Focusing functions correction in Marchenko imaging with deep learning and transfer learning

Abstract

The Marchenko method is a subsurface approach to calculate Green's functions from the subsurface to the surface. It requires only reflection response from the surface and direct arrivals from the selected subsurface focal points to the surface. Marchenko imaging can use these obtained Green's functions to create images for all the focal points (image points). Focusing functions are defined to relate Green's functions with the surface reflection response. Estimating focusing functions is the first step in the calculation of Marchenko imaging. However, the estimation of incorrect direct arrivals with the initial model can lead to errors in the focusing functions, thus affecting the effect of the image. In addition, Marchenko imaging is not an efficient imaging method, especially when the imaging area is particularly large, since the number of image points corresponds to the times of solving Marchenko equations. Therefore, we introduce a deep learning and transfer learning approach for the focusing functions correction. We construct a neural network and train the model in a small imaging region by deep learning. Then update this model for extended area by transfer learning which enables the network to work on new data dissimilar to the training data. Hence, our work can quickly obtain accurate focusing functions in a larger region instead of training an extra model for correcting new focusing functions. Numerical examples shows that our network not only helps to reduce errors in the focusing functions, but also can be applied to cope with other limitations of the Marchenko method like travel time error and imperfectly sampled reflection response.