中国西部及邻区的地壳三维速度结构

用网格频散反演技术计算了155条瑞利面波混合频散数据,将中国大陆分为目前最小分格2°×2°,得到了中国西部及邻区深至80km地壳和上地幔顶部的三维剪切波SV速度结构。结果表明:(1)天山褶皱系地壳平均厚度为54km,上地壳平均速度为3.3km/s,下壳平均速度3.93km/s,上地幔盖层平均速度为4.64km/s,都偏大。北天山壳厚比天山薄,壳和上地幔盖层下均有低速层。(2)塔里木盆地中部地壳厚46km,到其边缘的昆仑山、天山地带壳厚增加到52～55km。壳内无低速层,壳平均速度很低,为3.49km/s,地表有9km的沉积层。(3)青藏高原莫霍面呈凹形,平均壳厚为67km,平均壳速度为3.58km/s。东西端存在壳内低速层,埋深为15～35km。(4)南北带为构造复杂的区域,莫霍面深度具有东高西低,南北两端高、中间低的特点,带内普遍存在壳内低速层。南北带从群速度、速度、莫霍面等深线都可看到明显的横向差异。(5)准噶尔盆地地壳厚47km,无壳内低速层,中地壳不明显。该区呈稳定的大陆壳结构。(6)柴达木盆地在正常速度的中壳顶部有一高速夹层,速度为3.72km/s,厚10km,上顶部埋深14km。     

Stochastic perturbation analysis of groundwater flow. Spatially variable soils,semi-infinite domains and large fluctuations

As is well known, a complete stochastic solution of the stochastic differential equation governing saturated groundwater flow leads to an infinite hierarchy of equations in terms of higher-order moments. Perturbation techniques are commonly used to close this hierarchy, using power-series expansions. These methods are applied by truncating the series after a finite number of terms, and products of random gradients of conductivity and head potential are neglected. Uncertainty regarding the number or terms required to yield a sufficiently accurate result is a significant drawback with the application of power series-based perturbation methods for such problems. Low-order series truncation may be incapable of representing fundamental characteristics of flow and can lead to physically unreasonable and inaccurate solutions of the stochastic flow equation. To support this argument, one-dimensional, steady-state, saturated groundwater flow is examined, for the case of a spatially distributed hydraulic conductivity field. An ordinary power-series perturbation method is used to approximate the mean head, using second-order statistics to characterize the conductivity field. Then an interactive perturbation approach is introduced, which yields improved results compared to low-order, power-series perturbation methods for situations where strong interactions exist between terms in such approximations. The interactive perturbation concept is further developed using Feynman-type diagrams and graph theory, which reduce the original stochastic flow problem to a closed set of equations for the mean and the covariance functions. Both theoretical and practical advantages of diagrammatic solutions are discussed; these include the study of bounded domains and large fluctuations.     

Conditioning mean steady state flow on hydraulic head and conductivity through geostatistical inversion

Nonlocal moment equations allow one to render deterministically optimum predictions of flow in randomly heterogeneous media and to assess predictive uncertainty conditional on measured values of medium properties. We present a geostatistical inverse algorithm for steady-state flow that makes it possible to further condition such predictions and assessments on measured values of hydraulic head (and/or flux). Our algorithm is based on recursive finite-element approximations of exact first and second conditional moment equations. Hydraulic conductivity is parameterized via universal kriging based on unknown values at pilot points and (optionally) measured values at other discrete locations. Optimum unbiased inverse estimates of natural log hydraulic conductivity, head and flux are obtained by minimizing a residual criterion using the Levenberg-Marquardt algorithm. We illustrate the method for superimposed mean uniform and convergent flows in a bounded two-dimensional domain. Our examples illustrate how conductivity and head data act separately or jointly to reduce parameter estimation errors and model predictive uncertainty.This work is supported in part by NSF/ITR Grant EAR-0110289. The first author was additionally supported by scholarships from CONACYT and Instituto de Investigaciones Electricas of Mexico. Additional support was provided by the European Commission under Contract EVK1-CT-1999-00041 (W-SAHaRA-Stochastic Analysis of Well Head Protection and Risk Assessment).     

Another look at the conceptual fundamentals of porous media upscaling

We suggest a critical look at the epistemic foundations of the porous media upscaling problem that focuses on conceptual processes at work and not merely on form manipulations. We explore the way in which critical aspects of scientific methodology make their appearance in the upscaling context, thus generating useful effective parameters in practice. The fons et origo of our approach is a conceptual blending of knowledge states that requires the revision of the traditional method of scientific argument underlying most upscaling techniques. By contrast to previous techniques, the scientific reasoning of the proposed upscaling approach is based on a stochastic model that involves teleologic solutions and stochastic logic integration principles. The syllogistic form of the approach has important advantages over the traditional reasoning scheme of porous media upscaling, such as: it allows the rigorous derivation of the joint probability distributions of hydraulic gradients and conductivities across space; it imposes no restriction on the functional form of the effective parameters or the shape of the probability laws governing the random media (non-Gaussian distributions, multiple-point statistics and non-linear models are automatically incorporated); it relies on sound methodological principles rather than being ad hoc; and it offers the rational means for integrating the multifarious core knowledge bases and uncertain site-specific information sources about the subsurface system. Previous upscaling results are derived as special cases of the proposed upscaling approach under limited conditions of porous media flow, a fact that further demonstrates the generalization power of the approach. Our hope is that looking at the upscaling problem in this novel way will direct further attention to the methodological exploration of the problem at the length and the detail that it deserves.I would like to thank Drs. A. Kolovos and D.T. Hristopulos for their valuable comments. The work was supported by grants from the Army Research Office (Grant no. DAAG55–98–1-0289) and the National Institute of Environmental Health Sciences (P42-ES05948 & P30-ES10126).     

