Positional encoding for nonuniform seismic data reconstruction

Seismic shots or geophones are usually nonuniformly distributed due to environmental factors or intentional observation geometry design. Nonuniform traces should be reconstructed to a Cartesian grid since the following procedures of seismic data processing requires regular discretized datasets for conventional storage and computation. Traditional seismic reconstruction use binning to place data on a regular grid which lead to human artifacts. We proposed a possible strategy for integrating the coordinates into the input of the deep neural network based on positional encoding. We use true coordinates for positional encoding and add the coordinates into the seismic traces. The numerical experiments show that such a strategy can provide a better reconstruction quality than the method without positional encoding under the same network architecture.