Computing three-dimensional gravitational fields with equivalent sources

Existing techniques for computing the gravitational field due to a homogeneous polyhedron all transform the required volume integral, expressing the field due to a volume distribution of mass, into a surface integral, expressing the potential due to a surface mass distribution over the boundary of the source body. An alternative representation is also possible and results in a surface integral expressing the potential due to a variable-strength double layer located on the polyhedral source boundary. Manipulation of this integral ultimately allows the gravitational field component in an arbitrary direction to be expressed as a weighted sum of the potentials due to two basic source distributions. These are a uniform-strength double layer located on all faces and a uniform-strength line source located along all edges. The derivatives of the gravitational field components can also be expressed in a similar form as can the magnetic field components due to a homogeneous magnetic polyhedron. It follows that the present approach can be used to generate a universal program capable of modelling all the commonly used potential field responses due to 3D bodies of arbitrary shape.     

A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty

In this paper a very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.     

Possible Mechanism of Precursory Seismic Quiescence: Regional Stress Relaxation due to Preseismic Sliding

—We propose a new model to physically explain the seismic quiescence precursory to a large interplate earthquake. A numerical simulation is performed to quantitatively examine possible stress changes prior to a great interplate earthquake in a subduction zone. In the present study, the frictional force following a laboratory-derived friction law, in which the friction coefficient is dependent on slip rate and slip history, is assumed to act on a dip-slip fault plane of infinite width in a uniform elastic half-space. The values of friction parameters are determined so that the result of numerical simulation may explain some properties of great interplate earthquakes in subduction zones, such as the recurrence interval and the seismic coupling coefficient. The result of simulation reveals that significant quasi-stable sliding occurs prior to a great earthquake and, accordingly, stresses are changed on and around the plate boundary. In a relatively wide area of the overriding continental plate, the compres sional horizontal-stress perpendicular to the trench axis is decreased for a few years before the occurrence of a great earthquake. This decrease in regional compressional stress may account for the appearance of seismic quiescence prior to a great interplate earthquake.     

广东地震信息网的动态域名服务解决方案

动态域名服务是一种把固定域名解析为动态IP的网络新技术。简要地介绍了动态域名服务技术,并以广东省地震信息网的动态域名服务系统为例,介绍了如何在Windows 2000 Server下实现动态域名服务。     

On methods to select solutions in Euler deconvolution of gravitation and gradient measurements

Euler deconvolution is a standard technique in geophysical exploration to determine the depth of a subsurface mass density or magnetic anomaly from surface measurements of the corresponding field. Because the solution is unstable, some selection criterion must be employed to eliminate probably wrong depth estimates. An ad hoc decision criterion often used by geophysicists is compared here to a probabilistically founded test of the estimates using the Fisher F-distribution. It is shown that this test performs quite badly compared to the ad hoc criterion. However, a probabilistic foundation for the ad hoc criterion is also developed here using the coefficient of variation. Simulations are used to verify that it offers a methodological approach to selecting estimates based on a probabilistic relationship to their true values. That is, the depth estimate is selected based on a tolerance chosen to reflect the desired probability that the estimate should deviate not more than a given percentage from the true value.     

A stochastic approach for sustainability analysis under the green economics paradigm

Sustainability is an increasingly important factor in today’s globally competitive environment. How sustainability features are prioritized in terms of relevance and significance is a function of many factors, including variations in types of business, operational conditions, history and other characteristics particular to a company. The purpose of this paper is to propose a stochastic model that explicitly addresses the potential barriers and enablers to sustainability in order to measure and assess the sustainability level of a company. Given that the potential barriers and enablers to sustainability are context dependent, the stochastic model developed in this paper assumes that a variable characterization of sustainability functions can describe a realistic analytical model for a company’s sustainability behavior. By adopting the strong sustainability perspective, a case scenario is used to demonstrate the application of the proposed model in a major Canadian electric utility. By providing relatively simple and informative measurement, the proposed sustainability model can be used as a practical and effective tool to assess the sustainability level of any company under consideration and to evaluate sustainability fluctuation of the company over time.     

