  Seismic networks provide data that are used as basis both for public safety
decisions and for scientific research. Their configuration affects the data
completeness, which in turn, critically affects several seismological
scientific targets (e.g., earthquake prediction, seismic hazard...). In this
context, a key aspect is how to map earthquakes density in seismogenic areas
from censored data or even in areas that are not covered by the network. We
propose to predict the spatial distribution of earthquakes from the knowledge
of presence locations and geological relationships, taking into account any
interaction between records. Namely, in a more general setting, we aim to
estimate the intensity function of a point process, conditional to its censored
realization, as in geostatistics for continuous processes. We define a
predictor as the best linear unbiased combination of the observed point
pattern. We show that the weight function associated to the predictor is the
solution of a Fredholm equation of second kind. Both the kernel and the source
term of the Fredholm equation are related to the first-and second-order
characteristics of the point process through the intensity and the pair
correlation function. Results are presented and illustrated on simulated
non-stationary point processes and real data for mapping Greek Hellenic
seismicity in a region with unreliable and incomplete records.
