Laboratory sandbox validation of pollutant source location methods

Inverse methods can be used to recover the pollutant source location from concentration data. In this paper, the relative effectiveness of two proposed methods, simultaneous release function and source location identification (SRSI) and backward probability model based on adjoint state method (BPM-ASM) are evaluated using real data collected by using experimental equipment. The device is a sandbox that reproduces an unconfined aquifer in which all the variables are controlled. A numerical model was calibrated using experimental observations. The SRSI is a stochastic procedure which finds the source location and the release history by means of a Bayesian geostatistical approach (GA). The BPM-ASM provides the backward probability location of the pollutant detected at a monitoring point by means of a reverse transport simulation. The results show that both methods perform well. While the simultaneous release function and SRSI method requires a preliminary delineation of a probable source area and some weak hypotheses about the statistical structure of the unknown release function, the backward probability model requires some hypothesis about the contaminant release time. A case study was performed using two observation points only, and despite the scarcity of data, both methodologies were able to accurately reconstruct the true source location. The GA has the advantage to recover the release history function too, whilst the backward probability model works well with fewer data. If there are many observations, both methodologies may be computationally heavy. A transfer function approach has been adopted for the numerical definition of the sensitivity matrix in the SRSI method. The reliability of the experimental equipment was tested in previous laboratory works, conducted under several different conditions.     

煤矿矿震定位中异向波速模型的构建与求解

针对煤矿上覆岩层层状赋存和离层带的特点,构建矿井尺度的微震监测系统异向波速模型,模型中波速向量由地面探头速度与井下探头速度组成.研究了在只有强矿震信号和混有爆破信号两种条件下,以到时残差最小为目标和震源定位误差最小为目标的两种求解模型,模型求解选用具有全局寻优特性的遗传算法与CMEAS算法结合的混合算法.现场实际应用得出,只使用爆破信号的到时残差法最优,混有强矿震信号的到时残差法其次;与爆破信号定位所用的统一简化波速模型相比,震源定位误差大幅度降低.在此基础上进一步减低定位误差,还需从微震台网的优化布设方面解决.     

The determination of the best fitting and the extreme source models by a global inversion method

In this paper, a global inversion method is developed for seismic moment tensor inversion by using the body wave forms. The algorithm depends on neither the selection of starting model nor the forms of objective function and constraints. When the error function, measure of the difference between the observed and synthetic waveforms, is chosen as the objective function, the best fitting source model is found; when a certain combination in seismic moment tensor elements is selected as the objective function and the values of error function are constrained in a suitable bound, the extreme source models can be produced by minimizing or maximizing this combination. By changing the form of the combination of moment tensor elements, a variety of different source characteristics can be considered. Therefore the extreme solution provides an estimation of the uncertainty in the best fitting source model. The seismic waveform data was used to evaluate the effectiveness of this algorithm. This research was supported by the National Natural Science Foundation of China.     

Waveform inversion of weak vrancea (Romania) earthquakes

Summary The inversion of high-frequency seismograms is performed to retrieve source mechanisms, hypocentral depths and source time functions of two weak Vrancea earthquakes (M_L=3.3), one that occurred in the crust, the other in the lithospheric part of the mantle. The digital waveforms recorded by the local Romanian network are used. Synthetic seismograms are computed by the modal summation method, using the point source approximation, for horizontally layered anelastic media. For each source-to-station path a different structural model is adopted which represents the best 1-D approximation of the medium in this azimuth. Thus, lateral inhomogeneities are taken into account in a simplified way. The source is described by the full moment tensor, allowing both deviatoric and volumetric components to be resolved.Although the structural models are simplified for the range of epicentral distances (15<<<170 km) considered, we find that the fit between the synthetic and observed seismograms is satisfactory for frequencies less than a few Hz. The few P-wave polarities available are not sufficient to determine a reliable source mechanism by standard methods, while the waveform inversion allows us to retrieve source mechanisms that are stable with respect to different boundary conditions and in good agreement with the observed polarities. The source time function is the less stable inverted parameter, being the most influenced by the simplification of the structural models.     

Quasi-static Planar Deformation in a Medium Composed of Elastic and Thermoelastic Solid Half Spaces Due to Seismic Sources in an Elastic Solid

A two-dimensional problem of quasi static deformation of a medium consisting of an elastic half space in welded contact with thermoelastic half space, caused due to seismic sources, is studied. Source is considered to be in the elastic half space. The basic equations, governed by the coupled theory of thermoelasticity, are used to model for thermoelastic half space. The analytical expressions for displacements, strain and stresses in the two half spaces are obtained first for line source and then for dip slip fault. The results for two particular cases, adiabatic conditions and isothermal conditions, are also obtained. Numerical results for displacements, stresses and temperature distribution have also been computed and are shown.     

