The authors consider a bivariate point process \(X(t)=(X_1(t),X_2(t))\) on the plane \(R^2\) such that for some Gaussian \(Y_i(s)\), \(s\in R^2,\) conditionally on \((Y_1,Y_2)\), \(X_1(t)\) and \(X_2(t)\) are independent Poisson point processes with intensity functions \(\exp(Y_1(s))\) and \(\exp(Y_2(s))\), respectively. This model is called log Gaussian Cox process. The couple \((Y_1, Y_2)\) is supposed to be stationary and isotropic. Parametric and nonparametric (kernel) estimates for the covariances of \(Y_i\) are considered. Testing of nonstationarity and anisotropy is discussed. This technique is applied to the analysis of weeds proliferation.