海洋环流模式中不同近似假设下的海表高度

Boussinesq近似是现代海洋环流模式中经常采用的假设，但随着海洋模式的不断发展完善以及气候研究应用的需要，有必要估算Boussinesq近似造成的模式误差。分别利用一个非Boussinesq近似的海洋模式与另一个结构相同且采用Boussinesq近似的模式计算海表高度，并同时利用模式预报的温度、盐度资料计算了比容异常高度。分析结果显示，这3种不同定义的海表高度无论空间结构，还是时间演变，都基本类似，尤其在热带海区最接近，差值≤1cm。Boussinesq近似意味着在模式中以体积守恒代替质量守恒，通常的做法是对其进行简单的质量补偿来保持质量守恒。比较说明，以质量补偿方法进行的高度订正对减小Boussinesq近似带来的误差没有本质的意义。     

Estimated intensity needed for sampling flatfish assemblages in reference areas of tidal mud flats systems may be disproportionately costly and deleterious

Beam trawl surveys were carried out in a tidal stream system of the German Wadden Sea on two to three successive days of comparable weather conditions in three summers. The variability in time and space detected for plaice (Pleuronectes platessa), flounder (Platichthys flesus), dab (Limanda limanda), sole (Solea solea) and lemon sole (Microstomus kitt) was considerable even for species with a very high abundance. Other flatfish species such as turbot (Scophthalmus maximus) and brill (Scophthalmus rhombus) occurred only occasionally in the catches. Sampling effort calculated to detect a 50 or 20% difference between the surveys caused by immigration, emigration or mortality appears to be disproportionate. It is argued that such a major sampling effort of reference areas in tidal mud flat systems is likely to influence the results, to harm the environment, and to be very expensive.     

A new approach for predicting the extreme response of structures

In this article a method to estimate the mean upcrossing intensity, μ(u), of a stochastic process is proposed. It is assumed that the stochastic process is a sum of a Gaussian process and a second-order correction term. The method is based on the two-dimensional Saddlepoint approximation. The accuracy of the method is tested on processes having analytical solutions for μ(u). Numerical examples are given where the stochastic process represents (i) the horizontal response of a floating offshore structure in a Gaussian sea, and (ii) the response of a structure subjected to a Gaussian wind velocity process. In addition, the estimates are compared to empirical upcrossing intensities of simulated responses. For case (ii), the obtained μ(u) estimates are compared to estimates obtained by numerical integration.     

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.     

A comparative error analysis of manual versus automated methods of data acquisition for algebraic strain estimation

This paper presents a statistical analysis of the algebraic strain estimation algorithm of Shimamoto and Ikeda [Shimamoto, T., Ikeda, Y., 1976. A simple algebraic method for strain estimation from deformed eillipsoidal objects: 1. Basic theory. Tectonophysics 36, 315–337]. It is argued that the error in their strain estimation procedure can be quantified using an expected discrepancy measure. An analysis of this measure demonstrates that the error is inversely proportional to the number of clasts used. The paper also examines the role of measurement error, in particular that incurred under (i) a moment based and (ii) manual data acquisition methods. Detailed analysis of these two acquisition methods shows that in both cases, the effect of measurement error on the expected discrepancy is small relative to the effect of the sample size (number of objects). Given their relative speed advantage, this result favours the use of automated measurement methods even if they incur more measurement error on individual objects. Validation of these results is carried out by means of a simulation study, as well as by reference to studies appearing in previous literature. The results are also applied to obtain an upper bound on the error of strain estimation for various studies published in the literature on strain analysis.     

Investigating the scale of structural controls on chlorinated hydrocarbon distributions in the fractured-porous unsaturated zone of a sandstone aquifer in the UK

