Simultaneous identification of the pollutant release history and the source location in groundwater by means of a geostatistical approach

This paper describes an innovative procedure that is able to simultaneously identify the release history and the source location of a pollutant injection in a groundwater aquifer (simultaneous release function and source location identification, SRSI). The methodology follows a geostatistical approach: it develops starting from a data set and a reliable numerical flow and transport model of the aquifer. Observations can be concentration data detected at a given time in multiple locations or a time series of concentration measurements collected at multiple locations. The methodology requires a preliminary delineation of a probably source area and results in the identification of both the sub-area where the pollutant injection has most likely originated, and in the contaminant release history. Some weak hypotheses have to be defined about the statistical structure of the unknown release function such as the probability density function and correlation structure. Three case studies are discussed concerning two-dimensional, confined aquifers with strongly non-uniform flow fields. A transfer function approach has been adopted for the numerical definition of the sensitivity matrix and the recent step input function procedure has been successfully applied.     

Identification of contaminant point source in surface waters based on backward location probability density function method

A backward location probability density function (BL-PDF) method capable of identifying location of point sources in surface waters is presented in this paper. The relation of forward location probability density function (FL-PDF) and backward location probability density, based on adjoint analysis, is validated using depth-averaged free-surface flow and mass transport models and several surface water test cases. The solutions of the backward location PDF transport equation agreed well to the forward location PDF computed using the pollutant concentration at the monitoring points. Using this relation and the distribution of the concentration detected at the monitoring points, an effective point source identification method is established. The numerical error of the backward location PDF simulation is found to be sensitive to the irregularity of the computational meshes, diffusivity, and velocity gradients. The performance of identification method is evaluated regarding the random error and number of observed values. In addition to hypothetical cases, a real case was studied to identify the source location where a dye tracer was instantaneously injected into a stream. The study indicated the proposed source identification method is effective, robust, and quite efficient in surface waters; the number of advection–diffusion equations needed to solve is equal to the number of observations.     

Backward probabilistic model of groundwater contamination in non-uniform and transient flow

Backward location and travel time probabilities, which provide information about the former location of contamination in an aquifer, can be used to identify unknown contamination sources. Backward location probability describes the possible upgradient positions of contamination at a known time in the past, and backward travel time probability describes the time required for contamination to travel from a known upgradient location to an observation point. These probabilities are related to adjoint states of resident concentration, and their governing equation is the adjoint of a forward contaminant transport model. Using adjoint theory to obtain the appropriate governing equation, we extend the backward probability model for conservative solutes to more general non-uniform and transient flow fields. In particular, we address three important extensions, spatially-varying porosity, transient flow and temporally-varying porosity, and internal distributed sources and sinks of solute and water. For the first time we learn that forward and backward location and travel time probabilities are not necessarily equivalent to adjoint states, but are related to them. The extensions are illustrated using a vertically-integrated groundwater model, creating transient flow by a step change in pumping and using areal recharge as an internal distributed source. Both the movement and spread of probabilities are affected. With internal sources of water, there are two interpretations of backward probability, depending on whether or not the source of water is also a source of solute. The results demonstrate how the backward probability model can be applied to other, perhaps more important, non-uniform and transient flow conditions, with time- and space-varying water storage, such as time-varying pumping or unsaturated (or saturated–unsaturated) flow and transport with spatially- and temporally-varying moisture content.     

