Fast Simulation of Ultradeep Electromagnetic Logging-While-Drilling Tool Based on Physics-Driven Fourier Neural Operator

The ultradeep electromagnetic logging-while-drilling (LWD) instruments play an important role in geological guidance and reservoir evaluation. The main challenge that restricts the real-time inversion and application of electromagnetic ultradeep detection logging data is the lack of a fast and efficient forward algorithm. To enhance the efficiency of forward modeling, a physics-driven Fourier neural operator (PDFNO) is developed as a rapid solver for electromagnetic multicomponent logging responses simulation. PDFNO, which is implemented without data, uses electromagnetic equations in the wavenumber domain to constrain the training process. Three PDFNOs are trained, respectively, for magnetic dipole sources in the X-, Y-, and Z-directions. After training, PDFNO can output the distribution of the electromagnetic fields in the wavenumber domain in real-time. Numerical experiments are conducted on datasets to evaluate the simulation accuracy and generalization of electromagnetic ultradeep detection multicomponent logging response predicted by PDFNO. The results demonstrate agreement between the electromagnetic ultradeep detection multicomponent logging responses of PDFNO predictions and frequency-domain finite difference (FDFD) method. Importantly, PDFNO is hundred times faster than the FDFD method.