Even in absence of earthquakes, each site on earth experiences continuous elastic vibrations which are mostly traced to the non-linear interactions of sea waves. However, the fine structure of the spectrum at mHz frequencies shows hundreds of highly significant narrow bandwidth peaks, with a persistence and a coincidence with solar acoustic eigenmodes which are incompatible with any geophysical origin. The feasibility of a common cosmic origin is evaluated through an estimate of the gravitational wave cross-section of the earth, combined with its elastic response and with the stochastic amplification produced by the interference of the cosmic signal with tremor of oceanic origin. The measured spectral peaks appear compatible with a gravitational monochromatic illumination at strains $h \gtrsim 10^{-20} $. We analize in detail the band around 2.614 mHz, where the binary white dwarf J0651+2844 - which is the second strongest known gravitational stellar source - is expected to emit. Compatible spectral tremor peaks are found for both the earth and the sun, but their amplitude is 3 o.m. larger than independent estimates, so that a gravitational source attribution would call for a variety of unknown non-luminous sources with definite mass-distance ratios.
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