Multidimensional Nonstationary Maximum Entropy Spectral Analysis by Using Neural Net

A multidimensional version of the nonstationary maximum entropy spectral estimation method has been developed. By applying the neural net technique, the estimated maximum entropy spectral density function has more resolution power than the conventional nonstationary periodogram spectral density function. The application of spectral density functions to simulate multidimensional nonstationary random fields is also investigated.     

Spectral Estimation in Space and Time Domain by Nonstationary Minimum Variance Spectral Estimator

A multidimensional version of the nonstationary minimum variance spectral estimator has been developed. The numerical results have shown that this method has more resolution power than the conventional nonstationary spectral estimation methods based on periodograms. The application of the spectral estimation method to an irregularly sampled multidimensional nonstationary rainfall mode is also investigated. The other advantage of this spectral estimation method is that it does not require window selection.     

Multidimensional spectrum estimation for nonstationary processes

A spectrum estimation method for multidimensional nonstationary processes has been developed. The estimation method has been applied to a nonstationary two-dimensional random field. The numerical findings show that the results of the estimations are about what can be expected from a multidimensional estimation for a nonstationary process.     

A neurocomputing approach to the forecasting of monthly maximum temperature over Kolkata, India using total ozone concentration as predictor

The association between the monthly total ozone concentration and monthly maximum temperature over Kolkata (22.56° N, 88.30° E), India, has been explored in this paper. For this, the predictability of monthly maximum temperature based on the total ozone as predictor is investigated using Artificial Neural Network. The presence of persistence and similar cyclic patterns are revealed through autocorrelation and cross-correlation coefficients. Common cycles of length 12 and 6 have been identified through periodogram. Hence, a predictive model has been generated by Artificial Neural Network in the form of Multi Layer Perceptron (MLP) using scaled conjugate gradient learning with sigmoid non-linearity. After training and testing the network, an MLP with total ozone of month n as predictor and maximum temperature of month (n + 1) as the target output is found as the best model. Performance of the model has been judged statistically. Finally, the MLP model has been compared with linear and non-linear regressions and the efficiency of MLP has been established over the regression models.     

Analysis of Time of Occurrence of Earthquakes: A Functional Data Approach

There is no single method available for estimating the seismic risk in a given area, and as a result most studies are based on some statistical model. If we denote by Z the random variable that measures the maximum magnitude of earthquakes per unit time, the seismic risk of a value m is the probability that this value will be exceeded in the next time units, that is, R(m)=P(Z>m). Several approximations can be made by adjusting different theoretical distributions to the function R, assuming different distributions for the magnitude of earthquakes. A related method used to treat this problem is to consider the difference between the times of occurrence of consecutive earthquakes, or inter-event times. The hazard function, or failure rate function, of this variable measures the instantaneous risk of occurrence of a new earthquake, supposing that the last earthquake happened at time 0. In this paper, we will consider the estimation of the variable that measures the inter-event time and apply nonparametric techniques; that is, we do not consider any theoretical distribution. Moreover, because the stochastic process associated with this variable can sometimes be non-stationary, we condition each time by the previous ones. We then work with a multidimensional estimation, and consider each multidimensional variable as a functional datum. Functional data analysis deals with data consisting of curves or multidimensional variables. Nonparametric estimation can be applied to functional data, to describe the behavior of seismic zones and their associated instantaneous risk. The applications of estimation techniques are shown by applying them to two different regions and data catalogues: California and southern Spain.     

Moving averages for Gaussian simulation in two and three dimensions

The square-root method provides a simple and computationally inexpensive way to generate multidimensional Gaussian random fields. It is applied by factoring the multidimensional covariance operator analytically, then sampling the factorization at discrete points to compute an array of weighted averages that can be convolved with an array of random normal deviates to generate a correlated random field. In many respects this is similar to the LUdecomposition method and to the one-dimensional method of moving averages. However it has been assumed that the method of moving averages could not be used in higher dimensions, whereas direct application of the matrix decomposition approach is too expensive to be practical on large grids. In this paper, I show that it is possible to calculate the square root of many two- and three dimensional covariance operators analytically so that the method of moving averages can be applied directly to the problem of multidimensional simulation. A few numerical examples of nonconditional simulation on a 256×256 grid that show the simplicity of the method are included. The method is fast and can be applied easily to nested and anisotropic variograms.     

Optical and IR monitoring of the BL Lac object S5 0716+714 from 2001–2004

Multicolor (BV RIJHK) observations of the BL Lac object S5 0716+714 carried out irom 2001–2004 indicate that the spectral energy distribution of the slowly varying component remained constant over the entire wavelength interval and over the three-year observation period. The distribution can be represented by the power law F _v ∼ v ^−1.12, providing evidence that this component has a synchrotron nature. The color characteristics of very rapid variability detected on several nights are the same as those for the slowly varying component. An analysis of published data on the color variability of the object for previous years indicates that the color characteristics of the slowly varying component are stable, independent of the time intervals considered and the characteristic variability time scales.     

