Elastic FWI for orthorhombic media with lithologic constraints applied via machine learning

Full-waveform inversion (FWI) of 3D wide-azimuth data for elastic orthorhombic media suffers from parameter trade-offs which cannot be overcome without constraining the model-updating procedure. We present an FWI methodology that incorporates geologic constraints to reduce the inversion nonlinearity and increase the resolution of parameter estimation for orthorhombic models. These constraints are obtained from well logs, which can provide rock-physics relationships for different geologic facies. Because the locations of the available well logs are usually sparse, a supervised machine-learning (ML) algorithm (Support Vector Machine) is employed to account for lateral heterogeneity in building the lithologic constraints. The advantages of the facies-based FWI are demonstrated on the modified SEG-EAGE 3D overthrust model, which is made orthorhombic with the symmetry planes that coincide with the Cartesian coordinate planes. We employ a velocity-based parameterization, whose suitability for FWI was studied using the radiation-pattern analysis. Application of the facies-based constraints substantially increases the resolution of the P-and S-wave vertical velocities (V-P0, V-S0, and V-S1) and, therefore, of the depth scale of the model. Improvements are also observed for the P-wave horizontal and normal-moveout velocities (V-P1, V-P2, V-nmo,V-1, and V-nmo,V-2) and the S-wave horizontal velocity V-S2. However, the velocity V-nmo,V-3 that depends on Tsvankin's parameter delta((3)) defined in the horizontal plane is not well recovered from the surface data. On the whole, the developed algorithm achieves a much higher spatial resolution compared to unconstrained FWI, even in the absence of recorded frequencies below 2 Hz.