Analyzing spatial ecological data using linear regression and wavelet analysis

Spatial (two-dimensional) distributions in ecology are often influenced by spatial autocorrelation. In standard regression models, however, observations are assumed to be statistically independent. In this paper we present an alternative to other methods that allow for autocorrelation. We show that the theory of wavelets provides an efficient method to remove autocorrelations in regression models using data sampled on a regular grid. Wavelets are particularly suitable for data analysis without any prior knowledge of the underlying correlation structure. We illustrate our new method, called wavelet-revised model, by applying it to multiple regression for both normal linear models and logistic regression. Results are presented for computationally simulated data and real ecological data (distribution of species richness and distribution of the plant species Dianthus carthusianorum throughout Germany). These results are compared to those of generalized linear models and models based on generalized estimating equations. We recommend wavelet-revised models, in particular, as a method for logistic regression using large datasets.     

A review of numerical experiments on seismic wave scattering

This paper reviews applications of the finite-difference and finite-element methods to the study of seismic wave scattering in both simple and complex velocity models. These numerical simulations have improved our understanding of seismic scattering in portions of the earth where there is significant lateral heterogeneity, such as the crust. The methods propagate complete seismic wavefields through highly complex media and include multiply scattered waves and converted phases (e.g.,P toSV, SV toP, body wave to surface wave). The numerical methods have been especially useful in cases of moderate and strong scattering in complex media where multiple scattering becomes important. Progress has been made with numerical methods in understanding how near-surface, low-velocity basin structures scatter surface waves and vertically-incident body waves. The numerical methods have proven useful in evaluating scattering of surface waves and body waves from topography of both the free surface and interfaces buried at depth. Numerical studies have demonstrated the importance of conversions from body waves to surface waves (andvice versa) when lateral heterogeneities and topographic relief are present in the uppermost crust. Recently, several investigations have applied numerical methods to study seismic wave propagation in velocity models which vary randomly in space. This stochastic approach seeks to understand the effects of small-scale complexity in the earth which cannot be resolved deterministically. These experiments have quantified the relationships between the statistical properties of the random heterogeneity and the measurable properties of high-frequency (1 Hz) seismograms. These simulations have been applied to the study of many features observed in actual high-frequency seismic waves, including: the amplitude and time decay of seismic coda, the apparent attenuation from scattering, the dispersion of waveforms, and the travel time and waveform variations across arrays of receivers.     

相位编码多次波逆时偏移成像

随着勘探地质体复杂度日益增大, 反射波成像面临诸多挑战, 作为有潜力提升成像精度的重要补充或替代手段的多次波成像愈发受到重视.然而, 串扰噪声的产生阻碍了多次波成像的实际应用.近年来, 作为压制串扰噪声的有效技术之一, 可控阶多次波成像取得了较大研究进展, 但因其需重复计算各阶多次波成像结果, 计算成本昂贵.为此, 本文引入随机相位编码技术, 并与多次波分阶思想结合, 提出相位编码多次波逆时偏移方法: 首先, 对各阶多次波进行随机相位编码(含随机时间延迟与极性反转); 其次, 叠加编码后的各阶多次波, 产生多次波超道集; 最后, 以编码后0至(N-1)阶多次波组成的超道集为虚拟震源进行正向延拓, 同时反传编码后1至N阶多次波所组成的超道集, 并进行互相关, 得到各阶多次波联合成像结果.本文所提方法能够同步使用各阶多次波, 实现各阶多次波联合成像, 避免各阶多次波单独进行成像, 从而成倍提升计算效率.本文用两套模拟数据与一套实际数据算例对所提方法进行了测试, 成像结果验证了该方法的可行性、有效性与应用前景.

     

The elastic properties of single-crystal fayalite as determined by dynamical measurement techniques

We present new elasticity measurements on single-crystal fayalite and combine our results with other data from resonance, pulse superposition interferometry, and Brillouin scattering to provide a set of recommended values for the adiabatic elastic moduliC _ij and their temperature variations. We use a resonance method (RPR) with specimens that were previously investigated by pulse superposition experiments. The nineC _ij of fayalite are determined from three new sets of measurements. One set of our newC _ij data is over the range 300–500 K. We believe that the relatively large discrep ncies found in someC _ij are due in large part to specimen inhomogeneities (chemical and microstructural) coupled with differences in the way various techniques sample, rather than only systematic errors associated with experimental procedures or in the preparations of the specimens.Our recommendeaC _ij's (GPa) and (C _ij/T) _p (GPa/K) are: The resulting values for the isotropic bulk and shear moduli,K _s and , and their temperature derivatives are:K _s=134(4) GPa; =50.7(0.3) GPa; (K _s/T) _p =–0.024(0.005) GPa/K; and (/T) _p =–0.013(0.001) GPa/K. An important conclusion is thatK _s increases as the Fe/(Fe+Mg) ratio in olivine is increased.     

