Instead of estimating in the frequency domain, I now have a filter that is defined in frequency domain, but transformed into time domain and then applied to the seismometer data. The filtered seismometer data can then be used for the usual time-domain linear estimators. The results is perfect:

So what's left on the list? Although we don't need this, "historically" I had interest in PCA. Although it is not required anymore, analyzing the eigenvalues of the linear estimators may tell us something about the number of seismometers that we need. And it is simply cool to understand estimation of information in seismic noise fields.