On the use of Empirical Orthogonal Function (EOF) analysis in the simulation of random fields

In several fields of Geophysics, such as Hydrology, Meteorology or Oceanography, it is often useful to generate random fields, displaying the same variabilitity as the observed variables. Usually, these synthetic data are used as forcing fields into numerical models, to test the sensitivity of their outputs to the variability of the inputs. Examples can be found in subsurface or surface Hydrology and in Meteorology with General Circulation Models (GCM). Different techniques have already been proposed, often based on the spectral representation of the random process, with, usually, assumptions of stationarity. This paper suggests that Empirical Orthogonal Function (EOF) analysis, which leads to the decomposition of the covariance kernel on the set of its eigen-functions, is a possible answer to this problem. The convergence and accuracy of the method are shown to depend mainly on the number of EOFs retained in the expansion of the covariance kemel. This result is confirmed by a comparison with the turning band method and a matrix technique. Furthermore, a synthetic example of non-homogencous fields shows the interest of EOF analysis in the direct simulation of such fields.     

Edge wave and non-trapped modes of the 25 april 1992 Cape Mendocino tsunami

The 25 April 1992 Cape Mendocino earthquake generated a tsunami characterized by both coastal trapped edge wave and non-trapped tsunami modes that propagated north and south along the U.S. West Coast. Both observed and synthetic time series at Crescent City and North Spit are consistent with the zero-order edge wave mode solution for a semi-infinite sloping beach depth profile. Wave amplitudes at Crescent City were about twice that observed at North Spit, in spite of the fact that the source region was three times farther from Crescent City than North Spit. The largest observed amplitude was due to an edge wave which arrived almost three hours after the initial onset of the tsunami; since such waves are highly localized nearshore, this suggests that the enhanced responsiveness at Crescent City is at least partly due to local dynamic processes. Furthermore, the substantially delayed arrival of this wave, which was generated at the southern end of the Cascadia Subduction Zone, has significant implications for hazard mitigation efforts along the entire U.S. West Coast. Specifically, this study demonstrates that slow-moving but very energetic edge wave modes could be generated by future large tsunamigenic earthquakes in the CSZ, and that these might arrive unexpectedly at coastal communities several hours after the initial tsunami waves have subsided.     

Empirical Orthogonal Function (EOF) analysis of spatial random fields: Theory,accuracy of the numerical approximations and sampling effects

Empirical Orthogonal Function (EOF) analysis of spatial random fields involves calculation of the eigenfunctions of the covariance kernel of the field. For real-world applications, a numerical approximation is necessary because the process is spatially discretized. An approximation for two-dimensional fields is proposed and then, analytical solutions of the integral problem are derived and used to study the accuracy of the numerical approximations. Sampling effects are also considered.     

Simulation and analysis of point-source surface wave fields

The complexity of near surface intensifies the diversity of seismic wave fields, which makes study on near surface wavefields important in many aspects. The strong absorption of low velocity layer can affect the resolution of seismic data, and free boundary can cause surface wave. Considering the above problems, we focus on the Rayleigh wavefields simulation using finite-difference wave equation of higher-order staggered grids and PML boundary conditions. Free boundary, buried source and overlying low velocity layer are taken into consideration and point explosion source is adopted. Through some numerical simulation with different parameters, we quantitatively analyze relationship between wave intensity and source depth, as well as the energy variation with propagation and obtain some practical knowledge and conclusions.     

Reconstructing Regional Ionospheric Electron Density: A Combined Spherical Slepian Function and Empirical Orthogonal Function Approach

The computerized ionospheric tomography is a method for imaging the Earth’s ionosphere using a sounding technique and computing the slant total electron content (STEC) values from data of the global positioning system (GPS). The most common approach for ionospheric tomography is the voxel-based model, in which (1) the ionosphere is divided into voxels, (2) the STEC is then measured along (many) satellite signal paths, and finally (3) an inversion procedure is applied to reconstruct the electron density distribution of the ionosphere. In this study, a computationally efficient approach is introduced, which improves the inversion procedure of step 3. Our proposed method combines the empirical orthogonal function and the spherical Slepian base functions to describe the vertical and horizontal distribution of electron density, respectively. Thus, it can be applied on regional and global case studies. Numerical application is demonstrated using the ground-based GPS data over South America. Our results are validated against ionospheric tomography obtained from the constellation observing system for meteorology, ionosphere, and climate (COSMIC) observations and the global ionosphere map estimated by international centers, as well as by comparison with STEC derived from independent GPS stations. Using the proposed approach, we find that while using 30 GPS measurements in South America, one can achieve comparable accuracy with those from COSMIC data within the reported accuracy (1 × 10¹¹ el/cm³) of the product. Comparisons with real observations of two GPS stations indicate an absolute difference is less than 2 TECU (where 1 total electron content unit, TECU, is 10¹⁶ electrons/m²).     

