Deep Learning-Based Low-Frequency Extrapolation and Impedance Inversion of Seismic Data

Seismic inversion is an indispensable part of the earth exploration to precisely obtain the properties of subsurface media based on seismic data. However, the lack or inaccuracy of low-frequency (LF) information in seismic data constrains the correctness of the inversion. Traditional techniques encounter challenges in compensating the LF component of seismic data. Accessing the ability of deep learning to nonlinearly map inputs to expected outputs, we develop a neural network that can map poststack data to broader band data and then to impedance. We first propose an effective preprocessing scheme incorporating both well-logging and seismic data. Then, we extrapolate the LF information in the seismic data and invert the P-wave impedance with supervised and semisupervised frameworks, respectively. In the synthetic data example, the coefficient of determination ( $R^{\mathrm{ 2}}$ ) reaches 0.99 for LF extrapolation and 0.98 for impedance inversion. In the field data example, $R^{\mathrm{ 2}}$ is 0.826 between the inverted impedance and the real impedance of the validation well. Our experiments also reveal that the LF extrapolation improves the results of the impedance inversion.