Early arrival waveform inversion using data uncertainties and matching filters with application to near-surface seismic refraction data

Abstract

We develop an early arrival waveform inversion (EAWI) technique for high-resolution near-surface velocity estimation by iteratively updating the P-wave velocity model to minimize the difference between the observed and calculated seismic refraction data. Traditional EAWI uses a least-squares penalty function and an acoustic forward-modeling engine. Conventional least-squares error is sensitive to data with low signal-to-noise ratio (S/N) and iterations of EAWI stop at a local-minimum data misfit or at the preassigned maximum number of iterations. These stopping criteria can result in overfitting the data. In addition, fitting the elastic field data with an acoustic modeling engine can introduce artifacts in velocity estimation, especially in land data with significant elastic effects. To overcome these challenges, we develop a robust EAWI (REAWI) method by (1) incorporating the data uncertainties into the penalty function and (2) mitigating the elastic effects using a matching filter workflow. The data uncertainties are estimated from waveform reciprocal errors. When full-waveform reciprocity is not available, trace interpolation is applied. The proposed method prevents closely fitting data with low S/N, avoids overall overfitting by stopping the iterations when a normalized chi-square ( χ2) waveform misfit of one is achieved and is less affected by elastic effects. Numerical examples and application to near-surface refraction data at a groundwater contamination site suggest that the final REAWI models are more accurate than the corresponding EAWI models, at the same level of misfit. This is the first known application of a matching filter workflow to real land data. The final REAWI models satisfy an appropriate misfit between the real data and predicted elastic P-wave data, making this approach in this respect equivalent to elastic waveform inversion. We also develop a method to analyze model constraint by examining the energy of the wavefield Fréchet derivative thereby avoiding the influence of the data residuals in traditional Fréchet kernels.

2D Near‐Surface Full‐Waveform Tomography Reveals Bedrock Controls on Critical Zone Architecture

“…To date, applications of FWT to near-surface problems have been aimed at a wide diversity of targets and use a variety of approaches. Some studies have focused on exclusively using body waves to inform shallow subsurface structure (e.g., Cai & Zelt, 2022). For example, Sheng et al (2006) used first arrivals to invert for p-wave velocity (Vp) while other researchers have used both P and S body-wave phases to constrain both Vp and shear-wave velocity (vs.) (e.g., J.…”

“…As a result, FWT has been widely applied in global and exploration seismology (e.g., Choi & Alkhalifah, 2012; Lei et al., 2020; Mao et al., 2016; Pratt, 1999; Virieux & Operto, 2009). To date, however, FWT has only been used to study the near surface on a handful of occasions (e.g., Cai & Zelt, 2022; J. Chen et al., 2017; Köhn et al., 2018; X. Liu et al., 2022; Sheng et al., 2006; W. Wang, Chen, Keifer, et al., 2019; W. Wang, Chen, Lee, & Mu, 2019; Y. Wang, Miller, et al., 2019).…”

“…To date, applications of FWT to near‐surface problems have been aimed at a wide diversity of targets and use a variety of approaches. Some studies have focused on exclusively using body waves to inform shallow subsurface structure (e.g., Cai & Zelt, 2022). For example, Sheng et al.…”