A Lagrangian approach to modelling stable isotopes in precipitation over mountainous terrain

A Lagrangian (Rayleigh) distillation model is used to track the evolution of stable isotopes in precipitation over mountainous terrain from the Pacific Coast of Canada to two alpine field sites in the Canadian Rocky Mountains. Precipitation δ¹⁸O at Vancouver constrains the model and air–mass back trajectories provide the water vapour pathway for 10 winter storm events. Isotopic values along storm pathways are modelled with a classical Rayleigh model that prescribes a linear decrease in temperature and pressure from initial to final conditions, and two models that account directly for orographic precipitation processes by: (i) applying an orographic rainfall model and (ii) using North American Regional Reanalysis data to calculate the change in vapour content along storm pathways. All models are significant predictors of snowpack δ¹⁸O, but the orographic model provides the best fit to precipitation‐weighted δ¹⁸O for each storm. The improvement in modelled δ¹⁸O by accounting for terrain along storm trajectories illustrates the need to account for orographically driven moisture loss when modelling vapour transport to ice core sites with mountainous upwind terrain. This finding is also applicable to isotopic studies of paleoaltimetry and source areas of groundwater recharge. Copyright © 2011 John Wiley & Sons, Ltd.     

A New Theory of Love Waves in Multi-layered Media with Irregular Interfaces

In this article, we have derived a new and more general formulation of Love waves in arbitrarily irregular multi-layered media by using the global generalized reflection/transmission (abbreviated to R/T thereafter) matrices method developed earlier by Chen [17~20]. From the basic principle that the modal solutions are the non-trivial solutions of the free elastodynamic equation under appropriate boundary conditions, we naturally derived the characteristic frequencies and the corresponding distorted modes of Love wave in irregular multi-layered media. Moreover, we have derived the corresponding excitation formulation of Love waves in such laterally heterogeneous media by using the general solution of elastodynamic equation [17~20]. Similar to the result for laterally homogeneous layered structure, the Love waves radiated from a point source in irregular multi-layered media can be expressed as a superposition of distorted modes. Since the structure model used here is quite arbitrary, it can be used for so     

THE NON-LINEAR INVERSION OF SEISMIC WAVEFORMS CAN BE PERFORMED EITHER BY TIME EXTRAPOLATION OR BY DEPTH EXTRAPOLATION1

The classical aim of non-linear inversion of seismograms is to obtain the earth model which, for null initial conditions and given sources, best predicts the observed seismograms. This problem is currently solved by an iterative method: each iteration involves the resolution of the wave equation with the actual sources in the current medium, the resolution of the wave equation, backwards in time, with the current residuals as sources; and the correlation, at each point of space, of the two wavefields thus obtained. Our view of inversion is more general: we want to obtain a whole set of earth model, initial conditions, source functions, and predicted seismograms, which are the closest to some a priori values, and which are related through the wave equation. It allows us to justify the previous method, but it also allows us to set the same inverse problem in a different way: what is now searched for is the best fit between calculated and a priori initial conditions, for given sources and observed surface displacements. This leads to a completely different iterative method, in which each iteration involves the downward extrapolation of given surface displacements and tractions, down to a given depth (the‘bottom’), the upward extrapolation of null displacements and tractions at the bottom, using as sources the initial time conditions of the previous field, and a correlation, at each point of the space, of the two wavefields thus obtained. Besides the theoretical interest of the result, it opens the way to alternative numerical methods of resolution of the inverse problem. If the non-linear inversion using forward-backward time propagations now works, this non-linear inversion using downward-upward extrapolations will give the same results but more economically, because of some tricks which may be used in depth extrapolation (calculation frequency by frequency, inversion of the top layers before the bottom layers, etc.).     

