Ambient Noise Cross-Correlation¶

Seismologists traditionally rely on earthquakes as seismic sources to image Earth's interior. But what if there are no earthquakes in the region you want to study? Ambient noise cross-correlation solves this problem by extracting useful signals from the continuous background vibrations of the Earth — generated by ocean waves, wind, human activity, and other sources.

The key idea: if we cross-correlate long records of ambient noise between two seismic stations, the result approximates the Green's function — the signal we would observe at one station if the other were a source. In practice, this recovered signal is dominated by surface waves traveling between the two stations.

In this notebook, you will:

1. Find seismic stations in a region and compute inter-station distances
2. Download continuous ambient noise recordings
3. Compute cross-correlation functions (CCFs) between station pairs
4. Observe how surface waves emerge from noise cross-correlation
5. See how CCFs vary with distance and recording time

In [1]:

!pip install obspy cartopy -q

!pip install obspy cartopy -q

In [2]:

import numpy as np
import matplotlib.pyplot as plt
import cartopy.crs as ccrs
import cartopy.feature as cfeature
from obspy import UTCDateTime
from obspy.clients.fdsn import Client
from obspy.signal.cross_correlation import correlate
from obspy.geodetics import locations2degrees, degrees2kilometers

import numpy as np import matplotlib.pyplot as plt import cartopy.crs as ccrs import cartopy.feature as cfeature from obspy import UTCDateTime from obspy.clients.fdsn import Client from obspy.signal.cross_correlation import correlate from obspy.geodetics import locations2degrees, degrees2kilometers

1. Find Stations in a Region¶

We use Taiwan for this demonstration — it has a dense broadband seismic network with stations spaced ~20–300 km apart, ideal for ambient noise analysis. Its location between the Philippine Sea and Eurasian plates also means strong ocean-generated noise from multiple directions.

We query the FDSN web service for stations with broadband (BH) channels, which record in the frequency range where ambient noise is strongest (~0.05–1 Hz).

In [3]:

# Connect to FDSN data center
client = Client("IRIS")

# Query broadband stations in Taiwan
inventory = client.get_stations(
    minlatitude=22.1, maxlatitude=26.0,
    minlongitude=119.6, maxlongitude=121.8,
    starttime=UTCDateTime("2020-01-01"),
    endtime=UTCDateTime("2020-01-02"),
    channel="BH*",
    level="station",
)

# Store station names and coordinates
stations = {}
for network in inventory:
    for station in network:
        name = f"{network.code}.{station.code}"
        stations[name] = (station.latitude, station.longitude)

print(f"Found {len(stations)} stations:")
for name, (lat, lon) in stations.items():
    print(f"  {name}  ({lat:.2f}\u00b0N, {lon:.2f}\u00b0E)")

# Connect to FDSN data center client = Client("IRIS") # Query broadband stations in Taiwan inventory = client.get_stations( minlatitude=22.1, maxlatitude=26.0, minlongitude=119.6, maxlongitude=121.8, starttime=UTCDateTime("2020-01-01"), endtime=UTCDateTime("2020-01-02"), channel="BH*", level="station", ) # Store station names and coordinates stations = {} for network in inventory: for station in network: name = f"{network.code}.{station.code}" stations[name] = (station.latitude, station.longitude) print(f"Found {len(stations)} stations:") for name, (lat, lon) in stations.items(): print(f" {name} ({lat:.2f}\u00b0N, {lon:.2f}\u00b0E)")

Found 13 stations:
  IU.TATO  (24.97°N, 121.50°E)
  TW.CHGB  (24.06°N, 121.17°E)
  TW.HGSD  (23.49°N, 121.42°E)
  TW.NACB  (24.17°N, 121.59°E)
  TW.RLNB  (23.89°N, 120.36°E)
  TW.SSLB  (23.79°N, 120.95°E)
  TW.TATO  (24.98°N, 121.49°E)
  TW.TDCB  (24.25°N, 121.16°E)
  TW.TPUB  (23.30°N, 120.63°E)
  TW.TWGB  (22.82°N, 121.08°E)
  TW.WFSB  (25.07°N, 121.78°E)
  TW.YHNB  (24.67°N, 121.38°E)
  TW.YULB  (23.39°N, 121.30°E)

