Spatial Analysis Using Big Data

4.2. Geostatistical model

4.2.1. Spatial data and spatial process

The measurement of spatial data is often carried out at discrete locations. For instance, because of the cost, the boring exploration for seismic surveys can only be conducted with a limited number of locations. Geostatistical models use data from such discrete observation points to estimate the spatial processes and predict the random variables in arbitrary points. Here, the data obtained (observed values) from discrete observation points s _i (i   =   1, …, N) is defined as y( s _i ) or y _i and suppose that it can be decomposed as follows (Cressie and Wikle, 2011, p.121):

y ( s i ) = Y ( s i ) + ε ( s i ) , i = 1 , … , N ,

(4.2.1)