Research on inverse transform optimization algorithm of transient electromagnetic wave field based on wave field feature constraint

To utilize wave field characteristics for transient electromagnetic data interpretation, enhance the interpretation accuracy of electromagnetic detection, and overcome the limitations of traditional diffusion field interpretation capabilities. This paper proposes a multi-constrained wavefield transformation algorithm based on integral transform relationships between diffusion and wavefields, with its core being the construction of an objective function that integrates diffusion field data characteristics and wavefield frequency features. First, based on the wavefield transformation theory, this study constructs an objective function framework. Within this framework, filtering process constraints and wavefield characteristic constraints are introduced. The filtering constraints mitigate the loss of wavefield resolution caused by traditional smoothing constraints, while the wavefield characteristic constraints further narrow the solution space based on wavefield propagation features. These two constraint terms are integrated into a unified objective function to enhance the accuracy of inverse transformation. Next, for optimizing the objective function, a quasi-Newton algorithm is employed for iterative optimization. During computation, this approach eliminates the need to compute the complex Hessian matrix required in traditional methods, ensuring both efficiency and robustness. Through iterative calculations, a virtual wavefield that satisfies both data constraints and wavefield characteristics is ultimately obtained. Finally, the proposed algorithm is applied to perform wavefield transformation on Transient Electromagnetic (TEM) forward modeling data from layered and complex geological models, validating its effectiveness and stability in practical applications. During the wavefield transformation process, comparative analysis with forward modeling data is conducted to investigate the algorithm's performance under diverse geological models, ensuring broad applicability and accuracy. Numerical experimental results demonstrate that the transformed wavefields retain the propagation characteristics of the wavefield and align closely with the forward modeling results, fully confirming the validity of the inverse transformation algorithm proposed in this study. This study provides a theoretical foundation for interpreting transient electromagnetic quasi-wave equations and holds application value in deep mineral exploration and complex geological structure identification