In [4]:

fig = plt.figure(figsize=(6, 8))
ax = fig.add_subplot(1, 1, 1, projection=ccrs.PlateCarree())
ax.set_extent([119.5, 122.5, 21.5, 26.0], crs=ccrs.PlateCarree())

# Add map features
ax.add_feature(cfeature.LAND, facecolor='lightgray')
ax.add_feature(cfeature.OCEAN, facecolor='lightskyblue', alpha=0.3)
ax.add_feature(cfeature.COASTLINE, linewidth=0.8)
ax.gridlines(draw_labels=True, alpha=0.3)

# Plot stations
for name, (lat, lon) in stations.items():
    ax.plot(lon, lat, '^', color='steelblue', markersize=10,
            markeredgecolor='k', transform=ccrs.PlateCarree())
    ax.text(lon + 0.08, lat, name.split('.')[1], fontsize=7,
            transform=ccrs.PlateCarree())

ax.set_title('Broadband Stations in Taiwan')
plt.tight_layout()
plt.show()

fig = plt.figure(figsize=(6, 8)) ax = fig.add_subplot(1, 1, 1, projection=ccrs.PlateCarree()) ax.set_extent([119.5, 122.5, 21.5, 26.0], crs=ccrs.PlateCarree()) # Add map features ax.add_feature(cfeature.LAND, facecolor='lightgray') ax.add_feature(cfeature.OCEAN, facecolor='lightskyblue', alpha=0.3) ax.add_feature(cfeature.COASTLINE, linewidth=0.8) ax.gridlines(draw_labels=True, alpha=0.3) # Plot stations for name, (lat, lon) in stations.items(): ax.plot(lon, lat, '^', color='steelblue', markersize=10, markeredgecolor='k', transform=ccrs.PlateCarree()) ax.text(lon + 0.08, lat, name.split('.')[1], fontsize=7, transform=ccrs.PlateCarree()) ax.set_title('Broadband Stations in Taiwan') plt.tight_layout() plt.show()

2. Station Pair Distances¶

The inter-station distance determines where the surface wave signal appears in the cross-correlation function:

$$\tau_{\text{arrival}} = \frac{D}{c}$$

• $D$: inter-station distance
• $c$: surface wave speed (~2–4 km/s)
• $\tau_{\text{arrival}}$: expected lag time in the CCF

Let's compute all pairwise distances and pick station pairs for the next steps.

In [5]:

# Compute distances for the station pairs we will use later
pairs = [
    ("TW.NACB", "TW.YHNB"),
    ("TW.SSLB", "TW.TPUB"),
    ("TW.TPUB", "TW.YULB"),
    ("TW.NACB", "TW.SSLB"),
    ("TW.NACB", "TW.YULB"),
    ("TW.SSLB", "TW.YHNB"),
    ("TW.SSLB", "TW.TWGB"),
    ("TW.NACB", "TW.TPUB"),
]

for s1, s2 in pairs:
    lat1, lon1 = stations[s1]
    lat2, lon2 = stations[s2]
    dist = degrees2kilometers(locations2degrees(lat1, lon1, lat2, lon2))
    print(f"  {s1} — {s2}: {dist:6.1f} km")

# Compute distances for the station pairs we will use later pairs = [ ("TW.NACB", "TW.YHNB"), ("TW.SSLB", "TW.TPUB"), ("TW.TPUB", "TW.YULB"), ("TW.NACB", "TW.SSLB"), ("TW.NACB", "TW.YULB"), ("TW.SSLB", "TW.YHNB"), ("TW.SSLB", "TW.TWGB"), ("TW.NACB", "TW.TPUB"), ] for s1, s2 in pairs: lat1, lon1 = stations[s1] lat2, lon2 = stations[s2] dist = degrees2kilometers(locations2degrees(lat1, lon1, lat2, lon2)) print(f" {s1} — {s2}: {dist:6.1f} km")

