Distortion of Some “Squarish Pulses” in a Constant Gradient Medium

1969 ◽  
Vol 46 (1A) ◽  
pp. 111-111
Author(s):  
D. H. Wood
Keyword(s):  
Constant Gradient ◽  
Gradient Medium

scholarly journals Analytical approximations of diving-wave imaging in constant-gradient medium

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. S131-S140 ◽  
Author(s):  
Alexey Stovas ◽  
Tariq Alkhalifah
Keyword(s):  
Initial Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Image Point ◽  
Practical Applications ◽  
Analytical Approximations ◽  
Wave Imaging ◽  
Analytical Formulas ◽  
Constant Gradient ◽  
Gradient Medium

Full-waveform inversion (FWI) in practical applications is currently used to invert the direct arrivals (diving waves, no reflections) using relatively long offsets. This is driven mainly by the high nonlinearity introduced to the inversion problem when reflection data are included, which in some cases require extremely low frequency for convergence. However, analytical insights into diving waves have lagged behind this sudden interest. We use analytical formulas that describe the diving wave’s behavior and traveltime in a constant-gradient medium to develop insights into the traveltime moveout of diving waves and the image (model) point dispersal (residual) when the wrong velocity is used. The explicit formulations that describe these phenomena reveal the high dependence of diving-wave imaging on the gradient and the initial velocity. The analytical image point residual equation can be further used to scan for the best-fit linear velocity model, which is now becoming a common sight as an initial velocity model for FWI. We determined the accuracy and versatility of these analytical formulas through numerical tests.

scholarly journals An approximate elastic two-dimensional Green’s function for a constant-gradient medium

2001 ◽  
Vol 146 (1) ◽  
pp. 237-248 ◽  
Author(s):  
Francisco J. Sánchez-Sesma ◽  
Raul Madariaga ◽  
Kojiro Irikura
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Two Dimensional ◽  
Constant Gradient ◽  
Gradient Medium

Reflection of rays in a constant gradient medium: CRP geometry

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 707-712
Author(s):  
Franklyn K. Levin
Keyword(s):  
Velocity Gradient ◽  
Seismic Data ◽  
Constant Velocity ◽  
Finite Range ◽  
Velocity Increase ◽  
Rate Of Increase ◽  
Constant Gradient ◽  
Gradient Medium

In a medium having a velocity that increases linearly with depth (constant gradient), rays are arcs of circles (Slotnick, 1936). A constant gradient medium is not a good approximation to a real subsurface. Not only does velocity increase without limit with depth, but the rate of increase is constant. Nonetheless, over a finite range of depths, a constant gradient medium is closer to reality than a medium having constant velocity down to reflector of interest. For that reason, a number of investigators have considered the changes in processes applied to seismic data when a constant velocity gradient other than zero is assumed.

A constant gradient unilateral magnet for near-surface MRI profiling

2006 ◽  
Vol 183 (2) ◽  
pp. 228-234 ◽  
Author(s):  
Andrew E. Marble ◽  
Igor V. Mastikhin ◽  
Bruce G. Colpitts ◽  
Bruce J. Balcom
Keyword(s):  
Near Surface ◽  
Constant Gradient
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