Numerical implementation of a backward probabilistic model of ground water contamination

Backward location and travel time probabilities can be used to characterize known and unknown sources or prior positions of ground water contamination. Backward location probability describes the position of the observed contamination at some time in the past; backward travel time probability describes the amount of time prior to observation that the contamination was released from its source or was at a particular upgradient location. The governing equation for backward probabilities is the adjoint of the governing equation for contaminant transport, but with new load terms. Numerical codes that have been written to solve the forward equations of contaminant transport, e.g., the advection-dispersion equation, can also be used to solve the adjoint equation for location and travel time probabilities; however, the interpretation of the results is different and some new approximations must be made for the load terms. We present the governing equations for backward location and travel time probabilities, and provide appropriate numerical approximations for these load terms using the cell-centered finite difference method, one of the most popular numerical methods in ground water hydrology. We discuss some additional numerical considerations for the backward model including boundary conditions, reversal of the flow field, and interpretation of the results. We illustrate the implementation of the backward probability model using hypothetical examples in one- and two-dimensional domains. We also present a three-dimensional application of a pump-and-treat remediation capture zone delineation at the Massachusetts Military Reservation. The illustrations are performed using MODFLOW-96 for flow simulations and MT3DMS for transport simulations.     

利用多层横波各向异性测量方法计算两层介质的分裂参数

对实际两层各向异性介质,在一层假设条件下利用Silver和Chan（1991）的等效单层各向异性测量方法,以及在两层假设条件下利用剥去法和反演法,计算模型的分裂参数.首先利用理论雷克子波得到经过两层各向异性的观测数据,然后加入噪声之前和之后,分别计算不同反方位角覆盖条件下数据的各向异性,并与理论模型的分裂参数进行比较.结果发现在上层分裂特征已知的基础上,剥去法适用于任何模型,不管是否存在分裂,或者分裂特征在两层中如何分布;而反演法更适用于两层各向异性较强且不同的模型,其结果受噪声和方位角分布的影响.选取不同方位角分布的高信噪比数据,比较剥去法和反演法对下层分裂参数的计算结果,发现当入射方位角在两层快波方向之间时,反演结果比较可靠.最后利用这三种测量各向异性的方法,计算青藏高原东南缘CEArray台站观测到的SKS数据中记录的各向异性.除了云贵高原的台站YN.CUX表现出较明显的两层分裂特征,大部分台站下的岩石圈各向异性呈现一层或者较弱的各向异性.于是针对该台站,用反演法同时对这两层的分裂参数进行估计,上层的结果与接收函数计算的地壳分裂参数一致;下层的结果与剥去法计算的上地幔分裂参数一致,说明反演法同剥去法一样,都能有效的分析具有两层各向异性特征的介质.     

Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm

This study aims to model the joint probability distribution of drought duration, severity and inter-arrival time using a trivariate Plackett copula. The drought duration and inter-arrival time each follow the Weibull distribution and the drought severity follows the gamma distribution. Parameters of these univariate distributions are estimated using the method of moments (MOM), maximum likelihood method (MLM), probability weighted moments (PWM), and a genetic algorithm (GA); whereas parameters of the bivariate and trivariate Plackett copulas are estimated using the log-pseudolikelihood function method (LPLF) and GA. Streamflow data from three gaging stations, Zhuangtou, Taian and Tianyang, located in the Wei River basin, China, are employed to test the trivariate Plackett copula. The results show that the Plackett copula is capable of yielding bivariate and trivariate probability distributions of correlated drought variables.     

Field test of sub‐basalt hydrocarbon exploration with marine controlled source electromagnetic and magnetotelluric data