  TW.NACB — TW.YHNB:   59.4 km
  TW.SSLB — TW.TPUB:   63.5 km
  TW.TPUB — TW.YULB:   68.9 km
  TW.NACB — TW.SSLB:   78.0 km
  TW.NACB — TW.YULB:   92.0 km
  TW.SSLB — TW.YHNB:  107.0 km
  TW.SSLB — TW.TWGB:  108.6 km
  TW.NACB — TW.TPUB:  138.1 km

3. Download Ambient Noise for a Station Pair¶

Let's pick two stations and download one day of vertical-component (BHZ) data. We'll use this to demonstrate cross-correlation step by step.

Try changing the channel component (BHE, BHN instead of BHZ) — how do the results differ?

In [6]:

# Pick a station pair
sta1, sta2 = "TW.NACB", "TW.YHNB"

# Download one day of vertical-component data
starttime = UTCDateTime("2020-01-01")
endtime = UTCDateTime("2020-01-02")

net1, name1 = sta1.split(".")
net2, name2 = sta2.split(".")
st1 = client.get_waveforms(net1, name1, "", "BHZ", starttime, endtime)
st2 = client.get_waveforms(net2, name2, "", "BHZ", starttime, endtime)

print(f"Station 1: {st1[0]}")
print(f"Station 2: {st2[0]}")

# Pick a station pair sta1, sta2 = "TW.NACB", "TW.YHNB" # Download one day of vertical-component data starttime = UTCDateTime("2020-01-01") endtime = UTCDateTime("2020-01-02") net1, name1 = sta1.split(".") net2, name2 = sta2.split(".") st1 = client.get_waveforms(net1, name1, "", "BHZ", starttime, endtime) st2 = client.get_waveforms(net2, name2, "", "BHZ", starttime, endtime) print(f"Station 1: {st1[0]}") print(f"Station 2: {st2[0]}")

Station 1: TW.NACB..BHZ | 2020-01-01T00:00:00.019500Z - 2020-01-01T23:59:59.977740Z | 20.0 Hz, 1728000 samples
Station 2: TW.YHNB..BHZ | 2020-01-01T00:00:00.019500Z - 2020-01-01T23:59:59.985979Z | 20.0 Hz, 1728000 samples

At first glance, the recordings at both stations look like random noise. There's no obvious earthquake signal — just continuous background vibrations. Can we extract anything useful from this?

In [7]:

# Plot 24 hours of raw ambient noise
sr = st1[0].stats.sampling_rate
time1 = np.arange(st1[0].stats.npts) / sr / 3600  # convert to hours
time2 = np.arange(st2[0].stats.npts) / sr / 3600

plt.figure(figsize=(12, 5))
plt.plot(time1, st1[0].data, label=sta1, alpha=0.6)
plt.plot(time2, st2[0].data, label=sta2, alpha=0.6)
plt.xlabel('Time (hours)')
plt.ylabel('Amplitude (counts)')
plt.title('Raw Ambient Noise \u2014 1 Day of Recording')
plt.legend()
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()

# Plot 24 hours of raw ambient noise sr = st1[0].stats.sampling_rate time1 = np.arange(st1[0].stats.npts) / sr / 3600 # convert to hours time2 = np.arange(st2[0].stats.npts) / sr / 3600 plt.figure(figsize=(12, 5)) plt.plot(time1, st1[0].data, label=sta1, alpha=0.6) plt.plot(time2, st2[0].data, label=sta2, alpha=0.6) plt.xlabel('Time (hours)') plt.ylabel('Amplitude (counts)') plt.title('Raw Ambient Noise \u2014 1 Day of Recording') plt.legend() plt.grid(True, alpha=0.3) plt.tight_layout() plt.show()

4. Cross-Correlation¶

What is cross-correlation? It measures the similarity between two signals as a function of a time shift (lag):

$$C_{AB}(\tau) = \int u_A(t) \, u_B(t + \tau) \, dt$$

Why does this work for ambient noise? Imagine ocean waves generating seismic noise from all directions. Some noise travels from station A to station B with a time delay $\tau = D/c$. When we cross-correlate long records, these coherent arrivals add up while random noise cancels out. The result looks like a surface wave traveling between the stations.