唐山地震的破裂过程及其力学分析

由 P 波初动符号资料在 DJS-6机上计算了主震及17个较大余震的断层面解,并按照有限移动源模式测定了主震及三个最大余震的震源参数.主震是发生在一个近似直立的右旋走滑断层上,走向 N30°E,破裂方式为不对称的双侧破裂,以2.7公里/秒的平均速度向北东传播70公里,向南西传播45公里.测定的主震震源参数例如平均位错136厘米,地震矩1.24×1027达因·厘米,应力降12巴等.大多数M_L>5.0的余震是发生在主破裂面附近及主破裂面两端的扩展分支上,该扩展分支位于膨胀符号区并与主破裂偏离80°左右.较大余震的多数亦集中在这两个扩展分支上.本文试图从理论上分析这种断裂扩展的力学特征.对于脆性材料的复合变形情形,破裂不再沿原来平面扩展,而是与原来平面偏离一个角度的另一面内扩展.并提出一个力学模型,计算了断层扩展角,计算结果与观测事实比较吻合.根据以上结果,本文讨论了唐山地震特点及发生的力学条件,认为唐山地震不同于发生在大断层上能用粘滑机制解释的那类地震,它和海城地震类似的是,除水平应力场作用外,还可能有地下物质的变迁,由于这种变迁使局部地壳受到垂直力.它和海城地震不同的是,它发生在一个比较均匀的脆性介质内,因而能够积累能量发生大震而没有前震.      

A SIMPLIFIED WATER QUALITY MODEL FOR WETLANDS

The purpose of this study is to develop a simplified mathematical model to simulate suspended solids and total phosphorus concentrations in a wetland or detention pond. Field data collected from a wet detention pond during storms were used to demonstrate the application of this model. Favorable agreements between the model results and data were achieved. The ratio of average outlet method and summary of loads method were used to quantify the removal efficiency of pollutants, reflecting the efficiencies are very close. The results of this study can be used for nonpoint source pollution control, wastewater treatment or best management practices (BMPs) through the wetland.     

俯冲带板间地震竖向加速度谱的阻尼修正系数模型

我国台湾省和南海东部地区处于地质构造复杂和地震频发的俯冲带区域,这一地区的结构抗震设计影响着该地区的开发建设进程。为建立适用于该地区的俯冲带板间地震竖向加速度谱的阻尼修正系数模型,本文选用日本K-NET与KiK-net台网的3 552条俯冲带板间地震记录,分四类场地建立以阻尼比和谱周期为参数的阻尼修正系数模型,并分析其它未纳入模型的参数对误差的影响。结果表明：采用阻尼比对数的三次多项式表达式即可实现良好拟合;模型在短周期内的误差主要受场地效应与路径效应影响,在长周期和高阻尼比时误差主要受震源效应影响;分场地建立阻尼修正系数模型可有效降低场地效应产生的误差。本文的研究成果可用于求解俯冲带地区无震源效应与路径效应的竖向设计反应谱。     

End member and Bayesian mixing models consistently indicate near-surface flowpath dominance in a pristine humid tropical rainforest

The impacts of forest conversion on runoff generation in the tropics have received much interest, but scientific progress is still hampered by challenging fieldwork conditions and limited knowledge about runoff mechanisms. Here, we assessed the runoff generation, flow paths and water source dynamics of a pristine rainforest catchment in Costa Rica using end member mixing analysis (EMMA) and a Bayesian mixing model (MixSIAR). Geochemical tracer data collected over a 4-week field campaign were combined with tritium data used to assess potential deeper groundwater flow pathways to the perennial stream. The streamflow composition was best captured using three end-members, namely throughfall, shallow (5–15 cm) and deeper (15–50 cm) soil water. We estimated the end-member contributions to the main stream and two tributaries using the two mixing approaches and found good agreement between results obtained from EMMA and MixSIAR. The system was overwhelmingly dominated by near-surface sources, with little evidence for deeper and older groundwater as tritium-derived baseflow mean transit time was between 2.0 and 4.4 years. The shallow soil flow pathway dominated streamflow contributions in the main stream (median 39% and 49% based on EMMA and MixSIAR, respectively), followed by the deeper soil (32% and 31%) and throughfall (25% and 19%). The two tributaries had even greater shallow soil water contributions relative to the main stream (83% and 74% for tributary A and 42% and 63% for tributary B). Tributary B had no detectable deep soil water contribution, reflecting the morphology of the hillslope (steeper slopes, shallower soils and lower vegetation density compared to hillslope A). Despite the short sampling campaign and associated uncertainties, this study allowed to thoroughly assess runoff generation mechanisms in a humid tropical catchment. Our results also provide a first comparison of two increasingly used mixing models and suggest that EMMA and MixSIAR yield comparable estimates of water source partitioning in this tropical, volcanic rainforest environment.     

