Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015...
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Transcript of Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015...
![Page 1: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/1.jpg)
Trivial applications of NeoKinemawhich illustrate its algorithm
by Peter BirdUCLA
2002/2009/2015
Support from NSF & USGS are gratefully acknowledged.
![Page 2: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/2.jpg)
Many grids used for testing overlap the pole and the international date line.Thus, they demonstrate nicely that there are no singularities, and that the spherical algebra was done correctly.
![Page 3: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/3.jpg)
TEST01: No input data, zero velocity at two nodes → static solution.
![Page 4: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/4.jpg)
TEST02: No input data, one fixed node, and one boundary node that rotatesaround it.
Result is rigid-plate rotation, at rates on the order of 7×10-16{radian}/s.
![Page 5: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/5.jpg)
Strain-rates in earlyversions of NK:
Maximumstrain-rate of 210-20 /s =
0.3% in 4 Ga.
![Page 6: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/6.jpg)
Now, using NKv4.1: Maximum
strain-rate becomes 810-23 /s
[7 orders smaller thanthe rotation rate]
= 0.001% in 4 Ga.
![Page 7: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/7.jpg)
TEST03: No input data, uniform extension driven by boundary conditions.
![Page 8: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/8.jpg)
Note: In absence ofdata, lithospherebehaves as a uniformviscous sheet.Therefore, in uniformstress field far from BCs, it undergoes equal vertical andhorizontal shortening.
![Page 9: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/9.jpg)
TEST04:Data on the azimuth of themost-compressive horizontal principal stress are given:
![Page 10: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/10.jpg)
and NeoKinema interpolates these directions by the algorithm of Bird & Li [1996]:
N.B. This interpolationwas done with theindependent-data variantof the method ofBird & Li [1996].The alternate clustered-datamethod would infer largeruncertainties in the results.
![Page 11: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/11.jpg)
When the same velocity boundary conditions are given (as in Test03), NeoKinema attempts to find a velocity solution that will honor these interpolated directions:
![Page 12: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/12.jpg)
The new solution hasnonuniform strain-rates(large where stress directions are compatible with the velocity BCs; small elsewhere):
![Page 13: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/13.jpg)
and here is the (mis)match between the principal strain-rate azimuths of the solution and the target azimuths derived from the stress data:(Note that many of the red target azimuths are hidden by the yellow actual azimuths.)
![Page 14: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/14.jpg)
TEST05:Three faults of unknown slip-rate make up a plate boundary system. Each dip-slip fault has assumed rake of 90°.(Same velocity BCs as in Test03; however, no stress-direction data as in Test04.)
![Page 15: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/15.jpg)
NeoKinema finds a solution with most of the deformationassigned to slip on the faults:
![Page 16: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/16.jpg)
However, the requirement of purely dip-slip faulting on the twonormal faults requires some significant continuum strain-rates:
![Page 17: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/17.jpg)
TEST06:The same 3 faults of unknown slip-rate make up a plate boundary system. But now, each dip-slip fault has assumed rake of 90°20° ().(Same velocity BCs as in Tests03~05.)
![Page 18: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/18.jpg)
NeoKinema finds a solution with virtually all of the deformationassigned to slip on the faults, and continuum strain-rates are smaller:
Note oblique slip on these faults.
![Page 19: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/19.jpg)
TEST08:A strike-slip fault whosetrace is a small circleis entered with unknownslip rate.(Note that it is notnecessary to outlinefault zones with slenderelements, althoughone may choose todo so.)
![Page 20: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/20.jpg)
When the solution is driven indirectly by velocity at one node,the solution is Eulerian plate tectonics, with minimal strain-rates:
![Page 21: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/21.jpg)
TEST09:Example of a conveniencefeature, the type-4 boundarycondition, which allowsboundary nodes to be assignedto a major plate by simplygiving its abbreviation(e.g., “NA”, “PA”);the necessary velocity iscalculated within NeoKinemaby the Euler formula.
(Note: Lacking any data,such as fault locations,the program finds a uniform-viscous-sheet solution to thisproblem.)
PA
NA
![Page 22: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/22.jpg)
TEST10:Synthetic GPS velocities,which are consistent withuniform plate rotation,are input at many internalpoints.Model boundaries are free,except at 2 boundarynodes which are fixed:
![Page 23: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/23.jpg)
TEST11:Same as Test10,except that now thevelocity reference frameof the GPS data istreated as unknown, or free-floating.
The result is that the velocity reference frameis determined by the 2fixed boundary nodes,and all motion is reducedto less than 0.0004 mm/a.
![Page 24: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/24.jpg)
TEST13: Conversion of input short-term interseismic GPS velocities (left)to long-term corrected velocities (right), along a strike-slip faultwhich is temporarily locked down to 100 km depth.(In this test, velocity BCs “enforce” the right plate-motion solution.) INPUT: OUTPUT:
![Page 25: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/25.jpg)
TEST14: Conversion of input short-term interseismic GPS velocities (left)to long-term corrected velocities (right), along a strike-slip faultwhich is temporarily locked down to 100 km depth.(In this test, the southwestern plate is free, and GPS data determines its velocity.) INPUT: OUTPUT:
![Page 26: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/26.jpg)
TEST15: Conversion of input short-term GPS velocities (left)to long-term corrected velocities (right), along the Cascadia subduction thrust,which is temporarily locked from 10 km to 40 km depths.(Note that long-term relative velocities within NA are less than short-term.) INPUT: OUTPUT:
![Page 27: Trivial applications of NeoKinema which illustrate its algorithm by Peter Bird UCLA 2002/2009/2015 Support from NSF & USGS are gratefully acknowledged.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649eab5503460f94bb06fd/html5/thumbnails/27.jpg)
(end)