  Seismic wave velocity of underground rock plays important role in detecting
internal structure of the Earth. Rock physics models have long been the focus
of predicting wave velocity. However, construction of a theoretical model
requires careful physical considerations and mathematical derivations, which
means a long research process. In addition, various complicated situations
often occur in practice, which brings great difficulties to the application of
theoretical models. On the other hand, there are many empirical formulas based
on real data. These empirical models are often simple and easy to use, but may
be not based on physical principles and lack a proper formulation of physics.
This work proposed a rational function neural networks (RafNN) for data-driven
rock physics modeling. Based on the observation data set, this method can
deduce a velocity model which not only satisfies the actual data distribution,
but also has a proper mathematical form reflecting the inherent rock physics.
The Gassmann's equation, which is the most commonly used theoretical model
relating bulk modulus of porous rock to mineral composition, porosity and
fluid, is perfectly reconstructed by using data-driven RafNN. The advantage of
this method is that only observational data sets are required to extract model
equations, and no complex mathematical and physical processes are involved.
This work opens up for the first time a new avenue on constructing analytical
expression of velocity models using neural networks and field data, which is of
great interest for exploring the heterogeneous structure of the Earth.
