Earth-model discrimination method

Abstract

Investigation of the earth's interior is attempted via gravimetric terrestrial spectroscopy from superconducting gravimeter (SG) records containing all medium and large earthquakes that affected the SG. I introduce a general (single station, all-type earthquakes; no pre- or post-processing) method that enables discrimination amongst geophysical earth models by establishing if and when there exist high direct functional correlation values between the oscillations of the earth gravity field taken at a model's low eigenfrequencies, and the earth seismicity expressed in seismic energies and seismic magnitudes.Classically in geophysics - like in many sciences - the Fourier Spectral Analysis (and its derivatives) that requires evenly spaced input data, is used. On the other hand, the Vanicek Spectral Analysis (pronounce van-knee-check), being a least squares spectral fit, treats records with gaps as well as fully populated series. The former technique yields power spectra from evenly sampled data, whilst the latter one estimates both variance- and power-spectra from virtually any numerical record. Using this property, I demonstrate for the first time in geophysics the negative effect that the generating of input-data, for the purpose of completing the time-series, has on the Fourier spectral analyses. To accommodate the problem on existing computers and to create non-distorted 8-sec and 32-sec filtered records from the original one-second data, I design a non-equidistant filter that applies Gaussian weights while accounting for missing data within the filtering step. So filtered, the records are then used in computing the least-squares spectra.I deduce a quantifier of the earth's seismic activity, as the average gravity-spectra magnitude in the low eigenfrequencies band, from one-day, and from one week of data. Statistically significant lunar synodic semi-monthly and solar semi-annual periodicities, as extracted from a decade-long series of diurnal average magnitudes, and coinciding with the current knowledge on tidal triggering of large earthquakes, are revealed for the first time in a global geophysical quantity. The quantifier provides a relative measure of change in gravity field oscillations as due to emissions of, mostly seismic, kinetic energy reflected in noise.Earthquakes are the most common source of abrupt releases of kinetic energy on earth. I then exploit the Jeffreys's rule of thumb: in many earthquakes observations of only the horizontal earth movements during the passage of shear (S) waves can be used to estimate the order of the total released energy. From here I infer that the ratios of kinetic energy EK traveling throughout the earth and displacing the inner masses, vs. seismic energy ES as that part of kinetic energy, which is transmitted mostly through the lithosphere in the form of surface-waves and measured by the seismographs, ought to be constant in most earthquakes. I then hypothesize that the measure of the earth gravity field oscillations, as deduced in the form of median magnitudes of gravity spectra, stands in a direct correlation with earth seismicity along the low characteristic frequencies.In order to prove the hypothesis I process some 10.1 billion observations and compute the diurnal averages of non-reduced-gravity oscillation magnitudes for the last decade and for each long normal mode for three different earth models. I then directly correlate three series against the series containing seismic energies, as well as against the series containing seismic magnitudes of 381, M > 6.3 earthquakes for each day in the [-30, +30] days interval. Direct cross-correlation values as high as 0.97 were obtained, and the hypothesis thus proven. The direct functional correlation values between diurnal average magnitudes of the earth gravity field and all medium-to-large earthquakes from one decade are proposed as a tool for discriminating amongst earth models. If high functional correlation values can be obtained using this method, a tested earth model is to be considered a successful one. The functional correlation values computed from variance-spectra are shown to possess an absolute high for periods of ˜821 s, which could be used as a refinement constraint in earth-model design. For all three earth models the functional correlation values are higher when seismic energies are used rather than seismic magnitudes, as well as when variance-spectra are used rather than power-spectra.The method is unique in its rigor, since it enables assessments of earth models from single-station (gravity) measurements, by using all global earthquakes above certain strength, i.e., regardless of their type, faulting mechanism, etc., and without preprocessing or post-processing to enhance and correct either raw gravity data or their spectra. As such, the method serves as a basis for a definition of different discriminatory criteria.