Near-surface full-waveform inversion in a transmission surface-consistent scheme

Abstract

Land seismic velocity modeling is a difficult task largely related to the description of the near surface complexities. Full waveform inversion is the method of choice for achieving high-resolution velocity mapping but its application to land seismic data faces difficulties related to complex physics, unknown and spatially varying source signatures, and low signal-to-noise ratio in the data. Large parameter variations occur in the near surface at various scales causing severe kinematic and dynamic distortions of the recorded wavefield. Some of the parameters can be incorporated in the inversion model while others, due to sub-resolution dimensions or unmodeled physics, need to be corrected through data preconditioning; a topic not well described for land data full waveform inversion applications. We have developed novel algorithms and workflows for surface-consistent data preconditioning utilizing the transmitted portion of the wavefield, signal-to-noise enhancement by generation of CMP-based virtual super shot gathers, and robust 1.5D Laplace-Fourier full waveform inversion. Our surface-consistent scheme solves residual kinematic corrections and amplitude anomalies via scalar compensation or deconvolution of the near surface response. Signal-to-noise enhancement is obtained through the statistical evaluation of volumetric prestack responses at the CMP position, or virtual super (shot) gathers. These are inverted via a novel 1.5D acoustic Laplace-Fourier full waveform inversion scheme using the Helmholtz wave equation and Hankel domain forward modeling. Inversion is performed with nonlinear conjugate gradients. The method is applied to a complex structure-controlled wadi area exhibiting faults, dissolution, collapse, and subsidence where the high resolution FWI velocity modeling helps clarifying the geological interpretation. The developed algorithms and automated workflows provide an effective solution for massive full waveform inversion of land seismic data that can be embedded in typical near surface velocity analysis procedures.

Ultra‐resolution surface‐consistent full waveform inversion

“…Before showing, in the next section, a comprehensive test on the Society of Exploration Geophysicists Advanced Modelling arid model (Oristaglio, 2015), we demonstrate the validity of the VSG concept and of the 1.5D LF‐FWI on a simpler test performed on an abstract model showing complex shallow velocity conditions (Colombo et al., 2021).…”

“…A detailed explanation of the derivation of the wave equation and forward modelling in the Laplace–Fourier domain is provided in two recent publications (Colombo et al., 2021; Kontakis et al., 2023) such that we report only the main equations in the following discussion. The 1.5D LF‐FWI is implemented for acoustic, isotropic and constant/variable density 1D media using the Helmholtz wave equation (Jensen et al., 2011) that in the Laplace–Fourier domain can be written as $$$$\begin{equation}\left[ {{\nabla }^{2} - k{{\left( z \right)}}^{2}} \right]\tilde{p}\ \left( {{\bf x},s} \right) = \tilde{f}\ \left( {{\bf x},{s}} \right),\end{equation}$$$$where $${\bf x} = \ ( {x,y,z} )$$, $$s\ = \ \sigma + j\omega $$ is the Laplace–Fourier complex frequency specified by the damping parameter σ and angular frequency ω (with $$j\ = \sqrt { - 1} \ $$), $$\tilde{f}( {{\bf x},s} )$$ is the forcing term, $$\tilde{p}( {{\bf x},s} )$$ is the modelled pressure wavefield and $$k( z )$$ is the wavenumber: $$$$\begin{equation}k\ \left( z \right) = \ \frac{s}{{c\left( z \right)}},\end{equation}$$$$…”

“…Acoustic seismic data are simulated via a finite‐difference scheme using a minimum‐phase wavelet with peak frequency of 25 Hz. The 3D acquisition geometry consists of sources and receivers equally spaced at an interval of 100 m with each shot recorded by all the receivers in a ‘carpet’ acquisition setup (Colombo et al., 2021). The synthetic data are then organized in VSGs, as described, transformed to the Laplace–Fourier domain, and inversion is performed with the 1.5D LF‐FWI scheme described.…”

“…A detailed explanation of the derivation of the wave equation and forward modelling in the Laplace-Fourier domain is provided in two recent publications (Colombo et al, 2021;Kontakis et al, 2023) such that we report only the main equations in the following discussion. The 1.5D LF-FWI is implemented for acoustic, isotropic and constant/variable density 1D media using the Helmholtz wave equation (Jensen et al, 2011) that in the Laplace-Fourier domain can be written as…”

Efficient 1.5D full waveform inversion in the Laplace-Fourier domain

“…The method is part of a larger near-surface related processing framework and has been applied to field data [33], showing good correspondence of the produced velocity model features with results obtained from helicopter-borne time-domain electromagnetic data [34].…”