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Computing cross-correlation and spectrogram of two seismic traces (codes included)

Utpal Kumar   2 minute read      

Read the seismic traces from the miniseed files and compute the cross-correlation and spectrogram

I want to compute the relation between two seismic traces using the cross-correlation. First I compute the spectrogram of each trace using the spectrogram method in Obspy. Then, I cross-correlate the two seismic traces and plot its time-domain cross-correlation function and spectrogram.

For details on how to compute cross-correlation, visit my previous post:

Compute and plot spectrogram of each traces

I have a mseed file all_stream_HLZ_20071215_080316.mseed that contains multiple traces. I used the first two traces for this study. For plotting the time series, I first read the data using the read function from Obspy and then plot the “data” and “times” methods avilable for the Trace object.

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from obspy import read
from obspy import read, Trace, UTCDateTime
import numpy as np
import pandas as pd
import noise
import matplotlib.pyplot as plt
plt.rcParams['figure.figsize'] = [10,6]
plt.rcParams.update({'font.size': 18})
plt.style.use('seaborn')

filenameZ = 'all_stream_HLZ_20071215_080316.mseed'
fignameTrace = 'spectrogram_layout1.png'
figxcorr = 'spectrogram_layout2.png'
figxcorr2 = 'spectrogram_layout3.png'
st = read(filenameZ)
tr1 = st[0]
tr2 = st[1]

sta1 = tr1.stats['station']

fig, axx = plt.subplots(2,2, sharex=True, sharey='row')
axx[0, 0].plot(tr1.times(), tr1.data, 'k-', linewidth=0.2, label=tr1.stats['station'])
axx[0, 1].plot(tr2.times(), tr2.data, 'k-', linewidth=0.2, label=tr2.stats['station'])
axx[0, 0].set_title(f'Trace 1')
axx[0, 1].set_title(f'Trace 2')
axx[0, 0].set_ylabel('Amplitude')

tr1.spectrogram(log=True, wlen=50,show=False, axes=axx[1, 0], cmap='jet', samp_rate=tr1.stats.sampling_rate)
tr2.spectrogram(log=True, wlen=50,show=False, axes=axx[1, 1], cmap='jet', samp_rate=tr2.stats.sampling_rate)
axx[1, 0].set_title('Spectrogram 1')
axx[1, 1].set_title('Spectrogram 2')
axx[1, 0].set_xlabel('time (s)')
axx[1, 1].set_xlabel('time (s)')
axx[1, 0].set_ylabel('Amplitude')
plt.tight_layout()

## put legend
for col in axx[0,:]:
    ll = col.legend(loc=1)
    plt.setp(ll.get_texts(), color='red') #color legend

plt.savefig(fignameTrace, bbox_inches='tight', dpi=300)
plt.close('all')
Plot of the seismic traces and their corresponding spectrograms
Plot of the seismic traces and their corresponding spectrograms

Compute the cross correlation using the Pandas library

For computing the cross-correlation, I use the crosscorr function. Readers can refer to this function in this post. The steps for computing the cross-correlation is also very similar as the previous post.

However, I obtained the spectrogram using the spectrogram method of Obspy. This method is well optimized for seismic data. There are several other spectrogram functions available in Python and most of them work in the same way. The obtained spectrogram for this post is using window length for fft of 50 seconds (wlen), and output the frequencies in logarithmic scale.

### Cross Correlation using Pandas
series1, series2 = pd.Series(tr1.data),  pd.Series(tr2.data)
window = 1
maxlag = 500
lags = np.arange(-(maxlag), (maxlag), window)  # contrained
rs = np.nan_to_num([crosscorr(series1, series2, lag) for lag in lags])

traceCCF2 = Trace()
traceCCF2.data = rs
traceCCF2.times(reftime=tr1.stats.starttime)

fig, axx = plt.subplots(2,1)
axx[0].plot(lags, rs, 'k', linewidth=0.5)
axx[0].set_title('Cross Correlation')

traceCCF2.spectrogram(log=True, wlen=50,show=False, axes=axx[1], cmap='jet')
axx[1].set_title('Spectrogram')
plt.tight_layout()
plt.savefig(figxcorr2, bbox_inches='tight', dpi=300)
plt.close('all')
Spectrogram plot of the time series
Spectrogram plot of the time series

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