关键词: 浅地表成像, 全波形反演, 目标函数, 随机噪声

Abstract:

Full waveform inversion(FWI)has emerged as a highly effective approach for obtaining accurate and high-resolution S-wave velocity structure of the shallow subsurface. However, there exist several challenges when applying FWI in the field. The first challenge is the issue of local minima that arises when inaccurate initial models are used, especially when inverting shallow surface seismic data dominated by high-frequency and strongly dispersive surface waves. These local minima are caused by the non-linear misfit function that represents the differences between the measured and simulated data. Moreover, defining an appropriate minimization criterion to reduce the sensitivity of the inversion results to errors in the recorded seismic wave amplitudes is another significant challenge. Amplitude errors can arise from various factors, such as different coupling effects between seismic sources, receivers, and the ground, or variations in the strength of seismic sources excited at different shot locations. If the amplitude information of the recorded seismic wavefield is inaccurate, the reliability of the FWI inversion results will be effected negatively.

To overcome these problems, we propose a novel misfit function that incorporates exponential-phase coherency, thereby eliminating the reliance on amplitude information from the measured and simulated data. This new misfit function is designed to measure the coherency between the measured and simulated data based on exponential phase. It achieves a balance in extracting valuable information from various amplitude components of the recorded seismic wavefield, such as surface waves, reflections, and scattering waves. The method for computing this coherency is inspired by Phase-Weighted Stacking(PWS)method to detect weak but correlated seismic signals. In PWS, the exponential phase of the data is computed to obtain a phase-dependent coherency that is independent of amplitude. This correlation is then used to enhance the stacking of signals with similar instantaneous phases.

By utilizing the adjoint-state method, we efficiently calculate the gradient of the misfit function with respect to the model and conduct a thorough analysis of its shape and characteristics. To demonstrate the robustness of our proposed misfit function against random noise, we perform experiments by using simulated data contaminated with varying levels of noise. The results demonstrate that the misfit function based on exponential-phase coherency remains highly robust and reliable, even in the presence of significant random noise. This robustness is particularly crucial in practical applications where noise contamination is a common challenge.

To evaluate the performance of FWI employing exponential-phase coherency in a real field environment, we employ seismic data collected at an archaeological site as a benchmark dataset. This dataset presents a complex and challenging scenario due to the presence of complex subsurface structures. In addition to the inherent noise in the data, we introduce additional random noise to assess the robustness of our proposed misfit function.

The inversion results obtained with our novel FWI approach exhibit an impressive resemblance to the known velocity structure of the archaeological site. These results are further validated through independent archaeological excavations, which confirms the accuracy and reliability of our imaging technique. The success of using our method in accurately reconstructing subsurface features under challenging field conditions underscores the significant potential of FWI based on exponential-phase coherency to enhance the accuracy and reliability of shallow subsurface imaging in practical scenarios.

Key words: near-surface imaging, full-waveform inversion, objective function, random noise