摘要
地质统计学是数学地质领域最为活跃而实用的分支,它是以区域化变量理论为基础,以变异函数为基本工具,研究那些在空间分布上既具有随机性又具有结构性的自然现象的科学。在第四纪研究中的很多特征(变量)均可看成区域化变量进行地质统计学分析。作者在讨论了经典概率论及数理统计方法简单地应用于第四纪研究可能出现的问题后,着重介绍了用于第四纪研究中的若干地质统计学方法及基本理论,同时,对地质统计学方法应用于第四纪研究中的前景进行了分析。
Geostatistics is one of the most active and effective branch in mathematical geology. Geostatistics is based on the regionalized variable theory, using variograms as its basic tools and deals with the natural phenomenon with distribution charaterized by both randomness and structuralism. We can regard a lot of characters (variable) in Quaternary research as regionalized variable from which geostatistical analysis and estimation can be made. The paper has dealt mainly with four questions: 1. Some questions about application of classical probability and mathematical statistics methods in geological exploration and Quaternary research. 2. Difinition and some basic theories of geostatistics, including: regionalized variable theory, 2-order stationary hypothesis and intrinsic hypothesis, as well as variogram and structure analysis. 3. Some geostatistical methods are used in Quaternary research, including: ordinary kriging and lognormal kriging; universal kriging; non-parametric geostatistics and indicator kriging; multivariate geostatistics and cokriging; space-time kriging. (1) Ordinary kriging and lognormal kriging Common distribution of variables in nature are normal and/or lognormal distribution or three-parameter lognormal distribution. After basic theory and methods of ordinary kriging is studied in this paper, lognormal kriging and three-parameter lognormal kriging are discussed in detail. (2) Universal kriging When the observed values of variables are obviously varying in some directions, called non-stationary, we have to consider the existence of drift in the research area. Universal kriging is a non-bias linear estimation method. In this case, universal kriging systems are sum from i=1 to n λ_i()(x_i,x_i)-sum from l=0 to k μ_lf_l(x_i)=(x_i,x_o) (j=1,2,…,n) sum from i=1 to n λ_if_l(x_i)=f_l(x_o)(l=1, 1,…,k) where f_i(x_i) are polynomical function of samples x_i, f_i(x_o) polonomial function of estimated points x_o,μ_l are lograngian. (3) Nonparametric geostatistics and indicator kriging Geological data curves usually show a long-tail of the distribution, such an abnormal distribution feature will have an influence upon the precision of data processing and estimation. The long-tail of the distribution may be caused by following reasons: a) the appearence of outlier which is of great importance to data processing; b) data with a multiple (or mixed) population. The ordinary kriging or universal kriging are not suitable for such data. For this reason, a new geostatistical technique——nonparametric geostatistics is introduced in this paper. It is a branch of geostatistics comprising technique and its main method is indicator kriging. Indicator kriging aims at providing a model for the conditional distribution of the unknown attribute at any unsampled location. In this paper four questions are discussed: a) indicator function and its second order moments; b) indicator semivariogram; c) indicator kriging systems; d) indicator kriging estimation. In this case, indicator kriging systems are sum from β=1 to n λ_β(Z)(?)(x_α,x_β;Z)-μ(x_α,A;Z) (α=1,2,…,n) sum from α=1 to n λ_α(Z)=1 ~1 (4) Multivariate geostatistics and cokriging In earth science fields, sometime, we must synthesize and interpret multivariate information provided by samples which are characterized by their spatial location. In this paper, we introduce multivariate geostatistics which consists of two methods: factorial kriging and cokriging. Multivariate geostatistics based on the coregionalized theory and using covariogram or cross-covariance as its basic tools studies multivariate information space structure which is characterized by both statistical correlation and spatial correlation at same spacial domain. Cokriging is the basic method of multivariate geostatistics, and cokriging systems are sum from i=1 to N_V sum from β_i=1 to n_i λ_βi(?)(V_αi,V_βi)-μi=(?)_io,i(V_io.v_αi) (α_i=1,2,…n_i) (i=1,2,…N_V) sum from α_i=0 to n_io λ_α_io=1 (i≠i_o) sum from αi=1 to ni λ_αi=0 Factor kriging included the decomposition of regionalized vaiables and estimation of spatial components, as well as estimation of regionalized factors at given space scales. (5) Space-time kriging 4. Analysis of application foreground of geostatistics in Quaternary research.
出处
《第四纪研究》
CAS
CSCD
1993年第3期203-213,共11页
Quaternary Sciences
