;+ ; ; NAME:twavpol ; ;PURPOSE:To perform polarisation analysis of three orthogonal component time ; series data, using tplot variables. ; ;EXAMPLE: twavpol,'in_data',prefix='in_data',freqline=fl ; ;INPUTS: tvarname: the name of the tplot variable upon which it will ;operate ; ;prefix(optional): the prefix to be assigned to the tplot variables that will be ;output, defaults to tvarname ; ; ; Subroutine assumes data are in righthanded fieldaligned ; coordinate system with Z pointing the direction ; of the ambient magnetic field. ; ;Keywords: ; nopfft(optional) = Number of points in FFT ; ; steplength(optional) = The amount of overlap between successive FFT intervals ; ;OUTPUTS: ; error(optional): named variable in which to return the ; error state of this procedure call. 1 = success, 0 = failure ; ; freqline(optional): assign a named variable to this keyword ; to store the frequencies of each y-index ; ; timeline(optional): assign a named variable to this keyword ; to store the times of each x-index ; ;The program outputs five spectral results derived from the ; fourier transform of the covariance matrix (spectral matrix) ;This version stores these outputs as tplot variables with the ;specified prefix ; These are follows: ; ; Wave power: On a linear scale, at this stage no units ; ; Degree of Polarisation: ; This is similar to a measure of coherency between the input ; signals, however unlike coherency it is invariant under ; coordinate transformation and can detect pure state waves ; which may exist in one channel only.100% indicates a pure ; state wave. Less than 70% indicates noise. For more ; information see J. C. Samson and J. V. Olson 'Some comments ; on the description of the polarization states ; of waves' Geophys. J. R. Astr. Soc. (1980) v61 115-130 ; ; Wavenormal Angle: ; The angle between the direction of minimum variance ; calculated from the complex off diagonal elements of the ; spectral matrix and the Z direction of the input ac field data. ; for magnetic field data in field aligned coordinates this is the ; wavenormal angle assuming a plane wave. See: ; Means, J. D. (1972), Use of the three-dimensional covariance ; matrix in analyzing the polarization properties of plane waves, ; J. Geophys. Res., 77(28), 5551-5559, ; doi:10.1029/JA077i028p05551. ; ; Ellipticity: ; The ratio (minor axis)/(major axis) of the ellipse transcribed ; by the field variations of the components transverse to the ; Z direction (Samson and Olson, 1980). The sign indicates ; the direction of rotation of the field vector in the plane (cf. ; Means, (1972)). ; Negative signs refer to left-handed rotation about the Z ; direction. In the field aligned coordinate system these signs ; refer to plasma waves of left and right handed polarization. ; ; Helicity:Similar to Ellipticity except defined in terms of the ; direction of minimum variance instead of Z. Stricltly the Helicity ; is defined in terms of the wavenormal direction or k. ; However since from single point observations the ; sense of k cannot be determined, helicity here is ; simply the ratio of the minor to major axis transverse to the ; minimum variance direction without sign. ; ; ;NOTES: ;1. Although the input is in the form of a tplot variable, the ;output is currently in the form of arrays ; ;2. -If one component is an order of magnitude or more greater than ; the other two then the polarisation results saturate and erroneously ; indicate high degrees of polarisation at all times and ; frequencies. ; ;3. Time series should be eyeballed before running the program. ; For time series containing very rapid changes or spikes ; the usual problems with Fourier analysis arise. ; Care should be taken in evaluating degree of polarisation results. ; ;4. For meaningful results there should be significant wave power at the ; frequency where the polarisation approaches ; 100%. Remembercomparing two straight lines yields 100% polarisation. ; ; $LastChangedBy: pcruce $ ; $LastChangedDate: 2014-09-23 16:57:26 -0700 (Tue, 23 Sep 2014) $ ; $LastChangedRevision: 15847 $ ; $URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/trunk/general/science/wavpol/twavpol.pro $ ;- pro twavpol,tvarname,prefix = prefix, error=error, freqline = freqline, timeline = timeline,$ nopfft=nopfft,steplength=steplength error=0 if not keyword_set(tvarname) then begin dprint, 'tvarname must be set' return endif if not keyword_set(prefix) then prefix = tvarname var_names = tnames(tvarname) if(var_names[0] eq '') then begin dprint, 'No valid tplot_variables match tvarname' return endif get_data,tvarname,data=d dimx = size(/dim,d.x) dimy = size(/dim,d.y) if dimx[0] ne dimy[0] then begin dprint,'Number of time elements does not match number of magnetic field elements in tvarname' return endif if n_elements(dimy) ne 2 then begin dprint,'Data component of tvarname must be a 2 dimensional array' return endif if dimy[1] ne 3 then begin dprint,'Dimension 2 of data component of tvarname must have 3 elements' return endif wavpol, d.x, d.y[*, 0], d.y[*, 1], d.y[*, 2], timeline, freqline,$ powspec, degpol, waveangle, elliptict, helict, pspec3, nopfft=nopfft,steplength=steplength store_data, prefix+'_powspec', data = {x:timeline, y:powspec, v:freqline}, dlimits = {spec:1B} store_data, prefix+'_degpol', data = {x:timeline, y:degpol, v:freqline}, dlimits = {spec:1B} store_data, prefix+'_waveangle', data = {x:timeline, y:waveangle, v:freqline}, dlimits = {spec:1B} store_data, prefix+'_elliptict', data = {x:timeline, y:elliptict, v:freqline}, dlimits = {spec:1B} store_data, prefix+'_helict', data = {x:timeline, y:helict, v:freqline}, dlimits = {spec:1B} store_data, prefix+'_pspec3', data = {x:timeline, y:pspec3, v:freqline}, dlimits = {spec:1B} error=1 end