Direct inversion of Young's and Poisson impedances for fluid discrimination

Seismic inversion with prestack seismic data such as amplitude variation with offsets (AVO) inversion is an important tool in the estimation of elastic parameters for predicting lithology and discriminating fluid in conventional or unconventional hydrocarbon reservoirs. The product of Young's modulus and density (Young's impedance, YI) and the product of Poisson ratio and density (Poisson ratio impedance, PI) show great potential in lithology prediction and fluid discrimination of unconventional resources such as shale gas or oil. The high quality requirements for prestack data in density inversion render the estimation of YI and PI arduous and inaccurate with a conventional prestack inversion approach. In this study, a direct AVO inversion approach is proposed to estimate YI, PI, and density directly from P‐wave seismic data. The linearized P‐wave reflectivity approximate equation in terms of YI, PI, and density is initially derived. Five models, including four typical AVO classes, are utilized to verify the accuracy of the derived linearized P‐wave reflectivity equation in comparison with the exact P‐wave reflectivity equation and the frequently used linearized reflectivity approximate equation involving P‐ and S‐wave velocities and density. Parameter sensitivity analysis illustrates that YI and PI can reasonably be estimated from P‐wave reflectivity if a decorrelation scheme is utilized in the inversion algorithm. In addition, a pragmatic AVO inversion using a Bayesian scheme is suggested for the direct inversion of YI and PI from prestack seismic data. Synthetic and field data examples demonstrate the feasibility of the proposed inversion approach in the estimation of YI and PI and show the potential of this approach in fluid discrimination.     

Impacts of Multiple-Period Lags in Dynamic Logit Models

This paper will provide an introduction to a new field of research, viz. the sensitivity of the solution trajectory of a dynamic logit model (belonging to the class of discrete choice models) in the light of a multiperiod lag structure. It is well known from recent advances in the area of chaos and turbulence theory that the stability of a dynamic system is critically dependent on various factors, such as threshold values of parameters, initial conditions, and also the lag structure. This paper aims to identify the consequences of different lag structures in dynamic logit models (including also dynamic spatial interaction models). Various simulation experiments will be used to show that the onset of instability of the solution trajectory tends to decrease as the number of time lags increases (depending also on the growth rate of the system).     

The effect of a priori knowledge on parameter estimation errors with applications to incoherent scatter

The dependence of the width of the a posteriori distribution (i.e. parameter estimation error) in a multiparameter fit on the a priori width of another parameter is studied in the framework of linear statistical inversion theory. An exact formula is given which makes it possible to estimate how accurate the a priori information on a given parameter must be in order to obtain the other parameter with a prescribed accuracy. These estimates are useful in those cases where some errors are strongly correlated, like the ion temperature and the O⁺ content in incoherent scatter measurements with the EISCAT UHF radar. The dependence of the solution on the accuracy of the power profile estimates is given. Likewise, the behaviour of the error when a linear combination of the parameters is known exactly is given. The formulae given have a very simple geometrical meaning, and together they give a complete solution to the problem of estimating the accuracies in a multiparameter fit when a linear combination of the variables is known with a prescribed accuracy. It is shown that under the conditions considered in this paper, oxygen content can be determined to an accuracy of 10 % when the ion temperature is known to within 7 %, if we can assume that the collision frequency is zero.     

ELASTIC EARTH PRESSURES ON RIGID WALLS UNDER EARTHQUAKE LOADING

Elastic dynamic earth pressures induced by earthquakes are computed by analyzing a wall-foundation-backfill system. Both foundation and backfill are considered viscoelastic; the foundation is a semi-infinite space and the backfill, a uniform layer of constant thickness. A simple analytical solution is developed by assuming an approximate backfill-foundation interface condition and adopting the least squares method. The response functions computed indicate the large influence of the various system parameters on earth pressure, including the foundation characteristics,as well as wall geometry and mass. The transient response of the system is also studied by obtaining spectra for base shear. A large number of seismic records are analyzed to obtain average spectra and a total of three correction functions are used to take into account the foundation stiffness and density as well as wall inertia. A simple design method is proposed to estimate the maximum base shear.     

