用灰色马尔柯夫模型探讨新疆境内Ms≥6.0级地震的年发生概率分布

本文在灰色马尔柯夫模型的基础上,增加了一项二重状态转移概率矩阵,对马氏模型进行了修改,据此,研讨了新疆境内1902—1988年Ms≥6.0级地震在不同状态下的年发生概率分布,其结果是令人满意的。提出的灰色马氏模型可作为中期地震预报手段。     

新疆地震趋势的模糊灰色预测

从模糊数学和灰色系统理论两个不同角度来分析地震事件，把模糊数学的表达方式用于灰色灾变预测ＧＭ（１，１）中，建立了地震预测的模糊灰色模型。用此模型讨论了南北天山四个区（带）的震级序列，在等维情况下，对比了模糊灰色方法与单纯灰色方法的优劣，讨论了影响预测结果的因素，最后给出了不同目标震级下各区（带）的预测值。     

新疆北天山中长期地震活动形势分析

在收集全天山尽可能完整的地震目录资料和进行较为科学的天山地震活动分区的基础上，按照从大区到小区、从整体到局部的层次性分析思路，分析了新疆北天山地震活动的阶段性及关联性特征，并进行了b值外推和应变能累积预测分析，估计了新疆北天山强震发生的累积概率和马尔柯夫概率，从而对新疆北天山未来3－10年的中长期地震活动形势提出了分析预测意见。     

复杂记忆概率预测模型

复杂记忆概率预测模型王健（中国北京１０００８１北京国家地震局地球物理研究所）现行的地震概率预测方法是假定相邻地震之间的时间间隔符合某一分布，根据上一次地震的发生时间，便能够计算预测时段内的发震概率。时间间隔的分布可以是多种多样的，因而形成了许多模型。...     

四川甘孜—康定—西昌带大震的长期预测

本文论述四川省内甘孜—康定—西昌一带下次大震将在何时何地发生问题,给出了预测时间区间和最危险地区。这些结果是利用如下的两种方法获得的:其一是历史上地震数据的定性资料分析,其二是利用非齐次马尔柯夫模型的定量计算。     

山东沿黄河带地震活动性的研究

通过对历史地震和现代地震资料的分析，论述了山东沿黄河带地震活动的时空分布特征、应变能积累释放特征、地震震中迁移规律及其震级一频度关系，并运用灰色理论ＧＭ（１，１）模型对山东沿黄河带未来地震危险性进行预测。     

灰色马尔可夫理论在地震预测方面的研究

以陕南地区汶川地震余震资料数据为实例,提出灰色马尔可夫模型对地震进行预测.利用传统的GM(1,1)模型对数据进行拟合和初步预测,运用马尔可夫模型的状态区间和状态转移矩阵对初步预测值进行修正,并对下一组地震数据进行预测.结果表明,模型预测精度高,预测值与实际值接近,可以作为今后地震预报的辅助手段.     

日本发生中强地震的灰色预测

应用“灰色控制系统”理论，选取１９８０年１月至１９８８年１２月日本的地震序列资料，将（６．０，７．０］级地震作为样本，建立了预报地震发震时刻的动态模型。选取了最佳模型对日本未来发生中强地震的时间进行了预测。从函数变换的观点，对ＧＭ（１，１）模型进行了广义解释，指出序列建模必须从满足光滑度的时刻计起。大量计算表明，用“足够小量”样本建模比大量样本建模拟合与外推精度要高，并从信息论角度进行了剖析。     

甘肃南部地区强震危险性的统计分析

本文讨论了甘肃南部Ｍｓ６．０以上强震的危险性问题，给出了本地震区下次强震发生的地区、震级及危险时间的概率分布，这些结果是利用以下两种方法获得的：其一是历史上地震数据的定性资料分析，其二是利用非齐次马尔柯夫模型的定量计算。     

华北地震区地震平静幕持续时间的变化及其解释

本文研究了华北地震区地震平静幕持续时间的变化。发现在每个地震活动期里地震平静幕的持续时间以非线性方式衰减。笔者用灰色系统ＧＭ（１，１）模型拟合了这一非线性特点并用流变体模型对这个特点作了初步解释。     

New fuzzy neural network–Markov model and application in mid- to long-term runoff forecast

ABSTRACT

In this paper, a mid- to long-term runoff forecast model is developed using an ideal point fuzzy neural network–Markov (NFNN-MKV) hybrid algorithm to improve the forecasting precision. Combining the advantages of the new fuzzy neural network and the Markov prediction model, this model can solve the problem of stationary or volatile strong random processes. Defined error statistics algorithms are used to evaluate the performance of models. A runoff prediction for the Si Quan Reservoir is made by utilizing the modelling method and the historical runoff data, with a comprehensive consideration of various runoff-impacting factors such as rainfall. Compared with the traditional fuzzy neural networks and Markov prediction models, the results show that the NFNN-MKV hybrid algorithm has good performance in faster convergence, better forecasting accuracy and significant improvement of neural network generalization. The absolute percentage error of the NFNN-MKV hybrid algorithm is less than 7.0%, MSE is less than 3.9, and qualification rate reaches 100%. For further comparison of the proposed model, the NFNN-MKV model is employed to estimate (training and testing for 120-month-ahead prediction) and predict river discharge for 156 months at Weijiabao on the Weihe River in China. Comparisons among the results of the NFNN-MKV model, the WNN model and the SVR model indicate that the NFNN-MKV model is able to significantly increase prediction accuracy.