The recent use of marine electromagnetic technology for exploration geophysics has primarily focused on applying the controlled source electromagnetic method for hydrocarbon mapping. However, this technology also has potential for structural mapping applications, particularly when the relative higher frequency controlled source electromagnetic data are combined with the lower frequencies of naturally occurring magnetotelluric data. This paper reports on an extensive test using data from 84 marine controlled source electromagnetic and magnetotelluric stations for imaging volcanic sections and underlying sediments on a 128‐km‐long profile. The profile extends across the trough between the Faroe and Shetland Islands in the North Sea. Here, we focus on how 2.5D inversion can best recover the volcanic and sedimentary sections. A synthetic test carried out with 3D anisotropic model responses shows that vertically transverse isotropy 2.5D inversion using controlled source electromagnetic and magnetotelluric data provides the most accurate prediction of the resistivity in both volcanic and sedimentary sections. We find the 2.5D inversion works well despite moderate 3D structure in the synthetic model. Triaxial inversion using the combination of controlled source electromagnetic and magnetotelluric data provided a constant resistivity contour that most closely matched the true base of the volcanic flows. For the field survey data, triaxial inversion of controlled source electromagnetic and magnetotelluric data provides the best overall tie to well logs with vertically transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data a close second. Vertical transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data provided the best interpreted base of the volcanic horizon when compared with our best seismic interpretation. The structural boundaries estimated by the 20‐Ω·m contour of the vertical resistivity obtained by vertical transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data gives a maximum geometric location error of 11% with a mean error of 1.2% compared with the interpreted base of the volcanic horizon. Both the model study and field data interpretation indicate that marine electromagnetic technology has the potential to discriminate between low‐resistivity prospective siliciclastic sediments and higher resistivity non‐prospective volcaniclastic sediments beneath the volcanic section.     

Probability Theory as Logic: Data Assimilation for Multiple Source Reconstruction

Probability theory as logic (or Bayesian probability theory) is a rational inferential methodology that provides a natural and logically consistent framework for source reconstruction. This methodology fully utilizes the information provided by a limited number of noisy concentration data obtained from a network of sensors and combines it in a consistent manner with the available prior knowledge (mathematical representation of relevant physical laws), hence providing a rigorous basis for the assimilation of this data into models of atmospheric dispersion for the purpose of contaminant source reconstruction. This paper addresses the application of this framework to the reconstruction of contaminant source distributions consisting of an unknown number of localized sources, using concentration measurements obtained from a sensor array. To this purpose, Bayesian probability theory is used to formulate the full joint posterior probability density function for the parameters of the unknown source distribution. A simulated annealing algorithm, applied in conjunction with a reversible-jump Markov chain Monte Carlo technique, is used to draw random samples of source distribution models from the posterior probability density function. The methodology is validated against a real (full-scale) atmospheric dispersion experiment involving a multiple point source release.     

Towards an accurate real-time locator of infrasonic sources

Infrasonic signals propagate from an atmospheric source via media with stochastic and fast space-varying conditions. Hence, their travel time, the amplitude at sensor recordings and even manifestation in the so-called “shadow zones” are random. Therefore, the traditional least-squares technique for locating infrasonic sources is often not effective, and the problem for the best solution must be formulated in probabilistic terms. Recently, a series of papers has been published about Bayesian Infrasonic Source Localization (BISL) method based on the computation of the posterior probability density function (PPDF) of the source location, as a convolution of a priori probability distribution function (APDF) of the propagation model parameters with likelihood function (LF) of observations. The present study is devoted to the further development of BISL for higher accuracy and stability of the source location results and decreasing of computational load. We critically analyse previous algorithms and propose several new ones. First of all, we describe the general PPDF formulation and demonstrate that this relatively slow algorithm might be among the most accurate algorithms, provided the adequate APDF and LF are used. Then, we suggest using summation instead of integration in a general PPDF calculation for increased robustness, but this leads us to the 3D space-time optimization problem. Two different forms of APDF approximation are considered and applied for the PPDF calculation in our study. One of them is previously suggested, but not yet properly used is the so-called “celerity-range histograms” (CRHs). Another is the outcome from previous findings of linear mean travel time for the four first infrasonic phases in the overlapping consecutive distance ranges. This stochastic model is extended here to the regional distance of 1000 km, and the APDF introduced is the probabilistic form of the junction between this travel time model and range-dependent probability distributions of the phase arrival time picks. To illustrate the improvements in both computation time and location accuracy achieved, we compare location results for the new algorithms, previously published BISL-type algorithms and the least-squares location technique. This comparison is provided via a case study of different typical spatial data distributions and statistical experiment using the database of 36 ground-truth explosions from the Utah Test and Training Range (UTTR) recorded during the US summer season at USArray transportable seismic stations when they were near the site between 2006 and 2008.     