A nonlinear maximum entropy method for spectral estimation applied to incoherent scatter radar measurements: application to synthetic incoherent scatter data

The EISCAT measurements are based on the autocorrelation function technique. An alternative approach is to derive the ionospheric parameters from an estimate of the power spectrum for the received radar signal. We have used a nonlinear maximum entropy method to deduce parameters from the power spectrum of a generated signal. A comparison has been made with parameters obtained by the ACF method. This preliminary study suggests that the spectrum method could become useful, especially for determining the position of peaks in the incoherent scatter spectrum.     

Quantifying tomb geometries in resistivity images using watershed algorithms

Quantifying the geometries (defined here as width, height and depth of burial) of archeological structures within resistivity models produced as a result of the regularization constraints used in most inversion algorithms is difficult, especially when structures are closely spaced. Here we apply the watershed by simulated immersion method of boundary detection to smooth 2D resistivity images generated for synthetic and field data over 3D targets. The synthetic studies include a single cavity model, a model for two widely spaced cavities (spacing ? unit electrode spacing) and a model for two closely spaced cavities (spacing < unit electrode spacing). We also examine a single-cavity model where a relatively resistive overburden, common at archaeological sites in Egypt, is included. In the case of the single cavity models, the maximum error for any geometries are 18% for the model without the resistive overburden and 10% for the model where the overburden is included, whereas it increases to 24% for the widely spaced model and 40% for the closely spaced model. Despite, the higher errors in the closely spaced cavity model, application of the algorithm confirms the presence of two features, which is not ascertainable from the smooth resistivity images. Boundaries detected with the watershed algorithm are subsequently used to define a disconnect in the regularization, resulting in a markedly improved estimate of the resistivity structure (particularly for the closely spaced cavity model) in a second inversion step using the model obtained from the smoothness constraint inversion as the starting model. This revised resistivity model also results in a lower root-mean-square (rms) misfit between measured and theoretical data, and between synthetic and inverted models. We demonstrate how the method can be applied on images from the archaeological site at Qurnet Murai, Luxor City Egypt.     

An XFEM Model for Seismic Activity in Indian Plate

Empirical approaches based on the available earthquake catalog are popular among engineers to estimate seismic hazard. The seismic activity on individual faults inferred from these approaches is associated with a large number of uncertainties, especially due to lack of data. This article proposes a mechanistic approach to quantify seismic and fault activity, thereby overcoming the difficulties in the existing empirical procedure. A finite element (FE) model for Indian Plate, with the geological ‘cratons’ is developed and subject to plate driving forces namely, the ridge push and the slab pull forces. The material properties and the thickness of both plate and cratons are obtained through inversion using the recently available Global Positioning System (GPS) data. The tectonic faults are modeled using the well-known ‘extended FE method (XFEM)’. The simulated strains at fault level are compared with the computed strain rates from the earthquake catalog. Further, the procedure to quantify fault activity is demonstrated for Gujarat, India.     

EFFICIENT ALGORITHMS FOR CONSTRUCTING PROPER HIGHER ORDER SPATIAL LAG OPERATORS*

ABSTRACT. This paper extends the work of Blommestein and Koper (1992)–BK–on the construction of higher-order spatial lag operators without redundant and circular paths. For the case most relevant in spatial econometrics and spatial statistics, i.e., when contiguity between two observations (locations) is defined in a simple binary fashion, some deficiencies of the BK algorithms are outlined, corrected and an improvement suggested. In addition, three new algorithms are introduced and compared in terms of performance for a number of empirical contiguity structures. Particular attention is paid to a graph theoretic perspective on spatial lag operators and to the most efficient data structures for the storage and manipulation of spatial lags. The new forward iterative algorithm which uses a list form rather than a matrix to store the spatial lag information is shown to be several orders of magnitude faster than the BK solution. This allows the computation of proper higher-order spatial lags “on the fly” for even moderately large data sets such as 3,111 contiguous U. S. counties, which is not practical with the other algorithms.     

CELL-CORRECTED RAS METHOD (CRAS) FOR UPDATING OR REGIONALIZING AN INPUT–OUTPUT MATRIX

ABSTRACT.  The RAS method is used to update or regionalize a single matrix such that it conforms to new row and column totals. This paper presents a correction of the RAS method (CRAS) that uses cell variation distributions calculated from multiple matrices of different periods or different regions. After the solution of the regular RAS, an additional optimization problem is solved that produces the most likely cell-corrections to the regular RAS solution. To test the behavior of CRAS, several simulations with a time series of input–output tables for The Netherlands for 1968–1986 are made. They show that—in situations of structural change—applying CRAS improves the regular RAS estimate. The method will also be applicable to traffic, trade, and migration matrices.     

