Joint data and model-driven simultaneous inversion of velocity and density

SUMMARY Density is an important parameter for both geological research and geophysical exploration. However, for model-driven seismic inversion methods, high-fidelity density inversion is challenging due to seismic wave traveltime insensitivity to density and crosstalk that density has with velocity. To circumvent the challenge of density inversion, some inversion methods treat density as a constant value or derive density from velocity through empirical equation. On the other hand, deep learning approaches are completely driven by data and have strong target-oriented characteristics, offering a new way to solve multiparameter coupling problems. Nevertheless, the accuracy of the inversion results of data-driven algorithms is directly related to the amount and diversity of the training data, and thus, they lack the universality of model-driven algorithms. To achieve accurate density inversion, we propose a simultaneous inversion algorithm for velocity and density that combines the advantages of data- and model- driven approaches: A neural network model (U-T), combining the U-net and Transformer architectures, is proposed to construct non-linear mappings between seismic data as inputs and the velocity and density as predictions. Next, the model-driven inversion algorithm uses the U-T prediction as the initial model to obtain the final accurate solution. In the model-driven module, envelope-based sparse constrained deconvolution is used to obtain full-band seismic data, while a variable dominant frequency full waveform inversion algorithm is used to perform multiscale inversion, ultimately leading to accurate inversion results of velocity and density. The performance of the algorithm on the Sigsbee2A and Marmousi models demonstrates its effectiveness.