## PSN-L Email List Message

Subject: RE: Iris Waveform Chart
From: "Jorma Kanninen" jorma@.............
Date: Sat, 5 Feb 2005 23:42:20 +0000

FYI

The line caustic behavior has been discussed since Chang and Refs=
dal (1979) mentioned inverse-square-root-of-the-distance dependen=
ce of the amplification of the images near the critical curve in=20=
a study of a single point mass under the influence of a constant=20=
shear due to a larger mass. A quarter century later, Gaudi and Pe=
tters (2001) interprets that the distance is {\it a vertical dist=
ance to the caustic}. It is an erroneous misinterpretation.
We rehash Rhie and Bennett (1999) where the caustic behavior of t=
he binary lenses was derived to study the feasibility of limb dar=
kening measurements in caustic crossing microlensing events. ~({\=
it 1}) $J =3D \pm \sqrt{4\delta\omega_{2-} J_-}$ where ~$\delta\o= mega\parallel\bar\partial J$, and $\delta\omega_{2-}$ and $J_-$ a=
re $E_-$-components of $\delta\omega$ (the source position shift=20=
from the caustic curve) and $2\bar\partial J$ (the gradient of th=
e Jacobian determinant) respectively; ~({\it 2}) The critical eig=
envector $\pm E_-$ is normal to the caustic curve and easily dete=
rmined from the analytic function $\kappa$-field; ~({\it 3}) Near=
a cusp ($J_- =3D 0$) is of a behavior of the third order, and th=
e direction of $\bar\partial J$ with respect to the caustic curve=
changes rapidly because a cusp is an accumulation point; ~({\it=20=
4}) On a planetary caustic, $|\partial J|\sim \sqrt{1/\epsilon_{p= l}}$ is large and power expansion does not necessarily converge o=
ver the size of the lensed star. In practice, direct numerical su=
mmation is inevitable.
We also note that a lens equation with constant shear is intrinsi=
cally incomplete and requires supplementary physical assumptions=20=
and interpretations in order to be a viable model for a lensing s=
ystem.

Cheers,

Jorma

________________________________

From: psn-l-request@.............. [mailto:psn-l-request@webtroni=
cs.com] On Behalf Of Timothy Carpenter
Sent: 05 February 2005 21:33
To: psn-l@..............
Subject: RE: Iris Waveform Chart

I should probably know =E2=80=93 but I don't. What is the "causti=
c" distance? And for that matter, what is the "caustic"?

Regards,

-Tim-

Timothy Carpenter, P.E., Pres.,
GeoDynamics Consultants, Inc.
5043 Whitlow Ct.
Commerce Twp., Mi 48382
248-363-4529 (voice & fax)
248-766-1629 (cell)
geodynamics@........... (primary)
geodynamics@....... (secondary)

-----Original Message-----
From: psn-l-request@.............. [mailto:psn-l-request@webtroni=
cs.com] On Behalf Of Connie and Jim Lehman
Sent: Sunday, January 09, 2005 7:03 PM
To: psn-l@..............
Subject: Iris Waveform Chart

PSN--thanks for the Iris Waveform Chart for the 9.0 Sumatra  12/2=
6/04 event.  The surface wave arrivals of multiple stations exhib=
ited by distance, and text,  makes a super graphic.  I was wonder=
ing about  the occurrence of a seismic caustic at the appropriate=
degree distance.  Was the gap at 160 degree area due to no repor=
ting station near the "caustic" distance.  In periodic recording=20=
here we've copied three caustics  in 20 years--I believe the even=
ts were southwest of Australia for us--not a very hot spot.

The 18 sec long period system at James Madison Un.  (Virginia=
) working into a graphic readout read the 8.1 Macquarie Is. event=
-(l2/23) nicely, but the 9.0 event read 20 min after P-diff arriv=
ed and then went off scale for 100 minutes and returned to normal=
recording for the 7.1 event at 04:21.  One can conclude, surface=
wave arrivals for us (at approx. 145 degrees) were obscured.  Ke=
ep up the good work.

Jim Lehman

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