一种改进的基于网格搜索的微地震震源定位方法

震源定位是微地震监测技术要解决的主要问题.目前,井下微地震监测多采用走时拟合法计算震源位置.常规方法受到环境噪声、初至拾取误差、速度模型误差等因素的影响,定位结果存在一定误差.为了提高定位精度,本文提出了一种改进的基于网格搜索的微地震震源定位方法.本文方法根据P波的偏振特征参数计算概率密度函数求取震源方位角,并采用改进的目标函数和搜索算法计算震源的径向距离和深度.模型数据和实际资料的处理结果表明,本文方法具有较强的抗噪性,计算得到的震源方位角更加接近真实值;与常规目标函数相比,本文方法采用的目标函数具有更好的收敛性,其定位结果受初至拾取误差和速度模型误差的影响更小;本文提出的搜索算法能够消除由于错误拾取造成的观测到时中的异常值对定位结果的影响.     

A derived probability distribution approach to stormwater quality modeling

The closed-form analytical stormwater quality models are developed for simulating urban catchment pollutant buildup and washoff processes. By integrating the rainfall–runoff transformation with pollutant buildup and washoff functions, stormwater quality measures, such as the cumulative distribution functions (CDFs) of pollutant loads, the expected value of pollutant event mean concentrations (EMCs) and the average annual pollutant load can be derived. This paper presents methodologies and major procedures for the development of urban stormwater quality models based on derived probability distribution theory. In order to investigate the spatial variation in model parameters and its impact on stormwater pollutant buildup and washoff processes as well as pollutant loads to receiving waters, an extended form of the original rainfall–runoff transformation which is based on lumped runoff coefficient approach is proposed to differentiate runoff generation mechanisms between the impervious and pervious areas of the catchment. In addition, as a contrast to the aggregated pollutant buildup models formulated with a single lumped buildup parameter, the disaggregated form of the pollutant buildup model is proposed by introducing a number of physically-based parameters associated with pollutant buildup and washoff processes into the pollutant load models. The results from the case study indicate that analytical urban stormwater management model are capable of providing results in good agreement with the field measurements, and can be employed as alternatives to continuous simulation models in the evaluation of long-term stormwater quality measures.     

广东东源MS4.8地震序列震源位置及周边地区P波三维速度结构

利用震源位置和速度结构的联合反演, 得到2012年2月16日广东东源M_S4.8地震序列的震源位置及震源区速度结构模型, 并进一步采用双差定位法对该序列位置重新定位． 结果显示, 东源M_S4.8地震是一次自上而下、 自西向东的单侧破裂过程, 破裂面积约3 km×5 km． 震源区地壳结构复杂, 埋深712 km处为一个速度达6.2 km/s的高速体, 主震的起始破裂位置位于高速体的顶部速度梯度较大的区域, 破裂面穿越整个高速体, 余震止于高速体下方的低速区底部(埋深约16 km)． 东源县锡场镇下方的这种高、 低速相间的结构, 表明地壳层间相邻物质性状的差异利于应变能的积累和释放, 因此东源地区具备发生中强地震的构造条件．      

Stormwater pollutant runoff: A stochastic approach

Since stormwater wash-off of pollutants in urban areas is largely affected by environmental variability, it is very difficult to predict the amount of pollutants transported by stormwater runoff during and after individual rainfall events. We investigated the addition of a random component into an exponential wash-off equation of total suspended solids (TSS) and total nitrogen (TN) to model the variability of runoff pollutant concentrations. The model can be analytically solved to describe the probability distributions of TSS and TN concentrations as a function of increasing runoff depths. TSS data from six Australian catchments and TN data from three of these catchments were used to calibrate the model and evaluate its applicability. Using the results of the model, its potential use to determine the appropriate size of stormwater treatment systems is discussed, stressing how probabilistic considerations should be included in the design of such systems. Specifically, stormwater depths retained by a treatment system should result from a compromise between the recurrence of specific runoff depths and the probability to discharge a target pollutant concentration when such a runoff depth is exceeded.     

