Pre-Processing and Cross-Correlation Techniques for Time-Distance Helioseismology

Nan Wang1, Sjoerd de Ridder1, & Junwei Zhao2

(1) Geophysics and Planetary Sciences, University of Science and Technology of China, Hefei, China, (2) W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA, United States

Abstract

Introduction

Conclusions

In chaotic wave fields excited by a random distribution of noise sources, a cross-correlation of the recordings made at two stations yields the interstation wave-field response. We have much experience with pre-processing and correlation techniques for seismic noise data on the earth. This study applies some of the seismic processing schemes to Doppler data taken from the sun. By using the experiences from seismic interferometry we try to get a better correlation of helioseismology data. This research uses multidimensional autocorrelation to gain an averaged impulse response. We then apply sign-bit and spectral whitening to the Doppler data. We find that spectral whitening can improve the bandwidth of the autocorrelation results to span a frequency range of 2 to 7mHz, especially for the p-modes oscillations in the sun. The results of our research help us understand the effect of preprocessing techniques for the cross-correlation studies in both terrestrial- and helio-seismology.

The Doppler velocity data was obtained by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) satellite from August 1st to 5th, 2010. The data varies considerably between sunspots and quiet portions of the sun. We removed a running alpha-mean from the data and applied a soft clip to deal with data glitches. The recordings contain energy of both flow and waves. A frequency domain low-cut filter at 2mHz selected the wave energy. Then the data was input to several pre-processing and cross-correlation techniques, common to earth seismology.

Results

Methods1 Band-PassThe band-pass filter we designed applies a taper in the frequency domain, with the input being the desired upper and lower ends of the frequency-domain taper, and computes in frequency domain although the input and output of the filter function is in time domain for convenience. The conversion of time domain and frequency domain is done through the Discrete Fourier transform. This band-pass filter is used to select the wave energy in the data, and discard the flow energy at low frequencies. 2 Multidimensional AutocorrelationMultidimensional Autocorrelation is equivalent to doing pair-by-pair cross correlations and stacking over common offsets in both spatial dimensions. To do a multidimensional autocorrelation, we first shift the data and do a Discrete Fourier Transform, then compute the power spectrum in frequency domain. We then inversely Fourier transform the power spectrum back into time and space domain to analyze the results. The most important code-line in matlab script for this step is:

ifftshift(ifftn(abs(fftn(fftshift(data))).^2)) References

Acknowledgement

We first analyze one time slice of the original data and three time traces of the entire 5 days of original data (from three chosen areas). It is apparent that there are some glitches in the records, and also a very slowly varying trends. These are caused by the satellites orbit and remnant effects of the magnetic field influences on the data recordings.

We subtract a running alpha-mean from the data, which is computed over a sliding window to exclude the extreme values. We then compute the clip from the average amplitudes of the data and do a soft-clip to scale the extreme values down based on the average amplitudes. A time slice of the processed data, and three time traces of the first 8 hours of the processed data (from three chosen areas). This is a sentence.

The recordings contain energy of both flow and waves. The lower frequency energy is caused by convective flows of plasma in the sun. A frequency domain filter selects the energy of waves travelling through the plasma between 2mHz and 7mHz in frequencies.

To analyze the results of this processing, we stack over common radial offset (centering in the middle of the cube). We normalize the stack by the fold. Then we make an f-k spectrum by a two-dimensional Discrete Fourier.

 3 Sign-bitThe sign-bit is a bit in a signed number representation that indicates the sign of a number. Sign-bit only keeps the sign of the recordings value and makes the amplitude +1 for positive value or -1 for negative value.

4 Spectral WhiteningSpectral whitening aims to flatten the energy spectrum of the wave field and consequently the multidimensional autocorrelations. We did the calculation in frequency domain. The multidimensional autocorrelation value is divided by the absolute value of the power spectrum averaged over space. This could be seen as a quasi-deconvolution.

Time slices of the result of multidimensional autocorrelation, starting at t=0 s with 315 s interval:

To compare the achieved bandwidth and final spectra between the three different processing approaches, we compute the spectrum over time only and then average it over space.

Thompson, M. J. (2004) “Helioseismology and the Sun's interior” Astronomy & Geophysics, 45(4), 4-21.Bensen, G. D., M.H. Ritzwoller, M.P. Barmin, A.L. Levshin, F. Lin, M.P. Moschetti, N.M. Shapiro, and Y. Yang (2007) “Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements” Geophysical Journal International, 169(3), 1239-1260.de Ridder, S. A. L. (2014) “Passive seismic surface-wave interferometry for reservoir-scale imaging” PhD. Thesis, Stanford University.

I thank Junwei Zhao (Stanford University, W. W. Hansen Experimental Physics Laboratory) for the data used in this project and for helpful suggestions and explanations.I thank Prof. Sjoerd de Ridder for his guidance of my project.I thank Prof. Huajian Yao and Prof. Chenglong Shen for their help on this project. You cannot say “I” here, because everything in this poster is supposedly from three of us. So, you cannot thank Sjoerd or me, because it is like we thank ourselves.

With the multidimensional autocorrelation technique we can extract the impulse response signal out of the Doppler-velocity noise recordings. Sign-bit processing does not improve the bandwidth of the result. However, the spectral whitening does improve the bandwidth of the signal. These results may help researchers to obtain better signal and resolution from Doppler data. It will be interesting to see whether the spectral whitening performs better than sign-bit processing for cross-correlations in the terrestrial seismology.

In the frequency domain this looks like:

Here B is the spectrally whitened version of A. In the case of we added a little stability to the division by adding a small number to the denominator:

We apply sign-bit technique into the recordings before we do the multidimensional autocorrelation to look at the results of the multidimensional autocorrelation without the effects of amplitudes.

Earth seismologists have used spectral whitening to increase the bandwidth and flatten the spectrum of the cross-correlations. Additionally, this may reduce the effect of the noise-source spectra. We try to apply the spectral whitening method to the solar data together for multidimensional autocorrelation. We include spectral-whitening directly into the equation for multidimensional autocorrelation:

The denominator is the spectrum computed over time only, averaged over space: