Elastic least-squares reverse time migration using the energy norm

Abstract

Incorporating anisotropy and elasticity into least-squares migration is an important step toward recovering accurate amplitudes in seismic imaging. An efficient way to extract reflectivity information from anisotropic elastic wavefields exploits properties of the energy norm. We derive linearized modeling and migration operators based on the energy norm to perform anisotropic least-squares reverse time migration (LSRTM) describing subsurface reflectivity and correctly predicting observed data without costly decomposition of wave modes. Imaging operators based on the energy norm have no polarity reversal at normal incidence and remove backscattering artifacts caused by sharp interfaces in the earth model, thus accelerating convergence and generating images of higher quality when compared with images produced by conventional methods. With synthetic and field data experiments, we find that our elastic LSRTM method generates high-quality images that predict the data for arbitrary anisotropy, without the complexity of wave-mode decomposition and with a high convergence rate.

Elastic-reflection waveform inversion with petrophysical model constraints

“…Figure 7 shows the initial model (top), the reference model (middle) used in the definition of JM (equation 18), and a low-pass version of the true model (bottom) that corresponds to the maximum resolution possible with the source wavelet of 7.5 Hz. We apply image-guided interpolation (Hale, 2009(Hale, , 2010 to construct the reference model using as input the LSRTM energy image (Rocha et al, 2016(Rocha et al, , 2017Rocha and Sava, 2018) computed with the initial velocity (second image from top to bottom in Figure 11(b)), and the three velocity profiles from the well locations ( Figure 6). Figure 8 shows the inverted models for data-misfit minimization only (JD, top), data-misfit term plus reference model term (JD + JM , middle), and all three objection function terms including the petrophysical constraint (JD + JM + JC , bottom).…”

“…However, such sharp contrasts cause backscattering during wavefield extrapolation, thus producing low-wavenumber artifacts when implementing conventional imaging conditions, including the ones based on model perturbations. We address this problem by applying the energy imaging condition in a leastsquares sense (Rocha et al, 2016(Rocha et al, , 2017Rocha and Sava, 2018) for imaging with the total earth model.…”

Guided wave tomography based on least-squares reverse-time migration

“…64,65 When LSM uses RTM engine, it is referred to as least-squares reverse-time migration (LSRTM). [66][67][68] With all the potential benefits, however, LSRTM has not been implemented in ultrasonic guided wave-based damage imaging.…”