Solving Potential Data Inverse Problems Based On Equation Models And Deep Learning Methods

Gravity and magnetic field data originate from gravitational and magnetic fields.Their observations are position-dependent,so we call them collectively as potential-field data.The potential-field data inverse problem aims to invert the structure of the field source medium by the observed potential-field data,such as the structure of the mass by gravity data and the structure of the magnetic body by magnetic field data,which has important applications in geophysical exploration,oil and gas resource search,archaeological imaging,military exploration,etc.The inverse problem of potential-field data is extremely ill-posed,and the same measurement data can correspond to different inverse solutions,thus making it extremely difficult to invert.With the improvement of measurement technology,the size of the potential-field data obtained is increasing,and the accuracy of the inversion results is becoming more demanding,which motivates us to explore more efficient and stable algorithms for potential-field data inversion.This dissertation establishes a level-set inversion model for the potential-field modulus data,and proposes a sensitivity weighting term.Taking gravity modulus data and magnetic anomaly modulus data as examples,a level-set inversion model is established in this dissertation.To improve the inversion effect of deep medium structure,a sensitivity weighting term based on the integral kernel function is proposed in this dissertation under the framework of level-set inversion.In the numerical experiments,we demonstrate the inversion algorithm using simulated magnetic anomaly modulus data and obtain more accurate inversion results.Next,two end-to-end neural network structures are constructed in this dissertation to solve the potential-field data inverse problem.Based on the framework of fully connected neural networks,we propose a network structure with batch normalization layers（BFCN）.Based on the U-Net and adversarial generative network framework,we also construct another adversarial generative network（UGAN）with a symmetric structure.To test the effect of the algorithm,the above network is trained using the salt body dataset and simulated gravity modulus data,and then tested using test set samples and cut-plots of the 3D SEG/EAGE salt body model.The numerical results show that UGAN has excellent performance.To combine the advantages of equation modeling methods and deep learning methods,this dissertation proposes a joint network model（Model I）for potential-field linear data based on a two-step joint framework and truncated singular value decomposition technique.In addition,based on the two-step joint framework and the level-set method,this dissertation proposes two joint network models（Model II and Model III）for potential-field modulus data.To meet the requirements of the inversion task,a modified version of the U-Net networkis applied in this dissertation and used as the deep neural network structure in the joint model.In the neural network training of the joint model,we use the initial solutions obtained by the pseudo-inverse operation and the level-set method as the input and the real inverse images as the output labels.The numerical results on the test set show that the joint model is more competitive than UGAN.