港湾中海啸流的模拟及其时空演变特征对输入条件不确定性的响应分析

一直以来,海啸波特征作为表征海啸潜在破坏性的参数指标得到了广泛应用,特别是针对近场极端海啸事件造成的灾害来说,这种表征具有较好的适用性.然而总结分析历史海啸事件造成的损失发现：在远场近岸及港湾系统中,海啸诱导的强流却是造成损失的主要原因.陆架或港湾振荡导致海啸波幅快速升降诱发强流,可能促使港工设施受到威胁及损害,进而对海啸预警服务及海事应急管理提出了新的挑战.因此,全面理解与评估海啸在港湾中诱发的灾害特征,探索港湾中海啸流的数值模拟方法,发展针对港湾尺度的海啸预警服务指导产品尤为迫切.受限于海啸流验证数据的缺乏及准确模拟海啸流技术方法的诸多不确定性,大部分海啸数值模拟研究工作主要是针对水位特征的研究及验证,可能导致对港湾中海啸灾害危险性认识的曲解与低估.本研究基于非线性浅水方程,针对夏威夷群岛三个典型港湾建立了精细化海啸数值模型（空间分辨率达到10 m）,并联合有限断层破裂模型计算分析了日本东北地震海啸在三个港湾及其邻近区域的海啸特征,波、流计算结果与实测结果吻合较好,精细化的海啸港湾模型模拟结果可信.模拟发现港湾中较小的波幅,同样可以产生强流.综合分析日本东北地震海啸波、流特征对输入条件不确定性的响应结果发现：港湾中海啸波-流能量的空间分布特征差异较大,这与港湾系统中海啸波的驻波特性相关;相比海啸波幅空间特征,海啸流特征具有更强的空间敏感性;海啸流时空分布特征对输入条件的不确定性响应比海啸波幅对这些不确定性的响应更强,海啸流的模拟与预报更有挑战性;不确定性对海啸流计算精度的影响会进一步传导放大港湾海啸流危险性的评估及对港工设施产生的应力作用的误差,合理的输入条件对海啸流的精确模拟至关重要.最后,希望通过本文的研究可以从海啸波-流特征角度更加全面认识近岸海啸灾害特征,拓展海啸预警服务的广度与深度,从而为灾害应急管理部门提供更加科学合理的辅助决策产品.

     

SVD地震波场分离与去噪技术在鄂尔多斯盆地地震资料处理中的应用

针对鄂尔多斯盆地地区地震资料自身的特点,本文依据地震信号传播的特性和波场之间的差异,通过多域(多种线性变换域和频域)奇异值分解(SVD),然后提取目标信号的奇异值重构地震信号的方法,实现地震波场分离与去噪处理.与传统SVD地震波场分离与去噪技术相比较,该方法的目的性更强,直接针对感兴趣的地震信号成分进行SVD波场分离与去噪,在提高地震资料信噪比的同时,确保了信号的高保真度和分辨率;同时,避免了以往SVD技术应用空间狭窄,有效信号损失严重等缺陷性.从实际资料处理结果来看,取得了较好的效果.     

Empirical criteria for liquefaction in sands via standard penetration tests and seismic wave energy

Five empirical equations are presented, describing initiation of liquefaction in fully saturated sands, in terms of standard penetration values and initial overburden stress on level ground. These equations are based on 90 case histories of liquefaction, and relate empirically the pore pressure increase to earthquake magnitude, epicentral distance, energy of strong motion at the site, peak ground velocity, Fourier amplitude of velocity and duration of strong motion. The results are given in terms of raw standard penetration values corrected for overburden pressure. For all the models presented, the standard deviation of the residuals, representing the differences between the observed and predicted penetration values is less than six blow counts.     

关于高铁地震波场虚拟道集生成的理论分析

中国约80%的高铁运行于高架桥上, 高铁振动通过桥墩传入地面.本文对运行于等间隔桥墩的高架桥上高铁振动产生的地下地震波场形态进行了理论分析, 根据其在特定方向形成相干相位稳相点区域的特征, 设计了一种基于多个不同速度高铁列车振动记录叠加, 分离单桥墩激发虚拟地震波场的方法, 并对单层与多层介质的情形进行了理论验证.