Parameter mixing errors within a measuring volume with applications to incoherent scatter

The effect on parameter error estimates resulting from parameter variations within the measuring volume under consideration is studied in the framework of linear statistical inversion theory. It is shown that using estimates for the parameter averages is equivalent to having the theory corrected by the covariances of the variables coupled with the second derivatives of the theory function. If the parameter distributions were known exactly, this would only introduce a bias in the linear theory and hence a systematic error in the parameter centre point estimates. When the distributions are not known exactly, there is another source of error consisting of the uncertainties in the parameter variation estimates. This leads to new error bounds on the allowed parameter variability within the volume under consideration if some prescribed accuracy in the parameter average estimates is required. These considerations are applied to incoherent scatter (IS) radar measurements, where it is important to be able to estimate the effect of integrating both in space and time over a volume with varying parameters in order to obtain spectra or autocorrelation functions. Numerical examples are given in the case of the O⁺ content estimates in measurements with the EISCAT UHF radar, when for example the ion temperature varies over the integration ranges. The results obtained may be used in the design of experiments when high resolution composition measurements are required.     

A method of determining horizontal structure of the ionosphere from backscatter ionograms

We have developed a technique lor oblique backscatter sounding (OBS) ionogram inversion as a diagnostic tool for the horizontally inhomogeneous structure of the ionosphere. Input data for the method include the leading edge of a backscalter ionogram that is measured through soundings in a given direction, and the vertical electron density profile measured over the sounding station or over some other site lying in the sounding direction. The method may be useful for reconstructing the two-dimensional electron density distribution in a vertical plane aligned with the direction of sounding. The inverse problem has been solved using the Newton Konlorovich method and the Tikhonov regularization method. The algorithm we have developed was tested against model data, that is, OBS ionograms synthesized using geometrical optics calculations for different models of the inhomogeneous ionosphere. Test results demonstrate that our method converges reliably, is stable to measurement errors and provides a good accuracy of reconstruction of inhomogeneous structures with scales of 100 2000 km. This indicates that this method shows promise as an operative remote diagnostic tool for ionospheric irregularities of natural and artificial origin.     

Kriging the Local Risk of a Rare Disease from a Register of Diagnoses

A substantial problem in studying the geographical epidemiology of rare noncontagious diseases is to estimate the risks of their development within populations. A geostatistical solution is described and illustrated by a case study of cancer among children in the West Midlands of England for the years 1980 to 1984 inclusive. Data consist of the numbers of diagnosed cases of cancer and of healthy children in each of 838 electoral wards, the centroids of which are known accurately. The rate of incidence or frequency, equal to the number of cases divided by the number of children, is a binomial variable and is treated as a realization of the underlying risk of a child's developing the disease that varies from place to place. The experimental variogram of the frequency was computed using the standard formulation. The variogram of the risk was obtained from it taking into account the numbers of children at risk and the error associated with each observed frequency. The variogram of the risk increased monotonically from 0 at zero lag to about 50 kilometers, and it was modeled as Whittle's two-dimensional elementary correlation function. The covariances of frequency and cross-covariances between the frequency and the risk were derived from it, and these were then used together with the data to krige the risk and map it. The risk of developing the disease is shown to have a patchy distribution, strongly autocorrelated at the regional scale of the investigation.     

Distribution of Lateral Forces in Base-Isolated Buildings Considering Isolation System Nonlinearity

The ASCE 7 equivalent lateral force method for base-isolated buildings applies a triangular distribution of forces to the superstructure. This distribution attempts to approximately account for the observed effects of isolation system nonlinearity on the superstructure response, but a more rational approximation is needed. Using nonlinear regression analysis of median response data from nonlinear response history analysis of representative systems, improved equations are developed to estimate the lateral force distribution in the superstructure. The ASCE 7 distribution, a revision considered by a SEAONC committee, and the improved distribution developed here are evaluated. Only the improved equations are accurate over many system parameters.     

