DOI: 10.25592/uhhfdm.18151
title: Large-N cross-correlation functions of ambient seismic noise recorded in the Vienna basin, Austria.

description: This repository contains the C<sub>1 </sub>cross-correlation functions of the ambient seismic field and station metadata required to reproduce the results described in the manuscript "Source effects in higher-order ambient seismic field correlations" by Schippkus et al., 2025.

We provide a complete set of Jupyter notebooks that implements all processing described in the manuscript for full reproducibility. They make use of the data provided in this repository. The notebooks are hosted on GitHub at https://github.com/schipp/higher_order_correlations_c2.

The files hosted here are:


 <strong>stations_receivers.csv</strong>: List of 1990 stations used as receiver stations. Station OMV.GDT is used as the master station in the manuscript. Station names are arbitrary.
 <strong>stations_auxiliary.csv</strong>: List of 304 stations used as auxiliary stations.
 <strong>correlations_for_c1_data.pt</strong>: C<sub>1</sub> cross-correlations of all 1990 receiver stations with the master station OMV.GDT in the center. Saved as a PyTorch torch.tensor with shape [1990, 3001]. Sampling rate is 5 Hz, correlation functions are limited to 300 seconds of anti-causal and causal lapse time (=&gt; 3001 samples). First dimension (the receiver stations) is sorted alphabetically by station name.
 <strong>correlations_for_c2_data.pt</strong>: C<sub>1</sub> cross-correlations of all 1990 receiver stations with the 304 auxiliary stations surrounding them. Saved as a PyTorch torch.tensor with shape [1990, 304, 3001]. Sampling rate is 5 Hz, correlation functions are limited to 300 seconds of anti-causal and causal lapse time (=&gt; 3001 samples). First dimension (the receiver stations) and second dimension (the auxiliary stations) are sorted alphabetically by station name.


The cross-correlations are computed as described in the manuscript: ~4 weeks of continuous recordings are cut into 1-hr windows and spectrally whitened. All windows are cross-correlated and linearly stacked. No additional processing is applied. For more details on these data, please see the manuscript.

We provide a minimal Python code snippet to load the C<sub>1</sub> correlation functions with the master station ("OMV.GDT"), read station locations, filter the correlation functions with a narrowband-filter around 0.3 Hz, and plot the focal spot of the C<sub>1</sub> correlation wavefield in space:

<pre><code class="language-python">import torch
import polars as pl
import matplotlib.pyplot as plt
from scipy.signal import butter, filtfilt

# load correlation functions
sampling_rate = 5
lapse_times = torch.arange(-300, 300 + 1 / sampling_rate, 1 / sampling_rate)
corrs = torch.load("correlations_for_c1_data.pt", weights_only=False)

# load metadata
stations = pl.read_csv("stations_receivers.csv")
names = stations.select("station").to_series().to_list()
x, y = stations.select(["X", "Y"]).to_numpy().T
master_station = "OMV.GDT"

# apply acausal narrowband filter
frequency_band = (0.29, 0.31)
a, b = butter(4, frequency_band, btype="bandpass", fs=sampling_rate)
filtered_corrs = torch.tensor(filtfilt(a, b, corrs, axis=-1).copy())

# extract focal spot and set master station (=auto-correlation) to zero
focal_spot = filtered_corrs[:, torch.argmin(torch.abs(lapse_times))]
focal_spot[names.index(master_station)] = 0

# plot focal spot
fig, ax = plt.subplots()
ax.scatter(
 x,
 y,
 c=focal_spot,
 cmap="RdBu_r",
 vmin=-focal_spot.abs().max(),
 vmax=focal_spot.abs().max(),
)
ax.set(
 xlabel="Distance (km)",
 ylabel="Distance (km)",
 title="Focal spot",
 aspect="equal"
)</code></pre>

 
description: The authors thank OMV E&P GmbH for access to the seismic data and permission to publish the correlation functions. The authors acknowledge funding provided by the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 955515 (SPIN-ITN, https://spin-itn.eu). This research was partially funded by the Federal Ministry of Education and Research (BMBF) and the Free and Hanseatic City of Hamburg under the Excellence Strategy of the Federal Government and the Länder. This work was supported by the Research Council of Finland (Flagship of Advanced Mathematics for Sensing Imaging and Modeling grant 359182 and grant 322421).