Application of Point Spread Function in Tunnel Seismic Prediction

Tunnel seismic prediction (TSP) is essential for guaranteeing the safety of tunnel construction. Reverse time migration (RTM) plays a vital role in providing precise visualization of the geology located in front of the tunnel. However, anomalies like karst caves cause signal reflection and attenuation, leading to blurred images and artifacts. The point spread function (PSF) characterizes the blurring effect of a specific observing system on an imaging point, and the migration result can be viewed as the convolution of the true reflectance model with the PSF. Thus, the ambiguity of the migration result can be eliminated by using the inverse of the PSF. In this letter, we utilize the PSF in the context of TSP. First, the wavefields from the source and receiver sides are broken down into angle domain components through the Poynting vector approach. Then, the PSF operator is obtained by calculating the local illumination matrix (LIM) and is further applied to image correction. We designed various models to simulate the complex geology in front of the tunnel. Numerical experiments show that the application of PSF can improve the imaging accuracy of complex structures in TSP. The test results of actual tunnel seismic data also demonstrate the effectiveness of this method.