Anisotropic elastic wavefield imaging using the energy norm

Abstract

Based on the energy conservation principle, we derive a scalar imaging condition for anisotropic elastic wavefield migration. Compared with conventional imaging conditions that correlate displacement components or potentials from source and receiver wavefields, the proposed imaging condition does not suffer from polarity reversal, which degrades the image quality after stacking over shots. Our imaging condition also accounts for the directionality of the wavefields in space and time, leading to the attenuation of backscattering artifacts, which commonly appear in elastic reverse time migration images in the presence of strong model contrasts. In addition, our new imaging condition does not require wave-mode decomposition, which demands significant additional cost for elastic wavefields in anisotropic media. To properly image structures, we rely on the anisotropy parameters used in migration, as one would do for any other imaging condition. Our imaging condition is suitable for arbitrary anisotropy. We show the successful application of the anisotropic energy imaging condition by performing numerical experiments on simple and complex geologic models. We compare its quality with conventional counterparts by simulating complex geologic settings with vertical or tilted transverse isotropy.

Elastic reflection-based waveform inversion with a nonlinear approach

“…The latter which represents the high wavenumber components of the models has a more clearer physical meaning and fortunately it can be optimized naturally within the EFWI framework. In addition, Rocha et al (2017) are able to obtain one image for elastic inversion (not knowing what the image really represents physically).…”

Elastic least-squares reverse time migration using the energy norm

“…Although the energy image (Figure 1g) does not involve wave-mode decomposition, it exhibits crosstalk artifacts that are similar in amplitude from the ones in the conventional images. As stated elsewhere (Rocha et al, 2017), the energy imaging condition only attenuates events from source and receiver wavefields that share the same propagation and polarization directions, which is not the case for crosstalk between different wave modes from source and receiver wavefields. The space-time diagram in Figure 1h shows all the wave events related to this experiment, and indicates two crosstalk correlations that are independent of wave-mode decomposition.…”

“…For two anisotropic elastic source and receiver wavefields that are functions of space x and time t, u s ðx; tÞ and u r ðx; tÞ, we can form an image using the energy imaging condition (Rocha et al, 2017):…”

“…Incorporating elasticity and anisotropy into LSRTM is possible with elastic wavefield imaging using the energy norm (Rocha et al, 2017). This type of imaging exploits realistic vector displacement field extrapolation within a multiparameter anisotropic and elastic earth model, and it generates scalar images of the subsurface without costly decomposition of wave modes.…”

Polarized pass band for longitudinal waves in solid phononic crystals

“…In fact, elastic waves possess a rich variety of polarization characteristics, and the wave propagation in solids is intricate in view of the concurrence of P (longitudinal) and S (transverse) polarizations as well as the possible coupling and conversion between them. Elastic wave mode separation in solids has been theoretically investigated for many years in the field of geophysics [35][36][37][38]. In comparison, different wave modes can be decoupled physically with the use of the man-made structures, for which a typical example is the pentamode metamaterial (PMM).…”