Seismic inversion by hybrid machine learning

Full waveform inversion (FWI) has been widely used for recovering a high-resolution subsurface structure from the entire content of measured seismic data. However, FWI requires a good starting model which needs to be close to the true model. If it is not, FWI may converge to a local minimum and will yield an incorrect subsurface image. To mitigate this problem, we propose a hybrid machine learning (HML) inversion method that uses a low dimensional representation of the measured seismic data for inverting subsurface velocity distribution. This low dimensional representation, also denoted as latent space (LS) feature, is automatically extracted from seismic data by using an autoencoder neural network. A small dimensional LS feature mainly contains the kinematic information of seismic data, such as traveltime. However, a large dimensional LS feature can also preserve the dynamic information of seismic data, such as waveform variations. Therefore, HML inversion can recover both the low- and high-wavenumber velocity information by inverting the LS feature with different dimensions. Meanwhile, HML inversion does not require a good starting model and less prone to local minima compared to FWI. The calculation of the HML gradient requires computing the derivative between the LS feature and velocity. However, there are no existing equations used to describe the relationship between these two terms. To address this problem, we use automatic differentiation (AD) to connect the two terms. Following this step, we use the wave equation inversion to invert the LS features for the subsurface velocity distribution. The numerical tests show that HML inversion can efficiently recover both the low and high-wavenumber velocity information from a poor starting model.