Statistical simulation of isotropic random fields on a sphere (Q2755277)

The authors consider real-valued mean square continuous random fields \(\xi(\theta,\varphi)\), in which are isotropic on the unit sphere in the 3-dimensional space. These fields may be represented in the form NEWLINE\[NEWLINE\xi(\theta,\varphi)=\sum_{m=0}^{\infty}\sum_{l=0}^{m}c_{m,l} P_m^l(\cos (\theta))\left[\zeta_{m,1}^l\cos (l\varphi)+ \zeta_{m,2}^l\sin (l\varphi) \right], NEWLINE\]NEWLINE where \(\{\zeta_{m,k}^l\},k=1,2\), are sequences of uncorrelated random variables. To approximate the fields the authors use partial sums of the form NEWLINE\[NEWLINE\xi_N(\theta,\varphi)=\sum_{m=0}^N\sum_{l=0}^{m}c_{m,l} P_m^l(\cos (\theta))\left[\zeta_{m,1}^l\cos (l\varphi)+ \zeta_{m,2}^l\sin (l\varphi) \right]. NEWLINE\]NEWLINE The mean square error of this approximation is estimated.