基于随机反传和筛选模型的微震逆时定位成像

对于常规的逆时定位成像方法,成像结果中强震源的成像值通常远大于并且会掩盖弱震源;同时,成像结果中假象的压制与消除也一直是该技术中颇受关注且比较难解决的问题.对此,本文结合了混合成像条件与高通滤波,从图像对比度的角度加强定位成像效果.提出了反传检波点随机选择的方法,通过重复进行随机选择与随机分组,从而得到不同震源的、包括一些冗余在内的更多信息,通过对信息的融合以提高定位可靠性.提出了筛选模型的概念,将成像过程中各点的波场反传序列引入震源判断标准,构建函数以大致量化震源存在的可能性,结合阈值,构造出由0和1组成"筛选模型",对成像结果进行通过性选择,以此消除假象并提高震源识别的正确性.通过简单模型和复杂模型,验证了本文提出方法的有效性以及对各类干扰因素的适应性与抵抗性.     

多震相走时联合三参数同时反演成像

采用新近研制的分区多步不规则最短路径多震相地震射线追踪正演技术,结合流行的子空间反演算法,提出了一种联合多震相走时资料进行地震三参数 （速度、反射界面和震源位置） 同时反演的方法技术.数值模拟反演实例、以及与双参数 （速度和反射界面或速度和震源位置） 同时反演的对比分析表明：三参数同时反演成像结果大体接近双参数同时反演成像的结果.另外,噪声敏感性试验表明：所提算法对到时数据中可容许的随机误差并不敏感,结果说明多震相走时的联合三参数同时反演成像方法技术不失为一种提高走时成像空间分辨率、进而降低重建模型参数失真度、行之有效的方法技术.     

A combined simulation–genetic algorithm optimization model for optimal rule curves of a reservoir: a case study of the Nam Oon Irrigation Project,Thailand

A combined simulation–genetic algorithm (GA) optimization model is developed to determine optimal reservoir operational rule curves of the Nam Oon Reservoir and Irrigation Project in Thailand. The GA and simulation models operate in parallel over time with interactions through their solution procedure. A GA is selected as an optimization model, instead of traditional techniques, owing to its powerful and robust performance and simplicity in combining with a simulation technique. A GA is different from conventional optimization techniques in the way that it uses objective function information and does not require its derivatives, whereas in real‐world optimization problems the search space may include discontinuities and may often include a number of sub‐optimum peaks. This may cause difficulties for calculus‐based and enumerative schemes, but not in a GA. The simulation model is run to determine the net system benefit associated with state and control variables. The combined simulation–GA model is applied to determine the optimal upper and lower rule curves on a monthly basis for the Nam Oon Reservoir, Thailand. The objective function is maximum net system benefit subject to given constraints for three scenarios of cultivated areas. The monthly release is calculated by the simulation model in accordance with the given release policy, which depends on water demand. The optimal upper and lower rule curves are compared with the results of the HEC‐3 model (Reservoir System Analysis for Conservation model) calculated by the Royal Irrigation Department, Thailand, and those obtained using the standard operating policy. It was found that the optimal rule curves yield the maximum benefit and minimum damages caused by floods and water shortages. The combined simulation–GA model shows an excellent performance in terms of its optimization results and efficient computation. Copyright © 2007 John Wiley & Sons, Ltd.     