LEAST SQUARES ESTIMATES OF THE REGIONAL EMPLOYMENT MULTIPLIER: AN APPRAISAL*

Basically, we have attempted to show the following in the course of setting out the algebra of regression analysis of selected regional employment multiplier models: (1) When the basic features of the model are shaped by the assumption of an unlagged response of local employment to changes in export employment, the least squares estimates of the multipliers are highly sensitive to the export coefficients vector A, given the sample observation matrix X. In a completely disaggregated model such as Equation (21), the multipliers are solely determined by the export coefficients and thus are entirely independent of sample observations. However, this independence does not hold in the case of a partially disaggregated model. The identity relation is also destroyed when a lag relationship is introduced into a completely disaggregated model. (2) A simple lag model produces results bascially different from those obtained by an unlagged model if the overall differences between current and lagged observations are significant. (3) Given a matrix of sample observations on employment, it is possible to estimate the upper limits of a least-squares aggregate multiplier and its variance simply from knowledge of the export coefficients (4) The export coefficients vector has also an important bearing upon the correlation coefficient. The correlation is unity if and only if the export coefficients vector is proportional to the local employment coefficients vector, while it is zero if and only if the export coefficients vector is a vector all of whose elements are one. Also, the correlation coefficient is equal to one when a completely disaggregated model is used. There is finally the question of what these results mean in terms of the formulation of a multiplier model. First of all, in view of the crucial importance of the export coefficients and the difficulties of estimating them, most of the existing models do not seem to offer promising results. Furthermore, all the models examined here have made some simplifying assumption with respect to the constancy of the export coefficients. It remains highly uncertain whether these coefficients are reasonably stable over time. Of course, it would be theoretically more acceptable to relax the assumption of the invariance of export coefficients and to obtain such coefficients at different points of time for each industry. However, this would be accomplished only at the cost of increased difficulties of estimating larger numbers of export coefficients. In addition, there is some doubt as to the validity of the assumption that export employment is proportional to export sales. Since a lag relationship is important not only in terms of attempts to formulate multiplier models more realistically, but also in terms of its significant effect on the multiplier values obtained, the nature and the form of a lagged response and its estimation problems need to be investigated in depth. Finally, problems of least squares bias and efficiency, inference, and prediction which may arise in the context of various models presented here remain to be investigated. A detailed analysis of such problems must be the subject of further investigation.     

Simulation of the global structure of stationary planetary waves in the mesosphere and lower thermosphere

When simulating the global structure of stationary planetary waves (SPW) the problem of obtaining the numerical solution in the equatorial region appears. It results from the presence of apparent singularities in the operator of the SPW latitudinal structure when the Coriolis parameter is small. The new method based on SPW latitudinal operator inversion is proposed. This method permits the difficulties arising from the simulation of stationary large scale disturbances at low latitudes to be avoided. The global structure of SPW with zonal wave number m = 1 at the mesosphere and lower thermosphere heights has been calculated for the background zonal wind distribution representing a climatic picture of the solstice conditions. In the region of the mean zonal westerlies the SPW penetration across the equator is obtained. The SPW at low latitudes are shown to appear most significantly in the zonal component of the wind velocity. The influence of planetary wave motions on the distribution of longlived species in the ionospheric D-region and at the heights of lower thermosphere are discussed.     

SPATIAL AUTOCORRELATION IN BRITISH UNEMPLOYMENT

ABSTRACT. The recent literature on local unemployment in Britain and the U.S. is reviewed, and a model estimated for Britain which is consistent with the findings of that literature. Spatial econometric techniques are applied to test and elaborate on that model. The results indmte the presence of significant spillovers in adjustments to local demand shocks. These spillovers occur over a wide spatial field and are strongest after a lag, suggesting that they reflect migration behavior. In addition, highly localized spatial interactions are found, consistent with commuting adjustments in response to shocks. Incorporating these effects eliminates spatial autocorrelation from the residuals. A simulation exercise is undertaken to demonstrate the effects of supply- and demand-side shocks on the model solution.     