Interpreting the CCF:

• Positive lag ($\tau > 0$): waves traveling from station 1 $\to$ station 2
• Negative lag ($\tau < 0$): waves traveling from station 2 $\to$ station 1
• If noise sources are evenly distributed, the CCF is roughly symmetric
• If noise comes mainly from one direction, one side is stronger

Let's preprocess the data and compute the cross-correlation step by step.

In [8]:

# Copy traces so we can re-use the originals later
tr1 = st1[0].copy()
tr2 = st2[0].copy()

# Preprocessing
for tr in [tr1, tr2]:
    tr.detrend("demean")   # remove DC offset so signal centers on zero
    tr.detrend("linear")   # remove slow instrumental drift
    tr.taper(0.05)          # smooth edges to zero to prevent spectral artifacts

# Trim to common time window
t_start = max(tr1.stats.starttime, tr2.stats.starttime)
t_end = min(tr1.stats.endtime, tr2.stats.endtime)
tr1.trim(t_start, t_end)
tr2.trim(t_start, t_end)

# Cross-correlate (max lag = 300 seconds)
max_lag = 300
shift = int(tr1.stats.sampling_rate * max_lag)
ccf = correlate(tr1.data, tr2.data, shift=shift, normalize='naive')  # normalize by signal energy
lags = np.arange(-shift, shift + 1) / tr1.stats.sampling_rate

# Inter-station distance
lat1, lon1 = stations[sta1]
lat2, lon2 = stations[sta2]
dist_km = degrees2kilometers(locations2degrees(lat1, lon1, lat2, lon2))

# Plot
plt.figure(figsize=(10, 4))
plt.plot(lags, ccf, 'k', lw=0.8)

# Mark expected surface wave arrival (~3 km/s)
t_arrival = dist_km / 3.0
plt.axvline(t_arrival, color='r', ls='--', alpha=0.7,
            label=f'\u00b1{t_arrival:.1f} s (3 km/s)')
plt.axvline(-t_arrival, color='r', ls='--', alpha=0.7)

plt.title(f'Cross-Correlation: {sta1} \u2013 {sta2} ({dist_km:.0f} km)')
plt.xlabel('Lag time (seconds)')
plt.ylabel('Correlation coefficient')
plt.xlim(-100, 100)
plt.legend()
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()

# Copy traces so we can re-use the originals later tr1 = st1[0].copy() tr2 = st2[0].copy() # Preprocessing for tr in [tr1, tr2]: tr.detrend("demean") # remove DC offset so signal centers on zero tr.detrend("linear") # remove slow instrumental drift tr.taper(0.05) # smooth edges to zero to prevent spectral artifacts # Trim to common time window t_start = max(tr1.stats.starttime, tr2.stats.starttime) t_end = min(tr1.stats.endtime, tr2.stats.endtime) tr1.trim(t_start, t_end) tr2.trim(t_start, t_end) # Cross-correlate (max lag = 300 seconds) max_lag = 300 shift = int(tr1.stats.sampling_rate * max_lag) ccf = correlate(tr1.data, tr2.data, shift=shift, normalize='naive') # normalize by signal energy lags = np.arange(-shift, shift + 1) / tr1.stats.sampling_rate # Inter-station distance lat1, lon1 = stations[sta1] lat2, lon2 = stations[sta2] dist_km = degrees2kilometers(locations2degrees(lat1, lon1, lat2, lon2)) # Plot plt.figure(figsize=(10, 4)) plt.plot(lags, ccf, 'k', lw=0.8) # Mark expected surface wave arrival (~3 km/s) t_arrival = dist_km / 3.0 plt.axvline(t_arrival, color='r', ls='--', alpha=0.7, label=f'\u00b1{t_arrival:.1f} s (3 km/s)') plt.axvline(-t_arrival, color='r', ls='--', alpha=0.7) plt.title(f'Cross-Correlation: {sta1} \u2013 {sta2} ({dist_km:.0f} km)') plt.xlabel('Lag time (seconds)') plt.ylabel('Correlation coefficient') plt.xlim(-100, 100) plt.legend() plt.grid(True, alpha=0.3) plt.tight_layout() plt.show()

