1 / 10

Triple correlation Helioseismology

This document explores the concept of triple correlation in helioseismology, focusing on its definition, methods, and implications. Utilizing Fourier analysis, it discusses the expected travel times and the concentration of power in the Fourier domain. The study applies arc-averaging masks and standard phase-speed filtering to interpret the data. Insights include the visibility of ridges in Fourier modulus indicative of dispersion changes and the determination of differential travel times from triple correlation ratios. It highlights the computational requirements for extensive time series analysis.

tacita
Télécharger la présentation

Triple correlation Helioseismology

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Triple correlation Helioseismology Frank P. Pijpers Imperial College London with thanks to HELAS for financial support

  2. multiple correlations definition : c(τ1 ,τ2 , …,τn-1) = ∫ f1(t) f2(t+τ1)…fn(t+τn-1) dt Triple correlation in the Fourier domain : C(ω1,ω2) = F1(ω1 ) F2(ω2) F3*(ω1+ω2)

  3. The three arc-averaging masks used Use the standard phase-speed filter for this separation 3 2 1

  4. What to expect ? • The travel time over each of the three sides should be (almost) equal so that : τ1=τ2=τgrp • Power in Fourier domain concentrated around ridge(s) with ω1+ω2= cst. but with a lot of structure in each ridge. • Eliminate structure by dividing by mean triple correlation. If the wavelet is merely displaced one should find a clear signature in the Fourier phase

  5. Analogous to what is done in speckle masking. Figure from Lohmann, Weigelt, Wirnitzer, (1983) App. Opt. 22,4028 average triple correlation ratio

  6. The average triple correlation for a cube of 512 128 x 128 images with an averaging mask of arcs on an equilateral triangle (8 by 8 sets) Fourier modulus (logarithmic) Fourier phase

  7. Ratio of triple correlation of arc-set (4,4) and the average triple correlation Fourier modulus Fourier phase

  8. What is gained ? • the ridges are visible in the Fourier modulus : wavelet changes over field. This is indicative of dispersion changes • Differential travel times are directly determined from the triple correlation ratios. Fast and robust extraction of the quantity of interest

  9. The cost ? • Memory : for long time series the storage requirement goes up as N2. Working with large fields and long time series may require large cache/swap space • Time : on 8 cpu sparc machine the examples shown here took 11 minutes

More Related