基于精确震源函数的解调包络多尺度全波形反演

本文提出解调包络方法来重构地震记录中缺失的低频信号,同时该方法能够降低全波形反演的非线性程度;提出伴随状态震源函数反演方法来得到精确的震源函数,并推导了梯度计算公式;解调包络方法结合低通滤波技术,实现了从低频到高频的多尺度反演策略,有效缓解了全波形反演的周波跳跃问题.数值算例证明了解调包络、伴随状态震源函数反演方法和低通滤波多尺度反演策略的可行性及优越性.震源函数反演精度测试结果表明:即使观测记录在缺失低频信息的情况下,也能反演得到精确的震源函数.缺失低频测试和抗噪能力测试结果表明:即使地震数据中缺失9Hz以下的低频信号或者信噪比极低的情况下,利用反演得到的精确震源函数进行解调包络多尺度全波形反演,同样可以得到高精度的全波形反演结果.与Hilbert包络全波形反演对比结果表明:解调包络在重构低频和降低伴随震源主频方面具有一定优势.

Demodulation envelope multi-scale full waveform inversion based on precise seismic source function

Full waveform inversion (FWI) has become one of the most important means for high-precision velocity modeling. But there are still many problems in real seismic data processing, because FWI is a strongly nonlinear optimization problem and sensitive to cycle skipping. When seismic data lack low-frequency components or with an inaccurate seismic source function, the conventional multi-scale FWI strategy cannot solve the cycle skipping problem.In this paper, we propose to use demodulation envelope to reconstruct low-frequency information for FWI in the time domain. The Cubic Spline Interpolation (CSI) method is used to obtain the demodulation envelope (DE). In order to obtain the shot gather of demodulation envelope, we should use the CSI method to process seismic data trace by trace. Demodulation envelope ignores most of the details information and reflects the macro information of seismic data. Spectrum shows that the demodulation envelope contains abundant low-frequency information, so that the reconstructed ultra low-frequency components can be used to obtain the macro structure of velocity models. Demodulation envelope can not only reduce the degree of nonlinear for FWI, but also reconstruct low-frequency information, so that the initial model dependence of FWI can be reduced. And we also use a low-pass filter to conduct multi-scale demodulation envelope full waveform inversion (DEFWI) which is more suitable for real seismic data processing and able to suppress the cycle skipping problem. For seismic source function, in the process of FWI, which is very important, teeny mistakes may cause huge errors in the FWI results. In order to obtain a precise seismic source function, we propose to use the adjoint state method to invert the source function for FWI, where the theory of source function inversion is similar to FWI. The aim is to find a seismic source function by minimizing the data residual between the synthetic data and recorded data. Theoretical and numerical examples prove the feasibility and advantages of the demodulation envelope, the seismic source function inversion and multi-scale inversion strategy. The seismic source function inversion results show that even if under the condition of missing low-frequency components in seismic recorded data, the adjoint state source function inversion method still can get an accurate seismic source function. The FWI tests show that even if seismic data lack information below 9Hz or under the condition of a low signal to noise ratio, multi-scale DEFWI still can get high precision of inversion results with the precise seismic source function. Comparison of DEFWI and Hilbert envelope full waveform inversion (HEFWI) shows that DEFWI is superior to HEFWI in some aspects, such as reconstructing low-frequency information and lowering the dominant frequency.