     

山东日照地区沿海海啸探析

从概念上区分风暴潮和地震海啸,讨论风暴潮和地震海啸的形成、分布;通过对中国大陆沿海地震海啸和大陆架情况的分析,认为山东日照地区沿海既不具备形成地震海啸的条件,也不可能受非本地地震海啸的影响。日照沿海遭受的海洋灾害主要是风暴潮。     

水平分层孔隙介质中点源激发的震电波场数值模拟及分析

为认识地震波诱导的电磁场的特性,本文研究地震波在孔隙介质中由于动电效应引起的电磁场.基于Pride弹性-电磁耦合方程组推导了双力偶震源对应的位移-应力-电磁场间断向量的表达式,模拟了双力偶源激发的震电波场.作为比较,还模拟了爆炸点源激发的震电波场.结果表明：存在伴随纵波的电场,其各分量的波形与固相位移对应分量的波形相似,但相位相反;存在伴随横波的磁场,其波形与固相位移波形相似;双力偶震源还激发出了独立传播的辐射电磁场,其速度比纵波至少高一个数量级,几乎是“瞬间同时”到达了每个接收器,但是其强度比伴随电磁场小得多,且随着源距增大而迅速减小.本文研究还表明：伴随纵波的电场强度不仅与地震纵波幅度和动电耦合系数有关,还与由介质孔隙结构决定的流-固两相动力协调性有关,存在一种动力协调介质,纵波在这种介质中不引起电场.     

Numerical simulations of full-wave fields and analysis of channel wave characteristics in 3-D coal mine roadway models

Currently, numerical simulations of seismic channel waves for the advance detection of geological structures in coal mine roadways focus mainly on modeling twodimensional wave fields and therefore cannot accurately simulate three-dimensional (3-D) full-wave fields or seismic records in a full-space observation system. In this study, we use the first-order velocity–stress staggered-grid finite difference algorithm to simulate 3-D full-wave fields with P-wave sources in front of coal mine roadways. We determine the three components of velocity V_x, V_y, and V_z for the same node in 3-D staggered-grid finite difference models by calculating the average value of V_y, and V_z of the nodes around the same node. We ascertain the wave patterns and their propagation characteristics in both symmetrical and asymmetric coal mine roadway models. Our simulation results indicate that the Rayleigh channel wave is stronger than the Love channel wave in front of the roadway face. The reflected Rayleigh waves from the roadway face are concentrated in the coal seam, release less energy to the roof and floor, and propagate for a longer distance. There are surface waves and refraction head waves around the roadway. In the seismic records, the Rayleigh wave energy is stronger than that of the Love channel wave along coal walls of the roadway, and the interference of the head waves and surface waves with the Rayleigh channel wave is weaker than with the Love channel wave. It is thus difficult to identify the Love channel wave in the seismic records. Increasing the depth of the receivers in the coal walls can effectively weaken the interference of surface waves with the Rayleigh channel wave, but cannot weaken the interference of surface waves with the Love channel wave. Our research results also suggest that the Love channel wave, which is often used to detect geological structures in coal mine stopes, is not suitable for detecting geological structures in front of coal mine roadways. Instead, the Rayleigh channel wave can be used for the advance detection of geological structures in coal mine roadways.     

Fidelity and repeatability of wave fields reconstructed from multicomponent streamer data

Wave field reconstruction – the estimation of a three‐dimensional (3D) wave field representing upgoing, downgoing or the combined total pressure at an arbitrary point within a marine streamer array – is enabled by simultaneous measurements of the crossline and vertical components of particle acceleration in addition to pressure in a multicomponent marine streamer. We examine a repeated sail line of North Sea data acquired by a prototype multicomponent towed‐streamer array for both wave field reconstruction fidelity (or accuracy) and reconstruction repeatability. Data from six cables, finely sampled in‐line but spaced at 75 m crossline, are reconstructed and placed on a rectangular data grid uniformly spaced at 6.25 m in‐line and crossline. Benchmarks are generated using recorded pressure data and compared with wave fields reconstructed from pressure alone, and from combinations of pressure, crossline acceleration and vertical acceleration. We find that reconstruction using pressure and both crossline and vertical acceleration has excellent fidelity, recapturing highly aliased diffractions that are lost by interpolation of pressure‐only data. We model wave field reconstruction error as a linear function of distance from the nearest physical sensor and find, for this data set with some mismatched shot positions, that the reconstructed wave field error sensitivity to sensor mispositioning is one‐third that of the recorded wave field sensitivity. Multicomponent reconstruction is also more repeatable, outperforming single‐component reconstruction in which wave field mismatch correlates with geometry mismatch. We find that adequate repeatability may mask poor reconstruction fidelity and that aliased reconstructions will repeat if the survey geometry repeats. Although the multicomponent 3D data have only 500 m in‐line aperture, limiting the attenuation of non‐repeating multiples, the level of repeatability achieved is extremely encouraging compared to full‐aperture, pressure‐only, time‐lapse data sets at an equivalent stage of processing.     