Extensions of nonlinear error propagation analysis for explicit pseudodynamic testing

Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm (Chang, 2003) are presented. One extends the stability study from a given time step to a complete step-by-step integration procedure. It is analytically proven that ensuring stability conditions in each time step leads to a stable computation of the entire step-by-step integration procedure. The other extension shows that the nonlinear error propagation results, which are derived for a nonlinear single degree of freedom (SDOF) system, can be applied to a nonlinear multiple degree of freedom (MDOF) system. This application is dependent upon the determination of the natural frequencies of the system in each time step, since all the numerical properties and error propagation properties in the time step are closely related to these frequencies. The results are derived from the step degree of nonlinearity. An instantaneous degree of nonlinearity is introduced to replace the step degree of nonlinearity and is shown to be easier to use in practice. The extensions can be also applied to the results derived from a SDOF system based on the instantaneous degree of nonlinearity, and hence a time step might be appropriately chosen to perform a pseudodynamic test prior to testing.     

Ground Water Development—The Time to Full Capture Problem

Ground water systems can be categorized with respect to quantity into two groups: (1) those that will ultimately reach a new equilibrium state where pumping can be continued indefinitely and (2) those in which the stress is so large that a new equilibrium is impossible; hence, the system has a finite life. Large ground water systems, where a new equilibrium can be reached and in which the pumping is a long distance from boundaries where capture can occur, take long times to reach a new equilibrium. Some systems are so large that the new equilibrium will take a millennium or more to reach a new steady-state condition. These large systems pose a challenge to the water manager, especially when the water manager is committed to attempting to reach a new equilibrium state in which water levels will stabilize and the system can be maintained indefinitely.     

An algorithmic approach to the total least-squares problem with linear and quadratic constraints

Proper incorporation of linear and quadratic constraints is critical in estimating parameters from a system of equations. These constraints may be used to avoid a trivial solution, to mitigate biases, to guarantee the stability of the estimation, to impose a certain “natural” structure on the system involved, and to incorporate prior knowledge about the system. The Total Least-Squares (TLS) approach as applied to the Errors-In-Variables (EIV) model is the proper method to treat problems where all the data are affected by random errors. A set of efficient algorithms has been developed previously to solve the TLS problem, and a few procedures have been proposed to treat TLS problems with linear constraints and TLS problems with a quadratic constraint. In this contribution, a new algorithm is presented to solve TLS problems with both linear and quadratic constraints. The new algorithm is developed using the Euler-Lagrange theorem while following an optimization process that minimizes a target function. Two numerical examples are employed to demonstrate the use of the new approach in a geodetic setting.     

A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty

In this paper a very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.     

Simplified Approach for Calculating Building-Specific Attenuation Factors and Vapor Intrusion Mitigation System Flux-Based Radius of Influence

This article describes a simplified method to calculate a building-specific subslab to indoor air attenuation factor using data collected during pressure-field extension testing similar to industry standards for radon mitigation. It also describes a simplified method to calculate the radius of influence for a conventional suction point using a mass flux-balance model. The analysis is based on three simple measurements: (1) the extraction flow rate, (2) cross-slab applied vacuum at a radial distance of 3 feet, and (3) cross-slab applied vacuum at a radial distance of 10 feet. The intent is to provide a practitioner with a rapid and useful screening-level assessment of whether the benefits of reduced mitigation system costs warrant an investment in a more detailed mathematical analysis of the flow and vacuum data. In addition, this may also help a practitioner to make real-time decisions regarding placement of communication test points during pressure-field extension testing.     

The need for a better defined Egyptian geodetic datum for geodynamic studies

One of the main objectives of geodesy is to establish a framework of well distributed points (geodetic control points). The coordinates of these points should be known with sufficient accuracy in order to detect any crustal movement and to be also used in any application of geodynamics. These in turn need a better defined geodetic datum.Unfortunately, in Egypt such datum has not yet been adopted due to the lack in geodetic observations. The adopted ellipsoid is not the best or even a good fit to the geoid in Egypt. Therefore, the geodetic observations have not been completely and rigorously reduced to the reference ellipsoid. The network suffers from a fairly large distortion in scale and orientation. Quite a part of that distortion is due to the lack in reducing such observations. The objective of this paper is to review both the available geodetic data and to propose an approach to achieve a well defined geometric datum. Such approach should use all types of geodetic observations (astro-gravity-Doppler) in a combined study using a least squares collocation technique.     