A BME solution of the inverse problem for saturated groundwater flow

In most real-world hydrogeologic situations, natural heterogeneity and measurement errors introduce major sources of uncertainty in the solution of the inverse problem. The Bayesian Maximum Entropy (BME) method of modern geostatistics offers an efficient solution to the inverse problem by first assimilating various physical knowledge bases (hydrologic laws, water table elevation data, uncertain hydraulic resistivity measurements, etc.) and then producing robust estimates of the subsurface variables across space. We present specific methods for implementing the BME conceptual framework to solve an inverse problem involving Darcys law for subsurface flow. We illustrate one of these methods in the case of a synthetic one-dimensional case study concerned with the estimation of hydraulic resistivity conditioned on soft data and hydraulic head measurements. The BME framework processes the physical knowledge contained in Darcys law and generates accurate estimates of hydraulic resistivity across space. The optimal distribution of hard and soft data needed to minimize the associated estimation error at a specified sampling cost is determined. This work was supported by grants from the National Institute of Environmental Health Sciences (Grant no. 5 P42 ES05948 and P30ES10126), the National Aeronautics and Space Administration (Grant no. 60-00RFQ041), the Army Research Office (Grant no. DAAG55-98-1-0289), and the National Science Foundation under Agreement No. DMS-0112069.     

Stochastic estimation of facies using ground penetrating radar data

Explicitly defining large-scale heterogeneity is a necessary step of groundwater model calibration if accurate estimates of flow and transport are to be made. In this work, neural networks are used to estimate radar facies probabilities from ground penetrating radar (GPR) images, yielding stochastic facies-based models that honour the large-scale architecture of the subsurface. For synthetic GPR images, a neural network was able to correctly identify radar facies with an accuracy of approximately 90%. Manual interpretation of a set of 450 MHz GPR field data from the Borden aquifer resulted in the identification of four radar facies. Of these, a neural network was able to identify two facies with an accuracy of near 80% and one with an accuracy of 44%. The neural network was not able to identify the fourth facies, likely due to the choice of defining facies characteristics. Sequential indicator simulation was used to generate facies realizations conditioned to the radar facies probabilities. Numerical simulations indicate that significant improvements in the prediction of solute transport are possible when GPR is used to constrain the facies model compared to using well data alone, especially when data are sparse.This work was supported by funding to R. Knight under Grant No. DE-FG07–00ER15118-A000, Environmental Management Science Program, Office of Science and Technology, Office of Environment Management, United States Department of Energy (DOE). However, any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of DOE. Further support was provided by a Stanford Graduate Fellowship to S. Moysey. The authors would also like to thank James Irving for his assistance with processing of the radar data.     

An interval-parameter multi-stage stochastic programming model for water resources management under uncertainty

In this study, an interval-parameter multi-stage stochastic linear programming (IMSLP) method has been developed for water resources decision making under uncertainty. The IMSLP is a hybrid methodology of inexact optimization and multi-stage stochastic programming. It has three major advantages in comparison to the other optimization techniques. Firstly, it extends upon the existing multi-stage stochastic programming method by allowing uncertainties expressed as probability density functions and discrete intervals to be effectively incorporated within the optimization framework. Secondly, penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. Thirdly, it cannot only handle uncertainties through constructing a set of scenarios that is representative for the universe of possible outcomes, but also reflect dynamic features of the system conditions through transactions at discrete points in time over the planning horizon. The developed IMSLP method is applied to a hypothetical case study of water resources management. The results are helpful for water resources managers in not only making decisions of water allocation but also gaining insight into the tradeoffs between environmental and economic objectives.     

Steady- and transient-state inversion in hydrogeology by successive flux estimation

A calibration method to solve the groundwater inverse problem under steady- and transient-state conditions is presented. The method compares kriged and numerical head field gradients to modify hydraulic conductivity without the use of non-linear optimization techniques. The process is repeated iteratively until a close match with piezometric data is reached. The approach includes a damping factor to avoid divergence and oscillation of the solution in areas of low hydraulic gradient and a weighting factor to account for temporal head variation in transient simulations. The efficiency of the method in terms of computing time and calibration results is demonstrated with a synthetic field. It is shown that the proposed method provides parameter fields that reproduce both hydraulic conductivity and piezometric data in few forward model solutions. Stochastic numerical experiments are conducted to evaluate the sensitivity of the method to the damping function and to the head field estimation errors.     

Modeling the length of day and extrapolating the rotation of the Earth

The stochastic behavior of the length of day (LOD) process is analyzed and is modeled within statistical accuracy on a time-scale ranging from weeks to millennia by a three-component model comprising a global Brownian motion process, decadal fluctuations, and a 50-day Madden–Julian oscillation. While the model is intended to be phenomenological, some possible physical models underlying the three components are speculated upon. The model is applied to estimate long-range extrapolation errors. For example, it predicts a standard error of 1 h in the clock-time correction ΔT for extrapolation by 1,500 years from 500 to 2000 BC.     

Artificial ground motion compatible with specified peak velocity and target spectrum

In this paper, a method, which synthesizes the artificial ground motion compatible with the specified peak velocity as well as the target acceleration response spectrum, was proposed. In this method, firstly, an initial acceleration time history α8^（0） （t）, which satisfies the prescribed peak ground acceleration, the target spectral acceleration ST（ω, ζ）,and the specified intensity envelope, is generated by the traditional method that generates the requency domain; secondly,α8^（0） （t）is further modulated by superimposing narrow-band time histories upon it in the time domain to make its peak velocity, approach the target peak ground velocity, and at the same time to improve its fitting precision to the target spectrum. Numerical examples show that this algorithm boasts high calculation precisions.