Lunar seismograms for LM and S-IVB impacts interpreted as modulation mirage

Abstract

The symmetry of published power spectra of lunar seismograms in the Apollo 12 experiment suggests a modulation effect. The two sufficient conditions for the existence of a modulation effect are nonlinearity and some kind of oscillation. Capacity seismometers are inherently strongly nonlinear. Any attempt to linearize them with a large magnitude bias voltage introduces near-instability. This near-instability, however, does not seem to produce the kind of oscillation necessary for a mirage effect. The actual seismic signal is of very large amplitude and very low frequency content. The output from the seismometer is passed to a phase detector which sees only the small linearity left over after linearization with a bias voltage. Therefore, one must return to the basic nonlinear equations of motion where some near-instability related effect is undoubtedly present. One consequence of the use of phase detection here is to make the output extremely sensitive to any increase in nonlinearity caused by the strength of the incoming signal raising the operating point of the seismometer. Another effect is to introduce a very large conversion loss in creating the mirage effect at a higher frequency. This conversion loss together with the roughly 40 db drop in amplitude due to the seismometer spectral behavior at low frequencies allows very little of the seismic signal to get through. However, this same seismic signal induces a nonlinear behavior in the seismometer which permits noise excitation of the impulse response of the seismometer in a random manner and thus creates a noisy summation of damped oscillations all at the natural frequency (or its harmonics) of the seismometer. This acts as the oscillation necessary for the modulation mirage effect. The only propagation effect left in the modulation mirage is the duration of the seismic signal although the observed envelope which is a nonlinear distortion of the seismic signal may offer a useful estimate of its shape.