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Prestack seismic inversion has been widely used around the seismic exploration. It can precisely output the elastic properties of layers in subsurface, e.g., P-wave velocity (Vρ), S-wave velocity (V Rs), and density (ρ). These are utilized further to extract many reservoir properties, like saturation and porosity, which are very helpful for the successful oil field development. The accuracy of prestack...
In 2016 J. Koenigsmann refined a celebrated theorem of J. Robinson by proving that Q∖Z is diophantine over Q, i.e., there is a polynomial P(t,x1,…,xn)∈Z[t,x1,…,xn] such that for any rational number t we have t/∈Z⟺∃x1⋯∃xn [P(t,x1,…,xn)=0], where variables range over Q, equivalently t∈Z⟺∀x1⋯∀xn [P(t,x1,…,xn)/=0]. In this paper we prove that we may take n=32. Combining this with a result of Z.-W. Sun,...