The Seyfert 1 galaxy Ark 120 in 1996–2005. Temporal characteristics of the optical variability

We study the optical variability of the Seyfert galaxy Ark 120 using the autocorrelation and structure functions, as well as a periodogram analysis, based on our 1996–2005 U BV RI observations. The autocorrelation function indicates an increase in the correlation to 70% for time shifts of about 430 days. The structure function displays a decrease for these same time shifts, which is interpreted as evidence for periodic events on these timescales. The structure function indicates an increase in the variability amplitude with increasing duration of the variable process. On large time scales, the structure function can be presented as a power-law function with index 0.8–0.9, possibly indicating the presence of unstable processes in the accretion disk. Our search for periodicity in the light curves has revealed a possible period P = 430 days, which has been observed during 13 cycles, as follows from an analysis using continuum from spectral data obtained from 1988 to 2005.     

Digital simulation of multivariate two- and three-dimensional stochastic processes with a spectral turning bands method

The space domain version of the turning bands method can simulate multidimensional stochastic processes (random fields) having particular forms of covariance functions. To alleviate this limitation a spectral representation of the turning bands method in the two-dimensional case has shown that the spectral approach allows simulation of isotropic two-dimensional processes having any covariance or spectral density function. The present paper extends the spectral turning bands method (STBM) even further for simulation of much more general classes of multidimensional stochastic processes. Particular extensions include: (i) simulation of three-dimensional processes using STBM, (ii) simulation of anisotropic two- or three-dimensional stochastic processes, (iii) simulation of multivariate stochastic processes, and (iv) simulation of spatial averaged (integrated) processes. The turning bands method transforms the multidimensional simulation problem into a sum of a series of one-dimensional simulations. Explicit and simple expressions relating the cross-spectral density functions of the one-dimensional processes to the cross-spectral density function of the multidimensional process are derived. Using such expressions the one-dimensional processes can be simulated using a simple one-dimensional spectral method. Examples illustrating that the spectral turning bands method preserves the theoretical statistics are presented. The spectral turning bands method is inexpensive in terms of computer time compared to other multidimensional simulation methods. In fact, the cost of the turning bands method grows as the square root or the cubic root of the number of points simulated in the discretized random field, in the two- or three-dimensional case, respectively, whereas the cost of other multidimensional methods grows linearly with the number of simulated points. The spectral turning bands method currently is being used in hydrologic applications. This method is also applicable to other fields where multidimensional simulations are needed, e.g., mining, oil reservoir modeling, geophysics, remote sensing, etc.     

地震动信号的小波分析

小波分析是一种新的数学方法,因具有良好的时频局部化性质而优于传统的傅立叶分析。地震动是由于地城引起的地面运动,其时间历程函数表现为具有突变特征的非平稳随机过程,因此更适于利用小波变换进行频谱分析。我们在总结小波分析基本原理和方法的基础上,首次利用小波变换分别对地震动加速度时程和速度时程进行了分解和重构,对地震动信号分解结果做了相应频谱分析,并对其小波分析的工程意义进行了初步探索。     

基于离散Gabor变换迭代时变滤波实现地震信号去噪

基于离散Gabor变换时变滤波对宽带和非平稳信号估计具有强大的能力,迭代时变滤波不仅计算上有效,而且能得到较好的信噪比。鉴于迭代时变滤波方法的特点和地震信号的非平稳性,我们提出了基于离散Gabor变换迭代时变滤波方法实现地震信号的去噪,并根据实际地震信号的带限性及其频带分布规律,提出了简单的掩模函数求取方法。经大量的理论模型和实际资料计算表明该方法是有一定效果的。      

Conditional simulation of intrinsic random functions of order k

Conditional simulation of intrinsic random functions of orderk is a stochastic method that generates realizations which mimic the spatial fluctuation of nonstationary phenomena, reproduce their generalized covariance and honor the available data at sampled locations. The technique proposed here requires the following steps: (i) on-line simulation of Wiener-Levy processes and of their integrations; (ii) use of the turning-bands method to generate realizations in Rⁿ; (iii) conditioning to available data; and (iv) verification of the reproduced generalized covariance using generalized variograms. The applicational aspects of the technique are demonstrated in two and three dimensions. Examples include the conditional simulation of geological variates of the Crystal Viking petroleum reservoir, Alberta, Canada.     

