Need for a Large-N Array (and Wavelets and Differences) to Determine the Assumption-free 3-D Earth Model

One of the main objectives of geophysical seismic analysis is to determine the Earth’s structure. Usually, to determine this structure, geophysicists supplement the measurement results with additional geophysical assumptions. An important question is: when is it possible to reconstruct the Earth’s structure uniquely based on the measurement results only, without the need to use any additional assumptions? In this paper, we show that for this, one needs to use large-N arrays – 2-D arrays of seismic sensors. To actually perform this reconstruction, we need to use differences between measurements by neighboring sensor and we need to apply wavelet analysis to the corresponding seismic signals. 1 Formulation of the Problem The main objective of geophysical seismic analysis is to determine the mechanical properties of the Earth based on the observed seismic waves – waves generated both by actual earthquakes and by test explosions; see, e.g., [1]. Usually, in addition to data, we use a large number of additional assumptions [1]. A fundamental question is: when can we reconstruct the mechanical structure directly from data, without the need to involve additional geophysical assumptions?