Editor D. Koutsoyiannis; Associate editor Y. Gyasi-Agyei     

Prediction of hydrological drought durations based on Markov chains: case of the Canadian prairies

Abstract

Hydrological drought durations (lengths) in the Canadian prairies were modelled using the standardized hydrological index (SHI) sequences derived from the streamflow series at annual, monthly and weekly time scales. The rivers chosen for the study present high levels of persistence (as indicated by values exceeding 0.95 for lag-1 autocorrelation in weekly SHI sequences), because they encompass large catchment areas (2210–119 000 km²) and traverse, or originate in, lakes. For such rivers, Markov chain models were found to be simple and efficient tools for predicting the drought duration (year, month, or week) based on annual, monthly and weekly SHI sequences. The prediction of drought durations was accomplished at threshold levels corresponding to median flow (Q50) (drought probability, q?=?0.5) to Q95 (drought probability, q?=?0.05) exceedence levels in the SHI sequences. The first-order Markov chain or the random model was found to be acceptable for the prediction of annual drought lengths, based on the Hazen plotting position formula for exceedence probability, because of the small sample size of annual streamflows. On monthly and weekly time scales, the second-order Markov chain model was found to be satisfactory using the Weibull plotting position formula for exceedence probability. The crucial element in modelling drought lengths is the reliable estimation of parameters (conditional probabilities) of the first- and second-order persistence, which were estimated using the notions implicit in the discrete autoregressive moving average class of models. The variance of drought durations is of particular significance, because it plays a crucial role in the accurate estimation of persistence parameters. Although, the counting method of the estimation of persistence parameters was found to be unsatisfactory, it proved useful in setting the initial values and also in subsequent adjustment of the variance-based estimates of persistence parameters. At low threshold levels corresponding to q < 0.20, even the first-order Markov chain can be construed as a satisfactory model for predicting drought durations based on monthly and weekly SHI sequences.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Sharma, T.C. and Panu, U.S., 2012. Prediction of hydrological drought durations based on Markov chains in the Canadian prairies. Hydrological Sciences Journal, 57 (4), 705–722.     

四川和云南地区场地平均剪切波速vS20和vS30经验预测模型研究

利用四川和云南地区共973个工程场地钻孔资料,分别基于常速度外推模型、对数线性模型和条件独立模型的经验外推方法建立了该区域20 m和30 m平均剪切波速vS20和vS30的经验预测模型.研究表明常速度外推模型的预测误差最大,当波速资料深度小于10 m时,常速度外推方法会显著低估实际场地平均波速.基于对数线性外推方法建立...     

灰色系统预测在地电预报地震三要素中的应用

本文用灰色系统理论中的系统预测方法，分别建立震级Ｍ、震中距Ｒ、发震时间ｔ＿ｆ与地电异常幅度Ｕ、持续时间Ｔ的灰色预测模型ＣＭ（１，３）。由于引入了ＧＭ模型，就避免了人为确定统计函数形式，并且在震例较少的情况下也可以进行三要素预报，这样就可以建立起适合各个具体台站的预测关系，预测结果较目前统一的预报公式要好。该方法所需资料少，计算简单，给出的结果简明实用。     

A comparative study of nonlinear Markov chain models for conditional simulation of multinomial classes from regular samples

Simulating fields of categorical geospatial variables from samples is crucial for many purposes, such as spatial uncertainty assessment of natural resources distributions. However, effectively simulating complex categorical variables (i.e., multinomial classes) is difficult because of their nonlinearity and complex interclass relationships. The existing pure Markov chain approach for simulating multinomial classes has an apparent deficiency—underestimation of small classes, which largely impacts the usefulness of the approach. The Markov chain random field (MCRF) theory recently proposed supports theoretically sound multi-dimensional Markov chain models. This paper conducts a comparative study between a MCRF model and the previous Markov chain model for simulating multinomial classes to demonstrate that the MCRF model effectively solves the small-class underestimation problem. Simulated results show that the MCRF model fairly produces all classes, generates simulated patterns imitative of the original, and effectively reproduces input transiograms in realizations. Occurrence probability maps are estimated to visualize the spatial uncertainty associated with each class and the optimal prediction map. It is concluded that the MCRF model provides a practically efficient estimator for simulating multinomial classes from grid samples.     

