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 __________________________________________________________ Public Seismic Network Mailing List (PSN-L)