Some consequences of the differences in seismic properties in old and young continental plates for isostatic compensation

We present a short review of seismological data and show that a difference of upper mantle structure is clearly resolved between old and young continental plates. An Archean plate is approximately 1 second faster than a Paleozoic plate for P waves. Such a change in plate structure implies that the density of an Archean lithosphere should be greater than the density of a Paleozoic lithosphere, if they have the same chemical composition. Applying isostasy, we would expect a Precambrian plate to sink and its surface to stand at a level 8 km beneath that of a Paleozoic plate. We first check that the weight of a crustal column is not smaller for a Precambrian crust than for a Paleozoic crust. Explosion seismology data show that isostatic equilibrium is nearly achieved in the crust. Therefore a compensating mechanism has to be acting in the subcrustal lithosphere. Two hypotheses are presented. Provided that the chemical composition of the lower lithosphere does not vary with time, a simple condition for a continental plate not to sink when aging, would be that the density of the lower lithosphere be ?0.1 g/cm³ smaller than the density of the asthenosphere. Another condition that would prevent plates to sink would be a lowering of the density of the lower lithosphere with age due for example to a variation of its chemical composition and to a reduction in the mean atomic weight. Both hypotheses imply that isostatic equilibrium of old continental plates is maintained by a geochemical mechanism. Although thermal evolution is a key factor for explaining the evolution of continents, it has to be complemented by a hypothesis on the change of the chemistry of the lower continental lithosphere with respect to the asthenosphere and/or with respect to age.     

STACKING FILTERS AND THEIR CHARACTERIZATION IN THE (f—k) DOMAIN *

The implementation of a stacking filter involves the filtering of each trace with an individual filter and the subsequent summing of all outputs. The actual position of a trace in space as well as certain simultaneous shifts of traces and filter components in time do not influence the process. The resulting output is consequently invariant to various arbitrary coordinate transformations. For a certain useful class of ensembles of non-linear moveout arrival times for signals a particular transformation can be found which transforms a given ensemble into one consisting only of straight lines. It is thus possible to reduce, for instance, the analysis of a stacking filter designed for hyperbola-like moveout curves to the analysis of a velocity filter with linear moveout curves. As the (f—k) transform is a very useful concept to describe a velocity filter, it can consequently be applied to characterize a stacking filter in regard to its performance on input signals with non-linear moveout.     

Sensitivity of seismic waves to structure

We study how the perturbations of a generally heterogeneous isotropic or anisotropic structure manifest themselves in the wavefield, and which perturbations can be detected within a limited aperture and a limited frequency band. A short-duration broad-band incident wavefield with a smooth frequency spectrum is considered. In-finitesimally small perturbations of elastic moduli and density are decomposed into Gabor functions. The wavefield scattered by the perturbations is then composed of waves scattered by the individual Gabor functions. The scattered waves are estimated using the first-order Born approximation with the paraxial ray approximation. For each incident wave, each Gabor function generates at most 5 scattered waves, propagating in specific directions and having specific polarisations. A Gabor function corresponding to a low wavenumber may generate a single broad-band unconverted wave scattered in forward or narrow-angle directions. A Gabor function corresponding to a high wavenumber usually generates 0 to 5 narrow-band Gaussian packets scattered in wide angles, but may also occasionally generate a narrow-band P to S or S to P converted Gaussian packet scattered in a forward direction, or a broad-band S to P (and even S to S in a strongly anisotropic background) converted wave scattered in wide angles. In this paper, we concentrate on the Gaussian packets caused by narrow-band scattering. For a particular source, each Gaussian packet scattered by a Gabor function at a given spatial location is sensitive to just a single linear combination of 22 values of the elastic moduli and density corresponding to the Gabor function. This information about the Gabor function is lost if the scattered wave does not fall into the aperture covered by the receivers and into the legible frequency band.     

Can global sensitivity analysis steer the implementation of models for environmental assessments and decision-making?

 We illustrate a method of global sensitivity analysis and we test it on a preliminary case study in the field of environmental assessment to quantify uncertainty importance in poorly-known model parameters and spatially referenced input data. The focus of the paper is to show how the methodology provides guidance to improve the quality of environmental assessment practices and decision support systems employed in environmental policy. Global sensitivity analysis, coupled with uncertainty analysis, is a tool to assess the robustness of decisions, to understand whether the current state of knowledge on input data and parametric uncertainties is sufficient to enable a decision to be taken. The methodology is applied to a preliminary case study, which is based on a numerical model that employs GIS-based soil data and expert consultation to evaluate an index that joins environmental and economic aspects of land depletion. The index is used as a yardstick by decision-makers involved in the planning of highways to identify the route that minimises the overall impact.     

