Variance-based model interpolation for improved full-waveform inversion in the presence of salt bodies

Abstract

When present in the subsurface salt bodies impact the complexity of wave-equation-based seismic imaging techniques, such as least-squares reverse-time migration, and full-waveform inversion (FWI). Typically, the Born approximation used in every iteration of least-squaresbased inversions is incapable of handling the sharp, high-contrast boundaries of salt bodies.We develop a variance-based method for reconstruction of velocity models to resolve the imaging and inversion issues caused by salt bodies. Our main idea lies in retrieving useful information from independent updates corresponding to FWI at di↵erent frequencies. After several FWI iterations we compare the model updates by considering the variance distribution between them to identify locations most prone to cycle skipping. We interpolate velocities from the surrounding environment into these high-variance areas. This approach allows the model to gradually improve from identifying easily resolvable areas and extrapolating the model updates from those to the areas that are di cult to resolve at early FWI iterations. In numerical tests, our method demonstrates the ability to obtain convergent FWI results at higher frequencies.Downloaded 08/06/18 to 109.171.137.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/ de Hoop (2013), who used a total variation norm to invert a salt-a↵ected subsurface using FWI. Regularized inversion methods could be computationally expensive when multiple runs on a fine mesh are needed and these methods often require prior assumptions about the subsurface structure (Kadu et al., 2016).The second approach involves image or gradient manipulations with single iteration updates of FWI. Processed gradients can lead to shorter paths toward the global minimum without being trapped in the local minima (Alkhalifah, 2015b. Image-guided inversion (Ma et al., 2012), gradient optimization (Wu and Alkhalifah, 2016) or gradient conditioning through scattering angle-based filters (Alkhalifah, 2015a;Kazei et al., 2016) can serve the same purpose.The objective of FWI is to minimize both amplitude and phase di↵erences between observed and modeled seismic data. For successful inversion the Born approximation requires the initial velocity model to deliver mismatches in travel times less than half the period (Beydoun and Tarantola, 1988). Larger errors cause cycle-skipping artifacts on the wavepaths specific to each source-receiver pair. These artifacts in the image domain can be identified as repeated contrast velocity anomalies that, in turn, lead the inversion to convergence toward a local minimum on an objective function (Virieux and Operto, 2009).Inversion of mono-frequency data allows features to be resolved at a specific scale. The inversion results from di↵erent mono-frequencies therefore do not match exactly.When mono-frequency data are modeled, the phase of a harmonic plane wave at a given point on a wavepath depends on the frequency and travel time. Hence, at di↵erent frequencies, the phases of ...

Deep learning unflooding for robust subsalt waveform inversion

“…At low frequencies, $$J_{\rm {FWI}}$$ tends to be more convex with less local minima (Ovcharenko et al ., 2018). A multiscale approach to invert for successive bands of frequencies starting from low to high is often applied to ensure a stable convergence (Bunks et al ., 1995; Brenders and Pratt, 2007).…”

“…In salt regions, building a velocity model using FWI is unfeasible in the absence of salt bodies in the initial model, low frequencies and long offsets (Ovcharenko et al ., 2018). At best, FWI will construct the post‐salt sediments and the ToS boundary, but often yields poor Subsalt information, including the BoS.…”

Multi-Task Learning for Low-Frequency Extrapolation and Elastic Model Building From Seismic Data

“…Alternatively, constraints applied alongside the main objective might serve the same goal [12,13,14,15,16]. Conditioning and smoothing of gradients for model updates also help inversions to overcome inaccurate initial starting models [17,18,19,15]. These existing frameworks greatly advance FWI in seismic exploration, however, they might either require a different inversion engine to be used (e.g., advanced traveltime tomography) or require a large number of iterations of high-frequency seismic simulations.…”

Salt Body Flooding Using Activation Functions From Machine Learning

“…Conventional industry practice with salt regions is to apply the migrate-pick-flood flow, which is time consuming and prone to error as it requires human interpretation and decision making (Dellinger et al, 2017). For more automatic inversion with less human intervention: Ovcharenko et al (2018) used a variance-based interpolation to process the conventional FWI updates; Sun and Alkhalifah (2019b) proposed to use more robust objective functions such as the optimal-transport when inverting for the salt. Other studies suggested to apply an automatic flooding by constraining the inversion using a Hing loss (Esser et al, 2016) or regularizing it as a post-inversion process (Kalita et al, 2019).…”