Machine learning algorithms for solving some seismic inversion challenges

Seismic inversion is a popular quantitative approach to extract some of the subsurface properties from seismic amplitudes by utilizing the physics of the wave propagation through earth layers, in forms of the empirical formulations that simulate the energy distribution phenomenon. Typical inversions are performed with limited offset angles, and in a small time-window, within which the wavelet is assumed to be stationary, and the property contrasts are small across the boundaries. These exposes the process to several major problems: (1) the limited resolution due to wavelet effects, (2) the dependence on some rock physics models when inverting for petrophysical properties, and (3) the resolution discrepancy between the time domain seismic signal and well logs in depth domain. The primary goal of this research is to use machine learning to solve these challenges, by designing and applying proper neural network structures and suitable training schematics. Firstly, a single-layer Boltzmann machine is implemented as an unsupervised learning algorithm to predict the elastic properties at higher resolution than that can be achieved by conventional approaches, while still retaining the physical relationship between the seismic amplitudes and reflectivity series. The high-resolution results are produced from the accurate post-inversion reflectivity series, which is not bounded by the wavelet effects, and novel model update schemes. Secondly, a new multimodal Cross-shape deep Boltzmann machine is designed to simultaneously capture six possible relationships between four different input training data to invert for petrophysical properties from the pre-stack seismic amplitudes in datasets with limited well coverages. This algorithm has a significant advantage in avoiding the uncertainties associated with the data fitting algorithms to create the rock physics models to guide the solution. Last but not the least, a novel multimodal deep learning network is applied to predict the posterior distribution of the subsurface elastic properties from a seismic gather, to resolve the resolution discrepancy challenge, by a smart preparation of the training label in the form of time dependent probability distributions. The biggest advantage of this algorithm is the avoidance of the heuristic calculation of the partition function, which is required to calculate the posterior distributions of common neural network outputs. While the first algorithm requires an input wavelet to constraint the results, the other two algorithms do not, which make them appropriate for inversion in depth domain, or with nonstationary signals