Journal of Mathematics Research; Vol. 9, No. 1; February 2017 ISSN 1916-9795 E-ISSN 1916-9809 Published by Canadian Center of Science and Education Description of the Dependence Strength of Two Variogram Models of a Spatial Structure Using Archimedean Copulas Moumouni Diallo 1 , Diakarya Barro 2 1 FSEG, Universit´ e des SSG. BP: 2575 Bamako, R´ epublique du Mali 2 Universit´ e Ouaga II. BP: 417 Ouagadougou 12, Burkina Faso Correspondence: Moumouni Diallo, FSEG, Universit´ e des SSG. BP: 2575 Bamako, R´ epublique du Mali. E-mail: moudi- allo1@gmail.com Received: November 22, 2016 Accepted: January 5, 2017 Online Published: January 23, 2017 doi:10.5539/jmr.v9n1p117 URL: http://dx.doi.org/10.5539/jmr.v9n1p117 Abstract Variogram is a geostatistical tool which describes how the spatial continuity changes with a given separating distance between pairs of stations. In this paper, we study the dependence structure within a same class of bivariate spatialized archimedean copulas. Specifically, we point out properties of the gaussian variogram and the exponential one. A new measure of similarity of two copulas is computed particularly between the spatial independent copula and full dependence one. Keywords: variogram, gaussian distribution, Archimedean copulas, similarity, exponential variogram, tail dependent coefficient 2010 MSC: 62H20, 62H11, 60G15 1. Introduction The main objective of geostatistical analysis is the characterization of spatial phenomenos that are incompletely known. Different definitions of geostatistic have been proposed by spatial statistics researchers. Thereby, geostatistics can be defined as a branch of statistics focusing on spatial or spatio-temporal datasets. While G. Matheron (Matheron, G., 1969)found in geostatistics the application of probabilistic methods to regionalized variables, Issaks E. H. et all (Helena, F., 2012) rather defined them as a way of describing phenomenons and provides adaptation of classical regression technics to take advantages of this continuity. Geostatistics covers mainly three subdomains of statistical studies: analysis of variogram, krieging and stochastic simulation. All of these subdomains use variogram models, so that variogram lies at the earth of every geostatistical activity. The variogram function describes the degree of spatial dependence of a given spatial random field or stochastic process {Z( x), x ∈ D} . This tool plays with the madogram a key role in spatial modelling, estimations and inference properties given data constraints. The simple form for madogram is for all h ∈ R d M F (h) = 1 2 E(| F[Z( x + h)] − F[Z( x)]|), x ∈ R d (1) where h is the average value of the separating distance between the two points (Shepard, R. N., 1987). Moreover, the concept of F-madogram has been introduced by Cooley et al. (Shepard, R. N., 1987) to generalized is the λ-madogram associated to the distribution underlying the stochastic process {Z ( x)} . γ F (h) = 1 2 E {  [F (Y ( x))] λ − [F (Y ( x + h))] 1−λ    } ; λ ∈ ]0, 1[ . (2) In the same way, combining results of spatial statistics and multivariate dependence tools, Barro D. (Diakarya, B., 2012) used spatial extreme values copulas to characterize the λ−madogram of process distribution under a distortional assump- tion. Suppose H is a bivariate distribution satisfying the key assumption. If its associated multivariate EV distribution marginal are unit-Fr´ echet distributed, then, the λ-madogram is given by γ λ (h) = 1 D h (λ, 1 − λ) + λ − c (λ) where c (λ) = 2λ (1 − λ) + 1 2(λ + 1) (2 − λ) ; (3) where D h is a conditional spatial measure convex defined on the unit simplex of R 2 . In spatial prevision in particular, the 117