MTPA (Multi Prolate Taper Analysis)

This tool of spectral estimation has been devised originally by Thomson DJ (1982, Spectrum estimation and harmonic analysis, proc. IEEE,70, 1055-96). Basically, it provides the optimal tapers without removing informations at the start and the end of signal window, as with the use of traditionnal tapers like Hanning, Hamming, Blackman, ..etc.

A good description of this tools is given in the book: Time Series Analysis and Inverse Theory for geophysicists, by David Gubbins, Cambridge, 2004.

Organization of the directories of POLAR_x.xx


* it contains the files of tapers that are pre-calculated with various orders and number of tapers;

* NEVER DELETE THESE FILES: they are used by programs






  1. SAC_BIN or SAC_ASCII format

  2. DIRECTORY of signals to be analyzed

  3. DIRECTORY of results

  4. SELECTION of files (wild chars allowed)


    MTPA_spectra Sac_ASCII /Public/Data/Sac_ascii ~/Spectra_results 2005_12_26*DGAR*

    MTPA_spectra Sac_BIN /Public/Data/Sac_ascii ~/Spectra_results 2005_12_26*DGAR*LHZ*

Installation of programs:

Classically type :




the program uses a file of parameters that must be located in the same directory than the executable;

this file is pola.ini

edit this file : you will see that it contains some important parameters:

*the min. frequency in Hz of computation of polarization

*the max. frequency in Hz of computation of polarization

Running pola :

pola needs 4 arguments (like MTPA_Spectra):


  1.  SAC_BIN or SAC_ASCII format

    2.  DIRECTORY of signals to be analyzed

   3.  DIRECTORY of results

   4  SELECTION of files (wild chars allowed)


        pola Sac_ASCII /Public/Data/Sac_ascii ~/my_Pola_results 2005_12_26*DGAR*

        pola Sac_BIN /Public/Data/Sac_bini ~/my_Pola_results 2005_12_26*KMBO*

*be aware to SELECT ONLY ONE STATION with wild chars (and only 1 time_window);

*the 3 comp. N, Z E must exist in the directory of signal

Examples of results:

P WAVE with the 3 componants

Bottom : Azimth estimation vs period, with error-bar. The MTPA parameters are : order 3, number of tapers: 5.

Middle: Coefficient of polarisation for linarity , vs period ; the maximum is 1.0

Top: Phase delay in degree vs period, between the horizontal compoants: N & E. Theoretically the phase would be close to zero, for a pure linear polarisation. The non zero value of phase are probably caused by the addition of noise to the signal.