Angle domain generalized Radon transform for elastic multi-parameter inverse scattering inversion

Linearized algorithms based on the Born approximation are well-known and popular techniques for quantitative seismic imaging and inversion. However, linearization methods usually suffer from some significant problems, such as computational cost for the required number of iterations, requirement for background models, and uncertain and unstable multi-parameter extraction, which make the methods difficult to implement in practical applications. To avoid these problems, we propose an angle-domain generalized Radon transform (AD-GRT) inversion in 2D elastic isotropic media. This AD-GRT is an approximate transform between the seismic data and an angle-domain model, which acts as a scattering function, and the seismic data can be reconstructed accurately, even when the background models are incorrect. The density and Lam短oduli perturbation parameters can be extracted stably from the inverted angle-domain scattering function. Deconvolution of the source wavelet is taken into account to remove the effect of the wavelet and improve the resolution and accuracy of the inversion results. The derived AD-GRT inversion is non-iterative and is as efficient as the traditional elastic GRT method. The additional dimension of the angle domain has little effect on the computational cost of the AD-GRT, as opposed to other extended-domain inversion/migration methods. Our method also can be used to solve non-linear Born inversion problems using iteration, which can significantly improve their convergence rate. Three numerical examples illustrate that the angle-domain scattering function inversion, data reconstruction, and multi-parameter extraction using the presented AD-GRT inversion are effective.

Lithospheric structure beneath southern Iberia and northern Morocco constrained by 3D Kirchhoff-approximate GRT imaging

The slab beneath the Alboran Sea is a consequence of the collision between two continents (Europe and Africa), which was initiated along the northeastern Spanish coast, experienced slab rollback and migrated to the area adjacent to the two continents. The tectonic background in this area includes episodes of collisions with adjacent continents as well as extension of those basins in the western Mediterranean. Here, we present three-dimensional (3D) Kirchhoff-approximate generalized Radon transform (GRT) images to further constrain the lithospheric structures previously identified by other researchers. The GRT images were calculated from the same P-to-S (Pds or Ps) teleseismic receiver functions (RFs) as the previous common conversion point (CCP) stacking, but the GRT data provide figures with greater resolution than the Pds RFs CCP results. This study indicates that the Alboran Slab may have completely detached from the crustal base under the western Betics Mountains and that a larger range of lithospheric ‘peeling off’ developed beneath the western part of the Betics Mountains than some previous results have claimed. The observed thin lithosphere under the Middle Atlas (MA) and eastern High Atlas (HA) may have a geodynamic relationship with lithospheric delamination under the eastern part of the Rif Mountains, which has also led to the thin lithosphere under the eastern Rif. According to the thick lithosphere under the western HA, the shallow LAB under the MA and eastern HA may have no heat-flow connection with the Canary mantle plume, as stated in several previous studies.

The Funk–Radon transform for hyperplane sections through a common point

The Funk–Radon transform, also known as the spherical Radon transform, assigns to a function on the sphere its mean values along all great circles. Since its invention by Paul Funk in 1911, the Funk–Radon transform has been generalized to other families of circles as well as to higher dimensions. We are particularly interested in the following generalization: we consider the intersections of the sphere with hyperplanes containing a common point inside the sphere. If this point is the origin, this is the same as the aforementioned Funk–Radon transform. We give an injectivity result and a range characterization of this generalized Radon transform by finding a relation with the classical Funk–Radon transform.