Salinity sources of Kefar Uria wells in the Judea group aquifer of Israel. Part 2—quantitative identification model

The Kefar Uria group of wells have experienced an increase of salinity of the pumped water in the last two decades. The source of salinity is not known. Geohydrological and geochemical considerations of Part 1 (Avissar et al., in press) suggest two possible mechanisms and sources. The first source is infiltrating at the top of the aquifer, in contact with the overlaying formation and is close to the wells. The second source is deep and more distant and is attributed to salt leaching. In the present study, a methodology is developed in order to select the most probable source by quantitative modeling of flow and transport. The problem is more difficult than similar ones investigated in the literature, because of the complex three-dimensional flow pattern. However, simplified models can be used for the limited scope of source identification. The aquifer is modeled as a semi-infinite confined one under steady state conditions. The saline water input area and the 13 wells are represented by source distributions and an analytical solution is obtained for the flow field. A best fit between computed and measured well pressure heads leads to reasonable value of the identified permeability. Advective solute transport from salinity sources to wells is modeled numerically by particle tracking and leads to partition of solute flux among wells. Comparison of calculated wells salinity and the measured ones leads to the conclusive selection of one of the sources as the most probable one.     

浅壳与上地幔地震竖向加速度谱阻尼修正系数模型

本文基于日本KiK-Net,K-Net台网及汶川地震中6 000余条浅壳与上地幔地震竖向加速度记录,分场地类型建立了包含阻尼比和谱周期两个参数的阻尼修正系数模型,用以调整无震级和震源距信息的设计谱。基于固定效应模型对阻尼修正系数对数值及阻尼比对数值的三次多项式进行线性回归得到模型表达式,基于随机效应模型对阻尼修正系数模型的残差及残差的标准差进行分离,分析震源、路径以及场地效应对模型误差的影响。研究结果表明:高阻尼长周期震源效应引起的残差大于其他效应引起的残差;场地效应引起的残差小于其他效应引起的残差。对模型残差的标准差及阻尼比对数值进行线性回归,回归方程易于计算模型残差的标准差。     

Identifying threshold storm events and quantifying potential impacts of climate change on sediment yield in a small upland agricultural watershed of Ontario

Agricultural zones are significant sediment sources, but it is crucial to identify critical source areas (CSAs) of sediment yield within these zones where best management practices (BMPs) can be applied to the best effect in reducing sediment delivery to receiving water bodies rather than the economically nonviable alternative of randomly or sweepingly implementing BMPs. A storm event of a specific magnitude and hyetograph profile may, at different times, generate a greater or lesser sediment yield. The widely used agricultural nonpoint source (AGNPS) model was used to identify CSAs for sediment losses in Southwestern Ontario's agriculture‐dominated 374‐ha Holtby watershed. A storm threshold approach was adopted to identify critical periods for higher sediment losses. An AGNPS model for the Holtby watershed was set up, calibrated, and validated for run‐off volume, peak flow rate, and sediment yield for several storms. The calibrated and validated model was run for storms of increasing return periods to identify threshold storm events that would generate sediment yield greater than an acceptable value for early and late spring, summer, and fall seasons. Finally, to evaluate the potential impacts of climate change, we shifted shorter duration summer storms into spring conditions and quantified the changes in sediment yield dynamics. A 6‐hr, 7.5‐year early spring storm would generate sediment losses exceeding the acceptable limit of 0.34 t ha^?1 for the season. However, summer storms (2 hr, up to 100 years) tended to generate sediment yields below those of an identifiable threshold storm. If such shorter duration summer storms occurred in spring, the sediment yield would increase by more than fivefold. A 5‐year future storm would generate an equivalent effect of a 100‐year current spring event. The high sediment delivery to be expected will have significant implications regarding the future management of water quality of receiving waters. Appropriate placement of BMPs at CSAs will thus be needed to reduce such high sediment delivery to receiving waters.     

Variation of seismic source parameters and stress drops within a descending slab and its implications in plate mechanics

A least-squares searching technique has been developed to estimate the source dimensions of intermediate and deep focus earthquakes using azimuthal variations of body wave pulse-widths. With this method and also amplitude data, modes of rupture propagation, seismic moments, and stress drops of 17 intermediate and deep focus earthquakes in the Tonga-Kermadec region have been determined in order to investigate variations in source properties and the state of stress within the descending slab there. Three different modes of rupture; unilateral, bilateral, and circular faults, are compared and tested against observations. Results indicate that the unilateral fault is the best model for most of the earthquakes studied. Stress drops of the 17 events vary within a very large range, from 20 bar to about 4.6 kbar, and change significantly with depth. The magnitude of stress drops for depths between 220 and 430 km is very much higher than at shallower depths. This change in stress drop magnitude at about 220 km-depth seems to reflect a change in material properties both in the mantle and within the slab. Two regions of high stress drop are observed at depths of about 360 and 640 km. A relative minimum of stress drop is found at about 450–560 km where the earthquake frequency is particularly high. Earthquakes at the northern end to the Tonga arc, where the Benioff zone is laterally bent, show systematically higher stress drops than other events at comparable depths, but away from the bend. Also, events in regions of low seismicity appear to have higher stress drops than those in regions of high seismicity. The upper bound of seismic efficiency is found to decrease with depth, implying an increase of frictional force with depth at the earthquake source.     

