Deep learning

Combinatorics

Geology

Pattern recognition (psychology)

Mathematics

Midpoint

Algorithm

Statistics

Mean squared error

Recurrent neural network

Artificial intelligence

Seismology

Geometry

Interval (graph theory)

Computer science

Data set

Seismic velocity

Artificial neural network

Convolutional neural network

Geophysics

Applying deep learning to 3D velocity model building remains a challenge due to the sheer volume of data required to train large-scale artificial neural networks. Moreover, little is known about what types of network architectures are appropriate for such a complex task. To ease the development of a deep-learning approach for seismic velocity estimation, we have evaluated a simplified surrogate problem — the estimation of the root-mean-square (rms) and interval velocity in time from common-midpoint gathers — for 1D layered velocity models. We have developed a deep neural network, whose design was inspired by the information flow found in semblance analysis. The network replaces semblance estimation by a representation built with a deep convolutional neural network, and then it performs velocity estimation automatically with recurrent neural networks. The network is trained with synthetic data to identify primary reflection events, rms velocity, and interval velocity. For a synthetic test set containing 1D layered models, we find that rms and interval velocity are accurately estimated, with an error of less than [Formula: see text] for the rms velocity. We apply the neural network to a real 2D marine survey and obtain accurate rms velocity predictions leading to a coherent stacked section, in addition to an estimation of the interval velocity that reproduces the main structures in the stacked section. Our results provide strong evidence that neural networks can estimate velocity from seismic data and that good performance can be achieved on real data even if the training is based on synthetics. The findings for the 1D problem suggest that deep convolutional encoders and recurrent neural networks are promising components of more complex networks that can perform 2D and 3D velocity model building.

Seismic velocity estimation: A deep recurrent neural-network approach