LSTM Network Assisted Construction of the Angle-Dependent Point Spread Function and Its Applications in Seismic Imaging

Migration is the core link in reflection seismic exploration. Seismic images are often extended into angle domain for interpretations. However, affected by limited acquisition aperture and complex overburden, the generated images are far from ideal. The illumination is unbalanced, causing unreliable amplitude variation in angle gathers. Band-limited seismic data and wavelet stretch in large angles, lead to low-resolution angle gathers. Image-domain least-squares migration (IDLSM) implemented by point spread function (PSF) deconvolution is a promising solution. Extending the concept of IDLSM to the angle domain, we develop a new method to construct angle-dependent PSFs and optimize angle gathers. The essential element to construct PSFs is the Green's function. The proposed method reconstructs Green's functions using a bidirectional long short-term memory (LSTM) network. We use a ray tracing method to efficiently obtain wave propagation directions (travel-time gradients). And wave-equation forward modeling is used to accurately calculate wavefront amplitudes. The LSTM network is trained by labels composed of travel-time gradients and amplitudes to surrogate the solver of Green's functions. Angle-dependent PSFs are constructed according to the mathematical model of the angular local Hessian. And inversions with PSFs are performed to optimize angle gathers. Numerical tests on a 3-D synthetic model demonstrate that the proposed method is able to improve the image quality of prestack angle gathers and poststack seismic images. The proposed method compensates illumination and improves the resolution of angle-dependent seismic images. Both vertical and lateral resolution are enhanced. Amplitude versus angle (AVA) responses can be corrected for further analysis and interpretations.