Macrozooplankton Community Dynamics in Relation to Environmental Variables in Willapa Bay,Washington, USA

Willapa Bay is a large, economically and ecologically important estuary on the Washington coast, USA for which the zooplankton community has not previously been studied. Thus, in 2006 and 2007, six stations within Willapa Bay were sampled biweekly for macrozooplankton, chlorophyll, and various abiotic variables to elucidate the processes underlying community composition and dynamics. Non-metric multidimensional scaling identified water temperature and upwelling values as major factors defining two distinct temporal communities. High densities and a community dominated by oceanic species (Calanus pacificus, Centropages abdominalis) marked the winter season, while summer (or the upwelling season) was dominated by estuarine species (Palaemonidae, Clevelandia ios). Smaller scale changes in the community were characterized by variation in chlorophyll a concentration and salinity and were marked by the presence of other taxa (Neotrypaea californiensis, Mysidae). These results point to the importance of physical processes, including the import of marine organisms and retention of estuarine organisms, in the structuring of the macrozooplankton community in Willapa Bay.     

On nonhomogeneous models for volcanic eruptions

Recently, a special nonhomogeneous Poisson process known as the Weibull process has been proposed by C-H. Ho for fitting historical volcanic eruptions. Revisiting this model, we learn that it possesses some undesirable features which make it an unsatisfactory tool in this context. We then consider the entire question of a nonstationary model in the light of availability and completeness of data. In our view, a nonstationary model is unnecessary and perhaps undesirable. We propose the Weibull renewal process as an alternative to the simple (homogeneous) Poisson process. For a renewal process the interevent times are independent and distributed identically with distribution function F where, in the Weibull renewal process, F has the Weibull distribution, which has the exponential as a special situation. Testing for a Weibull distribution can be achieved by testing for exponentiality of the data under a simple transformation. Another alternative considered is the lognormal distribution for F. Whereas the homogeneous Poisson process represents purely random (memoryless) occurrences, the lognormal distribution corresponds to periodic behavior and the Weibull distribution encompasses both periodicity and clustering, which aids us in characterizing the volcano. Data from the same volcanoes considered by Ho were analyzed again and we determined there is no reason to reject the hypothesis of Weibull interevent times although the lognormal interevent times were not supported. Prediction intervals for the next event are compared with Ho's nonhomogeneous model and the Weibull renewal process seems to produce more plausible results.     

Regional coal seam gas distribution and burial history of the Hunter Coalfield,Sydney Basin

Basin modelling has been used to improve understanding of the origin and temporal evolution of coal seam gas in the Hunter Coalfield of the Sydney Basin. Burial history models were produced based on data from seven boreholes located in the southern, eastern, central and western areas of the coalfield. Mean random vitrinite reflectance (R_v,r) data, derived from measurements of mean maximum reflectance (R_v,max), were used for calibration of the models. A qualitative sensitivity analysis of one model shows that varying the paleoheat flow has a greater influence on calculated R_v,r than varying the eroded overburden thickness.

The differences between the constructed models are significant enough to provide plausible explanations for regional gas distribution in the Hunter Coalfield. Coals in the south of the coalfield appear to have the greatest potential for thermogenic gas generation. Modelling has shown that areas that have low gas contents and decreased permeability have been uplifted more, and buried less, compared with areas that have high gas contents. Burial history modelling shows noticeable variations in the extent of burial and uplift, and, consequently, in thermal maturities and potential for thermogenic gas generation; together with the assessment of other coal and gas property data, it appears that present-day gas contents may partially reflect coal ranks and adsorption capacities, with late-stage biogenic gas generation replenishing CH₄ volumes that were lost following uplift during the Late Cretaceous.     

A nonstationary parameter model for the sandstone creep tests

The rock masses of hydro-fluctuation belt experience seepage pressure following impoundment in the Three Gorges Reservoir; its creep behaviors are significant for reservoir bank slopes. To study the creep behaviors under seepage pressure (0, 1.45, and 1.75 MPa), we performed creep tests using representative landslide sandstone in the Three Gorges Reservoir and investigated the sandstone creep behaviors under the coupling effects of seepage pressure and stress. Previous researches on rocks have usually regarded the creep constitutive parameter as a constant; however, in this study, a nonlinear, nonstationary, plastic-viscous (NNPV) creep model which can describe the curve of sandstone creep tests is proposed. The rock-creep parameters under three levels of seepage pressure were identified, and theoretical curves using the NNPV model agreed well with the experimental data, indicating that the new model cannot only describe the primary creep and secondary creep stages under varying seepage pressures but also, in particular, perfectly describes the tertiary creep stage. Finally, the sensitivity of the NNPV model parameters is analyzed, and the result shows that the nonstationary coefficient α and the nonlinear coefficient m are main parameters affecting the tertiary creep stage.     