A COMPARISON BETWEEN KIRCHHOFF AND GRT MIGRATION ON VSP DATA1

A modern approach to migration is to perform wavefield extrapolation, subject to an imaging condition. Correct wavefield extrapolation requires that the boundary conditions at the array of geophones satisfy the wave equation. A sufficient condition is to perform the survey with a single stationary source. Contrary to this condition, many VSPs are conducted in deviated wells, where the source is maintained vertically above the down-hole geophone at each well station. Such a survey fails to provide the boundary conditions theoretically necessary for wave-equation migration. A recently published inversion scheme, referred to as acoustic generalized Radon transform migration (GRT migration), was developed to handle any configuration of sources and geophones, including moving-source deviated-well VSP surveys. GRT migration may be viewed as a weighted version of the generalized Kirchhoff migration, derived in this paper from the exploding-reflector model. When a VSP-survey geometry has been specified, GRT migration can be expressed in terms of array parameters, and compared with the equivalent expression for Kirchhoff (wave-equation) migration. The differences between the two integrals are significant and their effect is demonstrated on VSP data.     

Ground-motion modelling at regional distances for earthquakes in a continental interior,II. Effect of focal depth,azimuth and attenuation

Multiple-mode surface-wave signals are used to model ground motion at distances of 50 to 500 km for an earthquake source in a continental interior. Motion on a thrust fault is used as the earthquake model. Theoretical ground-motion time histories are generated for this source for various focal depths, receiver azimuths and medium-attenuation models. A shallow source will generate greater values for the ground motion than the same source at a greater depth. Two anelastic attenuation models are considered, one appropriate to the central and eastern United States and the other to southern California. The effects of the difference in the attenuation models are seen at distances greater than 100 km for periods greater than 1.5 sec.     

Predictability of currents on a mesotidal estuary (Ria de Vigo, NW Iberia)

In this contribution, the implementation, validation and sensitivity analysis of an operational forecasting system (three-dimensional hydrostatic model) in the Ría de Vigo is presented. A set of sensitivity tests for different atmospheric and hydrodynamic typical periods was performed. The goal is to determine the relative importance of forcing mechanisms in order to evaluate the source of errors in predictions. Previously, validations for three periods of about 15 days were compared with measured data. Sea-level evolution reveals low errors and correlation values close to 1. Surface velocities were compared with high-frequency radar and horizontal Acoustic Doppler Current Profiler data, showing acceptable results on radar area, where tidal and wind circulation patterns are well reproduced by the model. Conductivity, temperature, and depth profiles were used to validate simulated temperature and salinity. While modelled temperature profiles show good agreement with measured profiles, eventual errors are detected on salinity. The sensitivity analysis took three variables into account: sea level, currents at open boundary conditions, and winds (two different configurations). The results show that the most important source of errors on simulated surface currents is wind. Errors on open boundary conditions seem to be limited on the outermost part of the Ría. Although the results presented mainly focus on the Ría de Vigo, the method and conclusions may be applied to other mesotidal estuaries. Moreover, this work will allow a more effective operational system focused on coastal management to be performed.     

Mapping runoff generating areas using AGNPS-VSA model

ABSTRACT

In humid regions, surface runoff is often generated by saturation-excess runoff mechanisms from relatively small variable source areas (VSAs). However, the majority of the current hydrologic models are based on infiltration-excess mechanisms. In this study, the AGricultural Non-Point Source Pollution (AGNPS) model was used to integrate the VSA concept using topographic wetness index (TWI). Both the original and AGNPS-VSA models were evaluated for a small agricultural field in Ontario, Canada. The results indicate that the AGNPS-VSA model performed better than original model. The AGNPS-VSA model predicted that only the saturated portion of the field with higher TWI values produced runoff, whereas the original AGNPS model showed uniform hydrologic response from the entire field. The results of this study are important for accurately mapping the locations of VSAs. This new model could be a powerful tool in identifying critical source areas for applying targeted best management practices to minimize pollutant loads to receiving waters.