Traveltime inversion of offset vertical seismic profiles using an application of Fermat's principle

1986 ◽  
Author(s):  
C. Deplante ◽  
M. Oristaglio
Keyword(s):  
Seismic Profiles ◽  
Traveltime Inversion ◽  
Vertical Seismic Profiles ◽  
Fermat’S Principle ◽  
Fermat's Principle

Traveltime inversion of offset vertical seismic profiles—A feasibility study

Geophysics ◽  
1984 ◽  
Vol 49 (3) ◽  
pp. 250-264 ◽  
Author(s):  
L. R. Lines ◽  
A. Bourgeois ◽  
J. D. Covey
Keyword(s):  
Inverse Method ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Profile ◽  
Inversion Method ◽  
Earth Model ◽  
Seismic Profiles ◽  
Traveltime Inversion ◽  
Vertical Seismic Profiles ◽  
Inversion Techniques

Traveltimes from an offset vertical seismic profile (VSP) are used to estimate subsurface two‐dimensional dip by applying an iterative least‐squares inverse method. Tests on synthetic data demonstrate that inversion techniques are capable of estimating dips in the vicinity of a wellbore by using the traveltimes of the direct arrivals and the primary reflections. The inversion method involves a “layer stripping” approach in which the dips of the shallow layers are estimated before proceeding to estimate deeper dips. Examples demonstrate that the primary reflections become essential whenever the ratio of source offset to layer depth becomes small. Traveltime inversion also requires careful estimation of layer velocities and proper statics corrections. Aside from these difficulties and the ubiquitous nonuniqueness problem, the VSP traveltime inversion was able to produce a valid earth model for tests on a real data case.

Curved‐ray traveltime inversion of shallow vertical seismic profiles

2002 ◽  
Author(s):  
Geoff Moret ◽  
William P. Clement ◽  
Michael D. Knoll
Keyword(s):  
Seismic Profiles ◽  
Traveltime Inversion ◽  
Vertical Seismic Profiles

Inversion with a grain of salt

Geophysics ◽  
1985 ◽  
Vol 50 (1) ◽  
pp. 99-109 ◽  
Author(s):  
Larry R. Lines ◽  
Sven Treitel
Keyword(s):  
Least Squares ◽  
Jacobian Matrix ◽  
Quantitative Measure ◽  
Parameter Estimates ◽  
Inversion Problem ◽  
Seismic Profiles ◽  
Traveltime Inversion ◽  
Vertical Seismic Profiles ◽  
Model Response ◽  
Value Decomposition

Although least‐squares inversion is a useful tool in data analysis, nonuniqueness is an inevitable problem. This problem can be analyzed by considering the sensitivity of a model response to the parameter estimates. Such sensitivity methods produce extremal solutions which barely satisfy some resolution (or stability) criteria. Two closely related methods for producing such solutions are the “Edgehog” and “Most Squares” methods due to Jackson (1973, 1976). These techniques, which evaluate the “degree of nonuniqueness” in a least‐squares inversion, require only the information computed in a singular value decomposition (SVD) solution. While the “edgehog” and “most squares” techniques are mathematically similar, the “most squares” estimate is the simpler to compute. Both methods show that the credibility of an inversion depends on both the specified error criterion as well as on the properties of the Jacobian matrix associated with the least‐squares solution. The similar performance of these two closely related methods is demonstrated with the traveltime inversion of both synthetic and real vertical seismic profiles (VSPs). The sensitivity analysis of this inversion problem provides a quantitative measure of solution reliability.

Quantitative OCT image correction using Fermat's principle and mapping arrays

2002 ◽  
Author(s):  
Volker Westphal ◽  
Sunita Radhakrishnan ◽  
Andrew M. Rollins ◽  
Joseph A. Izatt
Keyword(s):  
Image Correction ◽  
Fermat’S Principle ◽  
Fermat's Principle ◽  
Mapping Arrays ◽  
Oct Image

scholarly journals Fermat’s principle in black-hole spacetimes

2018 ◽  
Vol 27 (14) ◽  
pp. 1847025 ◽  
Author(s):  
Shahar Hod
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Black Hole Spacetimes ◽  
Fermat’S Principle ◽  
Kerr Black Holes ◽  
Fermat's Principle ◽  
Asymptotic Observers

Black-hole spacetimes are known to possess closed light rings. We here present a remarkably compact theorem which reveals the physically intriguing fact that these unique null circular geodesics provide the fastest way, as measured by asymptotic observers, to circle around spinning Kerr black holes.

Three-dimensional Travel-time Calculation Based on Fermat’s Principle

2002 ◽  
pp. 1563-1582
Author(s):  
Valentin Meshbey ◽  
Evgeny Ragoza ◽  
Dan Kosloff ◽  
Uzi Egozi ◽  
Tal Wexler
Keyword(s):  
Travel Time ◽  
Three Dimensional ◽  
Time Calculation ◽  
Fermat’S Principle ◽  
Fermat's Principle
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