It is well-known that standard migration is not a true inverse operation and is based on the adjoint of the forward modeling operator. Due to this approximation the resulting migrated image can often suffer from various artifacts and uneven illumination issues, especially in regions of complex geology. Least-squares depth migration approximates the inverse of the forward modeling and can be use...

Seismic migration requires an accurate background velocity model that correctly predicts the kinematics of wave propagation in the true subsurface. Least-squares migration, which seeks the inverse rather than the adjoint of a forward modeling operator, is especially sensitive to errors in this background model, which can result in traveltime differences between predicted and observed data that ...

This paper presents least-squares wave equation AVP (Amplitude versus Ray Parameter) migration with non-quadratic regularization. We pose migration as an inverse problem and propose a cost function that makes use of a priori information about the AVP common image gather. In particular, we introduce two regularization goals: smoothness along the ray parameter direction and sparseness in the dept...

with ∆z being a small extrapolation step. The advantage of computation in the kx, ky-ω domain is that the desired result is obtained by multiplication of the data with the operator. However, to allow laterally varying medium functions a space variant convolution operator in the x, y-ω (space-frequency) domain should be applied. When the spatial extrapolation operator is used in an explicit recu...

‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...

Migration enables us to correctly interpret the GPR data from structurally complex areas and determine the geometry and correct location of reflectors (or scatterers) in the subsurface. The effects produced by heterogeneities, dispersion and attenuation are very important; they may cause mis-positioning of reflectors, degradation of resolution and reduction of the effective depth of observation...

this paper presents characterizations of m-fuzzifying matroids bymeans of two kinds of fuzzy operators, called m-fuzzifying derived operatorsand m-fuzzifying difference derived operators.

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

Abstract. In this paper, we revisit the reverse-time imaging procedure. We discuss an inverse scattering transform derived from reverse-time migration (RTM), and establish its relation with generalized Radon transform inversion. In the process, the explicit evaluation of the so-called normal operator is avoided, at the cost of introducing other pseudodifferential operator factors. Using techniq...