Mainstem and Backwater Fish Assemblages in the Tidal Caloosahatchee River: Implications for Freshwater Inflow Studies

Research strategies for investigating the freshwater-inflow requirements of estuarine fishes often integrate life-history information and correlative analyses of inflow and fish abundance. In tidal rivers, however, some fish have affinities for embayments, oxbows, and smaller tributaries, often referred to collectively as river “backwaters”. The objective of this study was to determine whether freshwater and estuarine fish assemblages differed between backwaters and the mainstem of the tidal Caloosahatchee River, a highly managed river system located in an urban setting in southwest Florida. Nonmetric multidimensional scaling of 21.3-m seine data revealed that fish assemblages did indeed differ between the backwater and mainstem habitats in each of three river sections. Univariate analyses identified species that differed in abundance between the habitats, which included ecologically and economically important fishes in the region. For example, striped mullet Mugil cephalus and pinfish Lagodon rhomboides were more abundant along the river's mainstem; common snook Centropomus undecimalis and bluegill Lepomis macrochirus were more abundant in the river's backwaters. For those species that were more abundant along the mainstem of the river or showed no difference, studies that measure changes in the distribution and abundance of these species with varying inflow along the mainstem of the river are justified. However, for species that were more abundant in backwater areas, geomorphological features should be considered in the design of studies that assess factors affecting fish use.     

Spatiotemporal analysis of groundwater storage variations based on extreme-point symmetric mode decomposition and independent component analysis in Murray-Darling Basin,Australia

The combination of GRACE and hydrological models is widely used for quantification and time-varying analysis of groundwater storage, and several signal-processing tools have been adopted in recent years. However, the popular empirical models constrained by a priori functions, such as least squares fitting, cannot comprehensively reveal the transient variation of nonlinear or nonstationary signal sequences. An emerging self-adaptive signal-processing tool named extreme-point symmetric mode decomposition (ESMD), used with independent component analysis (ICA), has been applied to investigate spatiotemporal characteristics of GRACE-derived groundwater storage (GWS) change in the Murray-Darling Basin, Australia. Although ESMD is firstly applied to GRACE signal analysis, the result is effective and credible. ESMD can explore finer periodic components than the least-squares fitting, and the adaptive ESMD method can more sensitively estimate transient trend change and anomalies in nonlinear or nonstationary signals compared with a priori models. These findings coincide well with hydrometeorological conditions, such as “the Millennium Drought” in Australia’s mainland and the 2010–2012 La Niña event. ICA can also separate the relative independent components of groundwater storage change and qualitatively investigate the spatial weights with corresponding time coefficients. The results suggest that rainfall may be the main input source or influencing factor of groundwater circulation. Contrasting long-term trends between the northern and southern parts of the basin are attributed to the diverse physical mechanism of discharge and recharge related to spatial distribution of surface-water bodies. Although with distinct working principles, the cooperative application of ESMD and ICA can provide cross-supported and complementary conclusions from different perspectives.

     

Changes in drilling density and discovery rates through time

An alternative to time sequence evaluation of field size distributions is presented. Oil fields are ranked in relation to level of prior exploration in the vicinity of discovery wells. Field size distribution patterns for discoveries at sequential levels of prior exploration are evaluated independently from the time sequence of discoveries within the region. Interregional comparisons are made in terms of field discoveries at equivalent levels of prior exploration. The study area covers a large region (approximately 78,000 Km ² ) of central and northwest Kansas.     

Thermal gradients in the Sri Lankan granulite terrane: a garnet–biotite thermometric approach

Thermal zoning of the Highland Complex, Sri Lanka has been delineated using the Fe²⁺–Mg distribution coefficient between garnet and biotite from garnet–biotite gneiss samples collected with wide geographical distribution. In order to minimize the potential for retrograde Fe–Mg exchange and maximize the potential for retaining peak equilibrium K_D (garnet–biotite) and temperature, garnet and biotite included within feldspar and quartz without other mineral inclusions have been selected. The calculated results indicate four distinct temperature contours with K_D values varying from 1.84 to 6.38 and temperature varying from 996 to 591 °C. From the present results, it is possible to divide the Highland Complex into two major metamorphic zones: a high‐temperature area in the central region and a low‐temperature area in the south‐western and north‐eastern region. In conjunction with the metamorphic pressure variations estimated from the granulites of the Highland Complex in previous studies, it is shown that the high‐ and low‐temperature areas are complemented by a high‐pressure region towards the eastern side and a low‐pressure region towards the western side of this complex. This thermal dome is interpreted to be an artifact of the different crustal levels exhumed following Pan‐African metamorphism.