Polar Cap Error Analysis with FJS
"Polar Cap Error Analysis with FJS" is a collection of various handwritten notes from Dahlen as well as back and forth emails between him and Frederik J. Simons, hereafter FJS. The collection began in July of 2005. The documents are contained within a light blue loose leaf binder. FJS was at the time a Lecturer of Geophysics at University College London before he became an Assistant Professor of Geosciences at Princeton University in 2006, joining Dahlen. The two worked together until Dahlen's death in 2007. Frederik's home page can be found at the bottom of this page, or here. The contents of this collection follow the process that both FJS and Dahlen took to ultimately publish their joint paper Spherical Slepian functions and the polar gap in geodesy in 2006. Most of the emails contained show the discussions that polished the paper as the two tried to figure out how to represent error in their polar cap analysis. This collection can be found at: Guyot Hall, Princeton, NJ, 08540. Back to Main Page
	Pages	Sheet Numbers
[FJS emails - discussing notation and equations of their work]	1–9	N/A
7/29/2005 – following several emails from FJS	10–17	1–8
Axisymmetric case	18–25	1–2, 1–6
[FJS emails - debate on axisymmetric case]	26–34	N/A
[Continued notes on Axisymmetric case]	35–38	1–2, 1–2
[FJS emails - fixing typos in code]	39–41	N/A
[Part of paper by FJS and Dahlen - "Geodetic Applications"]	42–45	N/A
[Proof that SG and SH spatial convergences are identical]	46–48	1–3
[FJS emails - discussion of proof]	49–50	N/A
Shannon number truncation	51–54	1–4
Reading FJS Aug. 10 e-mail	55–58	1–4
[FJS emails - trying to reduce error in SH + SG truncation	59–73	N/A
[Notes on calculation of error in SH + SG truncation]	74–84	1–11
Spatial variance – FJS point of view	85–99	1–5, 1–9
Errors...again	100–106	1–7
[FJS emails - realization of error mistakes	107–110	N/A
Error analysis – the right way, finally!	111–118	1–8
[FJS emails - discussion of figure readability	119–127	N/A
Damped SH	128–144	1–8, 1–9
[FJS emails - SIAM paper draft discussion	145–152	N/A
Spatial error analysis: a=0 case only	153–164	1–12
What if the noise is red?	165–169	1–5
[FJS emails - general red case	170–171	N/A
a>0 case	172–179	1–8
[FJS emails - continuous vs discrete data]	180–182	N/A
It works! - a>0 error analysis	183–193	1–11
[Faxes and emails from FJS about polar gap paper]	194–204	N/A
Truncated Slepian (hereafter TS) analysis	205–220	1–11, 1–3
λ_up and λ_down	221–224	1–4
Spectral leakage bias - undamped SH	225–243	1–4, 1–7, 1–6
[FJS emails - polishing of figures for paper]	244–279	N/A