.