scholarly journals Three-dimensional passive seismic waveform imaging around the SAFOD site, California, using the generalized Radon transform

2009 ◽  
Vol 36 (23) ◽  
Author(s):  
Haijiang Zhang ◽  
Ping Wang ◽  
Robert D. van der Hilst ◽  
M. Nafi Toksoz ◽  
Clifford Thurber ◽  
...  
Keyword(s):  
Radon Transform ◽  
Three Dimensional ◽  
Generalized Radon Transform ◽  
Seismic Waveform ◽  
Passive Seismic

Three-dimensional time-harmonic elastodynamic Green ’ s functions for anisotropic solids

1995 ◽  
Vol 449 (1937) ◽  
pp. 441-458 ◽  
Keyword(s):  
Differential Equations ◽  
Radon Transform ◽  
Transverse Isotropy ◽  
Three Dimensional ◽  
Surface Integral ◽  
Line Integral ◽  
Surface Integration ◽  
Time Harmonic ◽  
Inverse Radon Transform ◽  
Eigenvectors And Eigenvalues

A method based on the Radon transform is presented to determine the displacement field in a general anisotropic solid due to the application of a time-harmonic point force. The Radon transform reduces the system of coupled partial differential equations for the displacement components to a system of coupled ordinary differential equations. This system is reduced to an uncoupled form by the use of properties of eigenvectors and eigenvalues. The resulting simplified system can be solved easily. A back transformation to the original coordinate system and a subsequent application of the inverse Radon transform yields the displacements as a summation of a regular elastodynamic term and a singular static term. Both terms are integrals over a unit sphere. For the regular dynamic term, the surface integration can be evaluated numerically without difficulty. For the singular static term, the surface integral has been reduced to a line integral over half a unit circle. Reductions to the cases of isotropy and transverse isotropy have been worked out in detail. Examples illustrate applications of the method.

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

2021 ◽  
Vol 18 (2) ◽  
pp. 268-281
Author(s):  
Qinci Li ◽  
Imma Palomeras ◽  
Xiaohong Meng
Keyword(s):  
Three Dimensional ◽  
Receiver Functions ◽  
Western Mediterranean ◽  
Lithospheric Structure ◽  
Generalized Radon Transform ◽  
Conversion Point ◽  
Slab Rollback ◽  
Southern Iberia ◽  
Middle Atlas ◽  
Peeling Off

Abstract 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.

GPR imaging using the generalized Radon transform

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1553-1559 ◽  
Author(s):  
Tsili Wang ◽  
Michael L. Oristaglio
Keyword(s):  
Half Space ◽  
Radon Transform ◽  
Peak Frequency ◽  
Outer Diameter ◽  
Electromagnetic Data ◽  
Generalized Radon Transform ◽  
Plastic Pipes ◽  
Sharp Image ◽  
Imaging Algorithms ◽  
Ground Penetrating

A new algorithm for imaging ground‐penetrating radar (GPR) data follows from the theory of the generalized Radon transform (GRT), which was developed and has been used extensively for seismic imaging. The algorithm enables separate reconstructions (to first‐order accuracy) of subsurface permittivity and conductivity images. A pseudovector inverse adapts the original scalar Radon transform theory for vector electromagnetic data. Synthetic examples show that the algorithm can image plastic and metallic pipes buried in a half‐space. In the examples, the half‐space is 100 ohm-m with a relative permittivity of 10. The pipes are 2 cm thick and 15 cm in outer diameter and are buried at a depth of 2 m. The plastic pipes are assumed to be pure insulators, whereas the metallic pipes are assumed to be pure conductors with a conductivity value of 106 S/m. The transmitter waveform has a peak frequency of 200 MHz with a 500-MHz bandwidth. The results show that quantitative images are obtained for plastic pipes, whose scattering is weak (so the Born approximation is accurate). Good images are also obtained for metallic pipes. As with most imaging algorithms, a sharp image requires good estimates of the properties of the background medium.

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