Spherical integral formulas for upward/downward continuation of gravitational gradients onto gravitational gradients

2013 ◽  
Vol 88 (2) ◽  
pp. 179-197 ◽  
Author(s):  
Michal Šprlák ◽  
Josef Sebera ◽  
Miloš Val’ko ◽  
Pavel Novák
Keyword(s):  
Downward Continuation ◽  
Integral Formulas ◽  
Gravitational Gradients

scholarly journals Certain Unified Integrals Involving a Multivariate Mittag–Leffler Function

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 81
Author(s):  
Shilpi Jain ◽  
Ravi P. Agarwal ◽  
Praveen Agarwal ◽  
Prakash Singh
Keyword(s):  
Integral Formulas ◽  
Special Cases

A remarkably large number of unified integrals involving the Mittag–Leffler function have been presented. Here, with the same technique as Choi and Agarwal, we propose the establishment of two generalized integral formulas involving a multivariate generalized Mittag–Leffler function, which are expressed in terms of the generalized Lauricella series due to Srivastava and Daoust. We also present some interesting special cases.

High-precision Downward Continuation of Potential Fields Algorithm Utilizing Adaptive Damping Coefficient of Generalized Minimal Residuals

2021 ◽  
Author(s):  
Zhi-Hou Zhang ◽  
Xiao-Long Liao ◽  
Ze-Yu Shi ◽  
Anthony R. Lowry ◽  
Yao Yu ◽  
...  
Keyword(s):  
High Precision ◽  
Downward Continuation ◽  
Damping Coefficient ◽  
Potential Fields

Gaussian beam migration

Geophysics ◽  
1990 ◽  
Vol 55 (11) ◽  
pp. 1416-1428 ◽  
Author(s):  
N. Ross Hill
Keyword(s):  
Gaussian Beam ◽  
Wave Field ◽  
Seismic Source ◽  
Velocity Model ◽  
Downward Continuation ◽  
Gaussian Beams ◽  
Seismic Velocities ◽  
Migration Method ◽  
Gaussian Beam Migration ◽  
Lateral Variations

Just as synthetic seismic data can be created by expressing the wave field radiating from a seismic source as a set of Gaussian beams, recorded data can be downward continued by expressing the recorded wave field as a set of Gaussian beams emerging at the earth’s surface. In both cases, the Gaussian beam description of the seismic‐wave propagation can be advantageous when there are lateral variations in the seismic velocities. Gaussian‐beam downward continuation enables wave‐equation calculation of seismic propagation, while it retains the interpretive raypath description of this propagation. This paper describes a zero‐offset depth migration method that employs Gaussian beam downward continuation of the recorded wave field. The Gaussian‐beam migration method has advantages for imaging complex structures. Like finite‐difference migration, it is especially compatible with lateral variations in velocity, but Gaussian beam migration can image steeply dipping reflectors and will not produce unwanted reflections from structure in the velocity model. Unlike other raypath methods, Gaussian beam migration has guaranteed regular behavior at caustics and shadows. In addition, the method determines the beam spacing that ensures efficient, accurate calculations. The images produced by Gaussian beam migration are usually stable with respect to changes in beam parameters.

scholarly journals Homogeneous star products and closed integral formulas

2010 ◽  
Vol 62 (4) ◽  
pp. 559-573
Author(s):  
Khaled Tounsi
Keyword(s):  
Star Products ◽  
Integral Formulas

Green's integral formulas in magnetohydrodynamics

Meccanica ◽  
1966 ◽  
Vol 1 (3-4) ◽  
pp. 3-17
Author(s):  
Cataldo Agostinelli
Keyword(s):  
Integral Formulas
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