联合多点地质统计学与序贯高斯模拟的随机反演方法

岩相和储层物性参数是油藏表征的重要参数,地震反演是储层表征和油气藏勘探开发的重要手段.随机地震反演通常基于地质统计学理论,能够对不同类型的信息源进行综合,建立具有较高分辨率的储层模型,因而得到广泛关注.其中,概率扰动方法是一种高效的迭代随机反演策略,它能综合考虑多种约束信息,且只需要较少的迭代次数即可获得反演结果.在概率扰动的优化反演策略中,本文有效的联合多点地质统计学与序贯高斯模拟,并结合统计岩石物理理论实现随机反演.首先,通过多点地质统计学随机模拟,获得一系列等可能的岩相模型,扰动更新初始岩相模型后利用相控序贯高斯模拟建立多个储层物性参数模型;然后通过统计岩石物理理论,计算相应的弹性参数;最后,正演得到合成地震记录并与实际地震数据对比,通过概率扰动方法进行迭代,直到获得满足给定误差要求的反演结果.利用多点地质统计学,能够更好地表征储层空间特征.相控序贯高斯模拟的应用,能够有效反映不同岩相中储层物性参数的分布.提出的方法可在较少的迭代次数内同时获得具有较高分辨率的岩相和物性参数反演结果,模型测试和实际数据应用验证了方法的可行性和有效性.     

张北6.2级地震序列显著余震现场灰色预测

根据张家口地震台记录的１９９８年张北早期地震序列资料,对其显著余震（系指ＭＬ≥４．０,下同）建立了ＧＭ（１,１）动态灰色预测模型,并进而依此模型对张北震区主震后,短时内连续发生的５次显著余震进行了尝试性现场预测,结果与实事较吻合,表明灰色预测方法对于探讨如何简捷有效地预测地震序列早期强余震问题,可能具有一定的实际意义。     

Latin hypercube approach to estimate uncertainty in ground water vulnerability

A methodology is proposed to quantify prediction uncertainty associated with ground water vulnerability models that were developed through an approach that coupled multivariate logistic regression with a geographic information system (GIS). This method uses Latin hypercube sampling (LHS) to illustrate the propagation of input error and estimate uncertainty associated with the logistic regression predictions of ground water vulnerability. Central to the proposed method is the assumption that prediction uncertainty in ground water vulnerability models is a function of input error propagation from uncertainty in the estimated logistic regression model coefficients (model error) and the values of explanatory variables represented in the GIS (data error). Input probability distributions that represent both model and data error sources of uncertainty were simultaneously sampled using a Latin hypercube approach with logistic regression calculations of probability of elevated nonpoint source contaminants in ground water. The resulting probability distribution represents the prediction intervals and associated uncertainty of the ground water vulnerability predictions. The method is illustrated through a ground water vulnerability assessment of the High Plains regional aquifer. Results of the LHS simulations reveal significant prediction uncertainties that vary spatially across the regional aquifer. Additionally, the proposed method enables a spatial deconstruction of the prediction uncertainty that can lead to improved prediction of ground water vulnerability.     

基于MaPInfo的中长期地震预测动态系统

“中长期地震预测动态系统”（MapDEP2000 for Windows)是以强震时－空概率增益综合预测模型与单项地震预测模型的预测效能评价方法为理论基础，以强大的数据为支持，集成桌面地图信息系统（MapInfo0的主要功能而研制完成的运行于Windows9x或以上环境下的地震综合预测系统。系统具有中长期单项预测方法的计算，异常提取，效能评价，概率增益统计，外推预测和概率增益综合预测等计算与各种输入／输出，图形显示等强大而实用的功能，为运用数据库和GIS实现多手段，多尺度，动态和交互的信息综合，进行地震预测提供了一套实用的系统和完整的解决方案，本文对该系统的科学依据，设计思想和主要功能进行了介绍。     

Relative model score: a scoring rule for evaluating ensemble simulations with application to microbial soil respiration modeling

This paper defines a new scoring rule, namely relative model score (RMS), for evaluating ensemble simulations of environmental models. RMS implicitly incorporates the measures of ensemble mean accuracy, prediction interval precision, and prediction interval reliability for evaluating the overall model predictive performance. RMS is numerically evaluated from the probability density functions of ensemble simulations given by individual models or several models via model averaging. We demonstrate the advantages of using RMS through an example of soil respiration modeling. The example considers two alternative models with different fidelity, and for each model Bayesian inverse modeling is conducted using two different likelihood functions. This gives four single-model ensembles of model simulations. For each likelihood function, Bayesian model averaging is applied to the ensemble simulations of the two models, resulting in two multi-model prediction ensembles. Predictive performance for these ensembles is evaluated using various scoring rules. Results show that RMS outperforms the commonly used scoring rules of log-score, pseudo Bayes factor based on Bayesian model evidence (BME), and continuous ranked probability score (CRPS). RMS avoids the problem of rounding error specific to log-score. Being applicable to any likelihood functions, RMS has broader applicability than BME that is only applicable to the same likelihood function of multiple models. By directly considering the relative score of candidate models at each cross-validation datum, RMS results in more plausible model ranking than CRPS. Therefore, RMS is considered as a robust scoring rule for evaluating predictive performance of single-model and multi-model prediction ensembles.