Nowadays, Machine Learning (ML) is actively used in geophysical prospecting including seismic exploration. This study focuses on the applicability and feasibility of Deep Learning for the inverse problem in seismic exploration that is the estimation of the rock-physics parameters for a fractured reservoir, from seismic data. The main goal of this paper is to prove the efficiency of a neural network in estimating fractured medium parameters, represented as anisotropy parameters of HTI model. (HTI is "Horizontal Transverse Isotropy".) As such fracture parameters, we consider the normal and tangential weaknesses of fractures ΔN and ΔT, Thomsen anisotropy parameters ε, δ, γ, as well as the crack density e and the crack aspect ratio α (fracture opening). In addition, we consider a fractured medium, in which there are two fracture networks, characterized by two pairs of weaknesses (ΔN1, ΔT1) and (ΔN2, ΔT2); this is the so-called orthorhombic model.
We validate the accuracy of our neural network by comparing the predicted parameter values with the a priori given. We use mathematic formulae, which relate the considered parameters estimation to different effective-medium anisotropy models of a fractured medium, such as Schoenberg's Linear Slip model, Hudson's model for penny-shaped cracks and Thomsen's model for aligned cracks in porous rock.
In our study, seismic signatures (seismograms of the reflected waves PP and PS) of both the vertical UZ-component and the horizontal one UX are the inputs for the neural network. At the output, the network predicts fracture parameters and anisotropy parameters. The neural network is trained on synthetic seismograms of reflected waves, which were generated using 2D-elastic numerical finite-difference modelling.
Thus we demonstrate the applicability of Deep Learning for estimation of the fractured medium parameters, by training the neural network on synthetic seismograms. The normal and tangential weaknesses of fractures ΔN and ΔT, the crack density and the crack aspect ratio (crack opening) are successfully estimated as well as the anisotropy parameters ε(V), δ(V) and γ(V). In the prediction of ΔN and ΔT, the relative error does not exceed 1.7% and 1.4%, respectively, and in the prediction of crack density e — from 0.9% to 1.4%. In predicting the anisotropy parameters ε(V), δ(V) and γ(V), the error does not exceed 1.6%, 1.7%, and 1.8%, respectively. However, in estimating the value of crack opening α, the result is an order of magnitude worse, an error of 14.2%.
For the orthorhombic model, the prediction results are slightly worse than for the HTI model, but still within the acceptable accuracy. In predicting the fracture parameters for the first fracture network (ΔN1, ΔT1 and e1) the error does not exceed 2.3%, 4.2%, and 2.3%, respectively, and for the second fracture network (ΔN2, ΔT2 and e1) — respectively 4.3%, 5.7%, and 3.7%. This slight deterioration in the results (in comparison with HTI) is explained by the complicated formulation of the last task with the orthorhombic model, in which various deviations in the inclination of cracks were introduced (the angles β1 and β2).
In general, we have successfully developed a neural network to solve the problem on fractured reservoir characterization. Finally, it produces fairly accurate results that prove the effectiveness of Deep Learning in inversion for fracture parameters from the seismic data.