The design storm concept in flood control design and planning

The design storm approach, where the subject criterion variable is evaluated by using a synthetic storm pattern composed of identical return frequencies of storm pattern input, is shown to be an effective approximation to a considerably more complex probabilistic model. The single area unit hydrograph technique is shown to be an accurate mathematical model of a highly discretized catchment with linear routing for channel flow approximation, and effective rainfalls in subareas which are linear with respect to effective rainfall output for a selected “loss” function. The use of a simple “loss” function which directly equates to the distribution of rainfall depth-duration statistics (such as a constant fraction of rainfall, or a ?-index model) is shown to allow the pooling of data and thereby provide a higher level of statistical significance (in estimating T-year outputs for a hydrologic criterion variable) than use of an arbitrary “loss” function. The above design storm unit hydrograph approach is shown to provide the T-year estimate of a criterion variable when using rainfall data to estimate runoff.     

Simulations to verify horizontal flow measurements from a borehole flowmeter

This paper reports on experiments and simulations of subsurface flow from a slotted acrylic tube deployed in a sand-tank flow chamber for two different purposes. In the first instance, the slotted tube is used to represent a single fracture intersected by an uncased well. In the second instance, the slotted tube is used to represent a multislot well screen within a porous medium. In both cases, the scanning colloidal borescope flowmeter (SCBFM) measures ground water velocity within the well by imaging colloids traveling through a well to measure their speed and direction. Measurements are compared against model simulations. For the case of a slotted tube representing a single fracture, SCBFM and model results agree with respect to the flow direction and to within a factor of 1.5 for the speed near the well's center. Model and experimental agreement lend confidence that for an uncased well drilled in a fractured-rock medium, a calibrated SCBFM could be used to identify and quantify flowing features. Next, the SCBFM was deployed in a four-column multislotted casing with slots aligned with the flow direction. Another numerical model was developed to estimate the flow field within this well screen to evaluate the potential usefulness of employing the SCBFM in a screened well to estimate flow speed and direction in the surrounding porous medium. Results indicate that if the slots are not aligned with the flow, the SCBFM may only provide order-of-magnitude speed measurements and direction measurements with an uncertainty of approximately +/-25 degrees .     

Estimation of debris flow discharge coefficient considering sediment concentration

A sabo dam has a purpose to block the path of debris flow. However, when overflow occurs, a sabo dam works as a weir, a vertical obstruction, where the fluid must flow over. Many empirical formulas and discharge coefficients for weirs relating flow depth to discharge have been proposed to calculate overflow discharges. However, only a few studies about overflow discharge coefficients are available in the case of debris flow. In this paper, experiments and numerical simulations were done to estimate debris flow discharge coefficients by considering the sediment concentration. In the numerical simulation, a complete overflow equation and a free overfall equation were implemented to calculate debris overflow discharges at a sabo dam. To determine the discharge coefficients for each equation, single factor regression analysis was used. Laboratory experiments were done to calibrate and to compare with the simulation. Study results showed that the discharge coefficients increase as the sediment concentration increases. This finding suggests debris flow discharge coefficients are derived to calculate the debris overflow discharges at a sabo dam.     

Magnetic resonance microscopy of biofouling induced scale dependent transport in porous media

Non-invasive magnetic resonance microscopy (MRM) methods are applied to study biofouling of a homogeneous model porous media. MRM of the biofilm biomass using magnetic relaxation weighting shows the heterogeneous nature of the spatial distribution of the biomass as a function of growth. Spatially resolved MRM velocity maps indicate a strong variation in the pore scale velocity as a function of biofilm growth. The hydrodynamic dispersion dynamics for flow through the porous media is quantitatively characterized using a pulsed gradient spin echo technique to measure the propagator of the motion. The propagator indicates a transition in transport dynamics from a Gaussian normal diffusion process following a normal advection diffusion equation to anomalous transport as a function of biofilm growth. Continuous time random walk models resulting in a time fractional advection diffusion equation are shown to model the transition from normal to anomalous transport in the context of a conceptual model for the biofouling. The initially homogeneous porous media is transformed into a more complex heterogeneous porous media by the biofilm growth.