Contaminant migration behaviour in the unsaturated zone of a fractured porous aquifer is discussed in the context of a study site in Cheshire, UK. The site is situated on gently dipping sandstones, adjacent to a linear lagoon historically used to dispose of industrial wastes containing chlorinated solvents. Two cores of more than 100 m length were recovered and measurements of chlorinated hydrocarbons (CHCs), inorganic chemistry, lithology, fracturing and aquifer properties were made. The results show that selecting an appropriate vertical sampling density is crucial both to providing an understanding of contaminant pathways and distinguishing whether CHCs are present in the aqueous or non-aqueous phase. The spacing of such sampling should be on a similar scale to the heterogeneity that controls water and contaminant movement. For some sections of the Permo-Triassic aquifer, significant changes in lithology and permeability occur over vertical distances of less than 1 m and samples need to be collected at this interval, otherwise considerable resolution is lost, potentially leading to erroneous interpretation of data. At this site, although CHC concentrations were high, the consistent ratio of the two main components of the plume (tetrachloroethene and trichloroethene) provided evidence of movement in the aqueous phase rather than in dense non-aqueous phase liquid (DNAPL).     

Effect of sampling and linkage on fault length and length–displacement relationship

The power-law exponent (n) in the equation: D=cL ⁿ , with D = maximum displacement and L = fault length, would be affected by deviations of fault trace length. (1) Assuming n=1, numerical simulations on the effect of sampling and linkage on fault length and length–displacement relationship are done in this paper. The results show that: (a) uniform relative deviations, which means all faults within a dataset have the same relative deviation, do not affect the value of n; (b) deviations of the fault length due to unresolved fault tip decrease the values of n and the deviations of n increase with the increasing length deviations; (c) fault linkage and observed dimensions either increase or decrease the value of n depending on the distribution of deviations within a dataset; (d) mixed deviations of the fault lengths are either negative or positive and cause the values of n to either decrease or increase; (e) a dataset combined from two or more datasets with different values of c and orders of magnitude also cause the values of n to deviate. (2) Data including 19 datasets and spanning more than eight orders of fault length magnitudes (10⁻²–10⁵ m) collected from the published literature indicate that the values of n range from 0.55 to 1.5, the average value being 1.0813, and the peak value of n _d (double regression) is 1.0–1.1. Based on above results from the simulations and published data, we propose that the relationship between the maximum displacement and fault length in a single tectonic environment with uniform mechanical properties is linear, and the value of n deviated from 1 is mainly caused by the sampling and linkage effects.     

Probing mid-mantle heterogeneity using PKP coda waves

We investigate the utility of PKP coda waves for studying weak scattering from small-scale heterogeneity in the mid-mantle. Coda waves are potentially a useful probe of heterogeneity in the mid-mantle because they are not preferentially scattered near the CMB, as PKP precursors are, but are sensitive to scattering at all depths. PKP coda waves have not been used for this purpose historically because of interference with other late-arriving energy due to near-surface resonance and scattering. Any study of deep mantle scattering using coda waves requires the removal of near-surface effects from the data. We have analyzed 3624 recordings of PKP precursors and coda made by stations in the Incorporated Research Institutions for Seismology (IRIS) Global Seismographic Network (GSN). To study the range and time dependence of the scattered waves, we binned and stacked envelopes of the recordings. We have considered precursors that arrive within a 20 s window before PKP and coda waves in a 60 s window after PKP. The PKP scattered waves increase in amplitude rapidly with range as predicted by scattering theory. At ranges below 125°, we predict and observe essentially no scattered energy preceding PKP. Coda amplitudes at these ranges are independent of range and provide an estimate of energy due to near-surface effects that we can expect at all ranges. We use the average coda amplitude at ranges from 120 to 125° to correct coda amplitudes at other ranges. PKP coda waves show a strong dependence on time and range and are clearly influenced by scattering in the lower mantle. PKP coda waves, however, do not provide a tighter constraint on the vertical distribution of mantle heterogeneity than is provided by precursors. This is due, in part, to relatively large scatter in coda amplitudes as revealed by a resampling analysis. Modeling using Rayleigh–Born scattering theory and an exponential autocorrelation function shows that PKP coda amplitudes are not highly sensitive to the vertical distribution of heterogeneity in the mantle. To illustrate this we consider single-scattering in two extreme models of mantle heterogeneity. One allows heterogeneity just at the CMB; the other includes heterogeneity throughout the mantle. The amplitudes of precursors are tightly constrained by our stack and support our earlier conclusion that small-scale heterogeneity is uniformly distributed throughout the lower mantle. The best-fit model includes 8 km scale length heterogeneity with an rms velocity contrast throughout the mantle of 1%.