Statistical errors in the determination of wind velocities by the spaced antenna technique

This paper is concerned with the statistical errors which are present when wind velocities in the atmosphere are determined by the radar method known as the spaced antenna technique. It is assumed that the (complex) data is processed by the method known as full correlation analysis (FCA). A theory is first developed to give the error in the determination of the position of the maximum of a cross-correlation function and the value of lag such that the auto-correlation falls to a value equal to that of the crosscorrelation at zero lag. These are the basic quantities needed for the application of FCA. These error estimates are tested with a variety of numerically simulated data and shown to be realistic. The results are applied to real data and, using the standard techniques for the propagation of errors, they lead to estimates of the errors in the derived wind velocities. In order to test these estimates, an experiment was carried out in which two independent wind determinations were made simultaneously. The differences were used to obtain experimental estimates of the errors. It was found that the theory overestimates the error in the wind velocities by about 50%. Possible reasons for this are discussed.     

Geographically Weighted Extreme Learning Machine: A Method for Space–Time Prediction

Spatial heterogeneity has been regarded as an important issue in space–time prediction. Although some statistical methods of space–time predictions have been proposed to address spatial heterogeneity, the linear assumption makes it difficult for these methods to predict geographical processes accurately because geographical processes always involve complicated nonlinear characteristics. An extreme learning machine (ELM) has the advantage of approximating nonlinear relationships with a rapid learning speed and excellent generalization performance. However, determining how to incorporate spatial heterogeneity into an ELM to predict space–time data is an urgent problem. For this purpose, a new method called geographically weighted ELM (GWELM) is proposed to address spatial heterogeneity based on an ELM in this article. GWELM is essentially a locally varying ELM in which the parameters are regarded as functions of spatial locations, and geographically weighted least squares is applied to estimate the parameters in a local model. The proposed method is used to analyze two groups of different data sets, and the results demonstrate that the GWELM method is superior to the comparative method, which is also developed to address spatial heterogeneity.     

Effective hydration temperature of obsidian: a diffusion theory analysis of time-dependent hydration rates

An estimate of effective hydration temperature (EHT) is needed for chronological use of obsidian hydration data. This paper describes a method for calculating EHT by the practicing archaeologist, replacing three techniques that are in general use today: estimates based on mean temperature, numerical integration of models of diurnal and annual temperature variations, and use of temperature cells. The hydration (or diffusion) coefficient of obsidian is a function of temperature and thus is time varying, while the classic quadratic law of hydration is not valid for time-varying diffusion coefficients. This paper presents a mathematical solution to the case of a time-varying hydration coefficient, based on diffusion theory, with a concise definition of EHT. It is shown that the results are not affected by concentration dependence in the diffusion coefficient. A computer program to compute the rigorous solution is described, and data are presented to explore the resulting range of variation. That use of the Lee equation to compute EHT is not appropriate for obsidian hydration studies is evident from the data presented. The effects of paleoclimatic variation are estimated, and an algebraic best fit equation and worksheet are provided as practical aids to the archaeologist.     

Knowledge-Based Performance Assessment of Existing RC Buildings

One of the most challenging aspects of the seismic assessment of existing buildings is the characterization of structural modeling uncertainties. Recent codes, such as Eurocode 8, seem to synthesize the effect of structural modeling uncertainties in the so-called confidence factors that are applied to mean material property estimates. The confidence factors are classified and tabulated as a function of discrete knowledge levels acquired based on the results of specific in-situ tests and inspections. In this approach, the effect of the application of the confidence factors on structural assessment is not explicitly stated. This work presents probabilistic performance-based proposals for seismic assessments of RC buildings based on the knowledge levels. These proposals take advantage of the Bayesian framework for updating the probability distributions for structural modeling parameters based on the results of tests and inspections. As structural modeling parameters, both the mechanical material properties and also the structural detailing parameters are considered. These proposals can be categorized based both on the amount of structural analysis effort required and on the type of structural analysis performed. An efficient Bayesian method is presented which relies on simplified assumptions and employs a small sample of structural model realizations and ground motion records in order to provide an estimate of structural reliability. As an alternative proposal suitable for code implementation, the simplified approach implemented in the SAC-FEMA guidelines is adapted to existing structures by employing the efficient Bayesian method. This method takes into account the effect of both ground motion uncertainty and the structural modeling uncertainties on the global performance of the structure, in a closed-form analytical safety-checking format. These alternative proposals are demonstrated for the case study structure which is an existing RC frame. In particular, it is shown how the parameters for the safety-checking format can be estimated and tabulated as a function of knowledge level, outcome of tests, and the type of structural analysis adopted.