Dynamic stress concentration and scattering of SH-wave by interface elliptic cylindrical cavity

In this paper, the dynamic stress concentration and scattering of SH-waves by bi-naterial structures that possess an interface elliptic cavity are investigated. First, by using the complex function method, the Green‘s function is constructed. This yields the solution of the displacement field for an elastic half space with a semi-elliptic canyon impacted by an anti-plane harmonic line source loading on the horizontal surface. Then, the problem is divided into an upper and lower half space along the horizontal interface, regarded as a harmony model. In order to satisfythe integral continuity condition,the unknown anti-plane forces are applied to the interface. The integral equations with unknown forces can be established through the continuity condition, and after transformation, the algebraic equations are solved numerically. Finally, the distribution of the dynamic stress concentration factor (DSCF) around the elliptic cavity is given and the effect of different parameters on DSCF is discussed.     

Time domain solution for multiple scattering and the coda envelopes

This article summarizes work on multiple scattering based on models of media with randomly distributed scatterers. The scatterers are isotropic and statistically uniform. Measuring distance in terms of mean-free pathL _s and time in terms of the mean-free timesL _s/V, whereV is the velocity of scattered waves, we have more convenient dimensionless distance and time. It can be shown that after the dimensionless time equals 0.65 energy contributed from multiple scattering becomes predominant. Thus the later coda reflects the effect of multiple scattering rather than single scattering. Treating the seismic record, including starting and tail parts, as a whole, the diffusion theory predicts that at a dense distribution of scatterers and a small distance between source and receiver, codas reflect mainly intrinsicQ _i. Of course, this conclusion is coincident with the presumption of the diffusion theory,Q _s>Q _i. However, from a new integral equation of multiple scattering, which deals with the scattered waves and primary waves separately, the conclusion is similar but clearer. This article quotes the new expression for coda energy in two-dimensional space. It shows that if the receiver is close to the source, the coda decay reflects only intrinsicQ _i, then as the distance increases, effects of scatteringQ _s, are involved in the decay feature. The theoretical plots of coda decay show that it seems in most cases in the earthQ _i should not be smaller than one tenth ofQ _s.Project Sponsored by the Joint Earthquake Science Foundation of China.     

随机地震动场激励下拱坝多点输入的抗震可靠度分析

本文首次将空间随机地震场输入用于拱坝随机振动分析之中，与拱坝三维动力学有限元法结合，完成了三维拱坝在空间随机地震动场作用下的随机振动分析方法及算法的研究，另外考虑动力和静力的叠加，提出了三维空间随机地震动场的拱坝抗震可靠度分析方法，最后编制了相应的程序，对小湾拱坝进行了抗震可靠度分析，并与随机变量的结果进行了比较。     

高层建筑地震反应最优多重TLD控制

本文以坑层建筑地震反应进行了最优多重ＴＬＤ（ＭＴＬＤ）ｓ控制研究。文中阐述了ＴＬＤ系统的工作原理笔ＭＴＬＤｓ系统的参数；建立了多层结构－ＴＭＬＤｓ系统耦联体系的运动方程；分析了ＭＴＬＤｓ系统的参数对在谐波作用下多层结构动力反应的影响以及各参数之间的关系。     

Weak-contrast approximation of the elastic scattering matrix in anisotropic media

The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified.When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation.For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves.Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media.Presented at the Workshop Meeting on Seismic Waves in Laterally Inhomogeneous Media, Castle of Trest, Czech Republic, May 22–27, 1995.     

CodaQ as a combination of scattering and intrinsic attenuation: Numerical simulations with the boundary integral method

Numerical modelling ofSH wave seismograms in media whose material properties are prescribed by a random distribution of many perfectly elastic cavities and by intrinsic absorption of seismic energy (anelasticity) demonstrates that the main characteristics of the coda waves, namely amplitude decay and duration, are well described by singly scattered waves in anelastic media rather than by multiply scattered waves in either elastic or anelastic media. We use the Boundary Integral scheme developed byBenites et al. (1992) to compute the complete wave field and measure the values of the direct waveQ and coda wavesQ in a wide range of frequencies, determining the spatial decay of the direct wave log-amplitude relation and the temporal decay of the coda envelope, respectively. The effects of both intrinsic absorption and pure scattering on the overall attenuation can be quantified separately by computing theQ values for corresponding models with (anelastic) and without (elastic) absorption. For the models considered in this study, the values of codaQ ^–1 in anelastic media are in good agreement with the sum of the corresponding scatteringQ ^–1 and intrinsicQ ^–1 values, as established by the single-scattering model ofAki andChouet (1975). Also, for the same random model with intrinsic absorption it appears that the singly scattered waves propagate without significant loss of energy as compared with the multiply scattered waves, which are strongly affected by absorption, suggesting its dominant role in the attenuation of coda waves.