A New Method for the Estimation of Avalanche Distance Exceeded Probabilities

A crucial point in any methodology for avalanche hazard assessment is the evaluation of avalanche distance exceeded probability, i.e., the annual probability that any assigned location along a given path is reached or exceeded by an avalanche. Typically this problem is faced by estimating the snow volume in the starting zone that is likely to accumulate an average every T years by statistical analysis of snowfall record, and then using this volume as input to an appropriately calibrated avalanche dynamics model to determine the runout distancesfor this design event. This methodology identifies the areas that canbe affected by an avalanche for the considered value of the return period (i.e. the average interval of time for a certain event to repeat itself), ¯T. However, it does not allow us to evaluate the actual avalanche encounter probability for any given point in the runout zone. In the present work this probability is computed by numerical integration of the expression P(x) = ∫₀ ^∞ P^*(V)f(V) dV, where f is the probabilitydensity function (PDF) of the avalanche release volume V, and P^* is the probability of the point x being reached or passed by an avalanche if the release volume is V; this latter probability is calculated by avalanche dynamics simulations. The procedure is implemented using a one-dimensional hydraulic-continuum avalanche dynamic model, calibrated on data from different Italian Alpine ranges, and is applied to a real world hazard mapping problem.     

Experimental analysis and application of sparsity constrained deconvolution

Sparsity constrained deconvolution can improve the resolution of band-limited seismic data compared to conventional deconvolution. However, such deconvolution methods result in nonunique solutions and suppress weak reflections. The Cauchy function, modified Cauchy function, and Huber function are commonly used constraint criteria in sparse deconvolution. We used numerical experiments to analyze the ability of sparsity constrained deconvolution to restore reflectivity sequences and protect weak reflections under different constraint criteria. The experimental results demonstrate that the performance of sparsity constrained deconvolution depends on the agreement between the constraint criteria and the probability distribution of the reflectivity sequences; furthermore, the modified Cauchyconstrained criterion protects the weak reflections better than the other criteria. Based on the model experiments, the probability distribution of the reflectivity sequences of carbonate and clastic formations is statistically analyzed by using well-logging data and then the modified Cauchy-constrained deconvolution is applied to real seismic data much improving the resolution.     

Source-independent wave-equation based microseismic source location using traveltime inversion

A new source location method using wave-equation based traveltime inversion is proposed to locate microseismic events accurately. With a sourceindependent strategy, microseismic events can be located independently regardless of the accuracy of the source signature and the origin time. The traveltime-residuals-based misfit function has robust performance when the velocity model is inaccurate. The new Fréchet derivatives of the misfit function with respect to source location are derived directly based on the acoustic wave equation, accounting for the influence of geometrical perturbation and spatial velocity variation. Unlike the mostly used traveltime inversion methods, no traveltime picking or ray tracing is needed.Additionally, the improved scattering-integral method is applied to reduce the computational cost. Numerical tests show the validity of the proposed method.     

Exploring seismic inversion methodologies for non‐stationary geological environments: a benchmark study between deterministic and geostatistical seismic inversion

This paper presents a comparison between subsurface impedance models derived from different deterministic and geostatistical seismic inversion methodologies applied to a challenging synthetic dataset. Geostatistical seismic inversion methodologies nowadays are common place in both industry and academia, contrasting with traditional deterministic seismic inversion methodologies that are becoming less used as part of the geo‐modelling workflow. While the first set of techniques allows the simultaneous inference of the best‐fit inverse model along with the spatial uncertainty of the subsurface elastic property of interest, the second family of inverse methodology has proven results in correctly predicting the subsurface elastic properties of interest with comparatively less computational cost. We present herein the results of a benchmark study performed over a realistic three‐dimensional non‐stationary synthetic dataset in order to assess the performance and convergence of different deterministic and geostatistical seismic inverse methodologies. We also compare and discuss the impact of the inversion parameterisation over the exploration of the model parameter space. The results show that the chosen seismic inversion methodology should always be dependent on the type and quantity of the available data, both seismic and well‐log, and the complexity of the geological environment versus the assumptions behind each inversion technique. The assessment of the model parameter space shows that the initial guess of traditional deterministic seismic inversion methodologies is of high importance since it will determine the location of the best‐fit inverse solution.