A practical method for analysis of river waves and for kinematic wave routing in natural channel networks

The behaviour of river waves is described using a simplified dimensionless form of the momentum equation in conjunction with the continuity equation. Three dimensionless parameters were derived based on a quantitative linear analysis. These parameters, which depend on the Froude number of the steady uniform flow and the geometric characteristics of the river, permit quantification of the influence of inertia and pressure in the momentum equation. It was found that dynamic and diffusion waves occur mainly on gentle channel slopes and the transition between them is characterized by the Froude number. On the other hand, the kinematic wave has a wide range of applications. If the channel slope is greater than 1%, the kinematic wave is particularly suitable for describing the hydraulics of flow. Since slopes in natural channel networks are often greater than 1%, an analytical solution of the linearized kinematic wave equation with lateral inflow uniformly distributed along the channel is desirable and was therefore derived. The analytical solution was then implemented in a channel routing module of an existing simple rainfall–runoff model. The results obtained using the analytical solution compared well with those obtained from a non‐linear kinematic wave model. Copyright © 2000 John Wiley & Sons, Ltd.     

Identification of lateral discontinuities via multi‐offset phase analysis of surface wave data

Surface wave methods are based on the inversion of observed Rayleigh wave phase‐velocity dispersion curves. The goal is to estimate mainly the shear‐wave velocity profile of the investigated site. The model used for the interpretation is 1D, hence results obtained wherever lateral variations are present cannot be considered reliable. In this paper, we study four synthetic models, all with a lateral heterogeneity. When we process the entire corresponding seismograms with traditional f‐k approach, the resulting 1D profiles are representative of the subsurface properties averaged over the whole length of the receivers lines. These results show that classical analysis disregards evidences of sharp lateral velocity changes even when they show up in the raw seismograms. In our research, we implement and test over the same synthetic models, a novel robust automated method to check the appropriateness of 1D model assumption and locate the discontinuities. This new approach is a development of the recent multi‐offset phase analysis with the following further advantages: it does not need previous noise evaluation and more than one shot. Only once the discontinuities are clearly identified, we confidently perform classical f‐k dispersion curve extraction and inversion separately on both sides of the discontinuity. Thus the final results, obtained by putting side by side the 1D profiles, are correct 2D reconstructions of the discontinuous S‐wave distributions obtained without any additional ad‐hoc hypotheses.     

Empirical fragility analysis of building damage caused by the 2011 Great East Japan tsunami in Ishinomaki city using ordinal regression,and influence of key geographical features

Tsunamis are disastrous events typically causing loss of life, and extreme damage to the built environment, as shown by the recent disaster that struck the East coast of Japan in 2011. In order to quantitatively estimate damage in tsunami prone areas, some studies used a probabilistic approach and derived fragility functions. However, the models chosen do not provide a statistically sound representation of the data. This study applies advanced statistical methods in order to address these limitations. The area of study is the city of Ishinomaki in Japan, the worst affected area during the 2011 event and for which an extensive amount of detailed building damage data has been collected. Ishinomaki city displays a variety of geographical environments that would have significantly affected tsunami flow characteristics, namely a plain, a narrow coast backed up by high topography (terrain), and a river. The fragility analysis assesses the relative structural vulnerability between these areas, and reveals that the buildings surrounding the river were less likely to be damaged. The damage probabilities for the terrain area (with relatively higher flow depths and velocities) were lower or similar to the plain, which confirms the beneficial role of coastal protection. The model diagnostics show tsunami flow depth alone is a poor predictor of tsunami damage for reinforced concrete and steel structures, and for all structures other variables are influential and need to be taken into account in order to improve fragility estimations. In particular, evidence shows debris impact contributed to at least a significant amount of non-structural damage.     

利用地震噪声准实时监测短周期面波波速变化

依据由噪声信号提取面波格林函数的原理,利用福建省地震台网25个宽频带台站2007年7月2日—8月29日的脉动观测资料,得到了瑞雷波群速度在福建地区的分布,并将该结果作为下一步相对变化动态成像的背景速度分布．分布结果表明,福建地区周期为3—5s的瑞雷波群速度大致在2.9—3.1km/s之间,平均速度为3.0km/s,瑞雷波群速度分布呈北高南低的现象,这与福建地区北部多山、南部多平原盆地的地理环境有很好的吻合．而且,该群速度分布图在漳州盆地地区表现出一个非常明显的低速,这主要是因为受到盆地沉积层的影响．通过滑动窗（窗长为20d,步长1d）技术得到了观测区内周期约为3-5s的瑞雷波波速分布变化的连续图像;再利用扣除背景影响的技术,得到了2007年8月14日—2008年7月1日福建地区瑞雷波波速的相对变化时空动态图像．通过分析相对变化时空动态图像与该时间范围内发生的地震的对应关系,表明福建地区瑞雷波波速在多次网内中等强度的地震或震群（ML＞3.0）中均表现出震前波速升高,震后下降恢复的变化趋势．初步分析认为,这可能与震前整个地区受到的应力增大震后应力得到释放所导致的介质变化有关．