Least-squares migration — Data domain versus image domain using point spread functions

Abstract

Conventional amplitude inversion assumes that the migrated image preserves relative-amplitude information. However, illumination effects caused by complex geologic settings, undersampled acquisition geometry, and limited recording aperture pose a challenge to even the most advanced imaging algorithms. In addition, standard depth-migration images can suffer from lack of resolution caused by wavelet stretch, attenuation, and suboptimal deghosting. Least-squares migration (LSM) can mitigate many of these problems and produce better resolved migration images suitable for AVO inversion. However, whether formulated in the data domain or the image domain, LSM is an inversion algorithm and is sensitive to inaccuracies in the source wavelet, velocity model, data preprocessing, and the propagator used. Practical considerations to mitigate these problems under nonideal conditions and cost-reduction strategies differ between the data- and image-domain formulations. The relative merits of each approach are evaluated by using example inversions for complex synthetic models, including free-surface ghost and attenuation effects. When a data-domain implementation of LSM is considered necessary, the image-domain implementation should be considered at the same time, especially when targeting localized reservoir targets under complex overburdens. Application of image-domain least-squares migration on a Gulf of Mexico field data set produces significant improvements in resolution and event continuity in the subsalt target region.

Migration of viscoacoustic data using acoustic reverse time migration with hybrid deblurring filters

“…where ⊗ denotes spatial convolution and i indicates the ith local window. The hybrid deblurring filter can be estimated by solving equation 15 by the least-squares method: (Aoki and Schuster, 2009;Dai and Schuster, 2009;Fletcher et al, 2016) [f ]…”

“…This means a large number of iterations are required to improve the image quality, which makes the Q-LSRTM technique computationally expensive compared to standard RTM. Except for the data-domain method, seismic attenuation can be also compensated in the image-domain within the framework of depth-domain inversion (Cavalca et al, 2015;Fletcher et al, 2016).…”

Improving reflection FWI reflectivity using LSRTM in the curvelet domain

“…One way to improve the RFWI reflectivity model without dramatically increasing its cost is by using so-called singleiteration LSRTM methods, which aim to fully compensate for the Hessian effects while requiring at most two migrations. Many different ideas have been proposed to achieve this goal, e.g., the approximate inverse Born modeling operator (Hou and Symes, 2014), point-spread function deconvolution (Fletcher et al, 2016), and nonlinear Hessian filters (Guitton, 2004).…”

Least-squares RTM: Reality and possibilities for subsalt imaging

“…The cost-reducing alternative is to approximate the Hessian matrix. Lecomte (2008) and Fletcher et al (2016) proposed to obtain the Hessian matrix using point spread functions (PSFs). The PSF method computes the impulse response (Hessian) on a coarse grid (to reduce interference between PSFs) of scattered points.…”