5. Cross-Correlations at Different Distances¶

Now let's compute CCFs for multiple station pairs at different distances. If the signal in the CCF is a real surface wave, its arrival time should scale linearly with distance: $\tau = D/c$.

We'll plot the CCFs stacked by distance, with reference moveout lines.

Some pairs may show stronger signal on one side — what does that tell you about the noise source direction? Taiwan faces the Pacific Ocean to the east, so ocean-generated microseism noise arrives preferentially from that direction, which can make the CCF asymmetric.

In [9]:

def download_and_correlate(sta1, sta2, starttime, endtime, max_lag=300):
    """Download noise for two stations, preprocess, and cross-correlate."""
    net1, name1 = sta1.split(".")
    net2, name2 = sta2.split(".")

    st1 = client.get_waveforms(net1, name1, "", "BHZ", starttime, endtime)
    st2 = client.get_waveforms(net2, name2, "", "BHZ", starttime, endtime)

    tr1 = st1[0].copy()
    tr2 = st2[0].copy()

    for tr in [tr1, tr2]:
        tr.detrend("demean")
        tr.detrend("linear")
        tr.taper(0.05)

    # Resample if sampling rates differ
    if tr1.stats.sampling_rate != tr2.stats.sampling_rate:
        tr2.resample(tr1.stats.sampling_rate)

    # Trim to common time window
    t1 = max(tr1.stats.starttime, tr2.stats.starttime)
    t2 = min(tr1.stats.endtime, tr2.stats.endtime)
    tr1.trim(t1, t2)
    tr2.trim(t1, t2)

    # Cross-correlate
    shift = int(tr1.stats.sampling_rate * max_lag)
    ccf = correlate(tr1.data, tr2.data, shift=shift, normalize='naive')
    lags = np.arange(-shift, shift + 1) / tr1.stats.sampling_rate

    # Distance
    lat1, lon1 = stations[sta1]
    lat2, lon2 = stations[sta2]
    dist = degrees2kilometers(locations2degrees(lat1, lon1, lat2, lon2))

    return lags, ccf, dist

def download_and_correlate(sta1, sta2, starttime, endtime, max_lag=300): """Download noise for two stations, preprocess, and cross-correlate.""" net1, name1 = sta1.split(".") net2, name2 = sta2.split(".") st1 = client.get_waveforms(net1, name1, "", "BHZ", starttime, endtime) st2 = client.get_waveforms(net2, name2, "", "BHZ", starttime, endtime) tr1 = st1[0].copy() tr2 = st2[0].copy() for tr in [tr1, tr2]: tr.detrend("demean") tr.detrend("linear") tr.taper(0.05) # Resample if sampling rates differ if tr1.stats.sampling_rate != tr2.stats.sampling_rate: tr2.resample(tr1.stats.sampling_rate) # Trim to common time window t1 = max(tr1.stats.starttime, tr2.stats.starttime) t2 = min(tr1.stats.endtime, tr2.stats.endtime) tr1.trim(t1, t2) tr2.trim(t1, t2) # Cross-correlate shift = int(tr1.stats.sampling_rate * max_lag) ccf = correlate(tr1.data, tr2.data, shift=shift, normalize='naive') lags = np.arange(-shift, shift + 1) / tr1.stats.sampling_rate # Distance lat1, lon1 = stations[sta1] lat2, lon2 = stations[sta2] dist = degrees2kilometers(locations2degrees(lat1, lon1, lat2, lon2)) return lags, ccf, dist

In [10]:

# Station pairs at various distances
pairs = [
    ("TW.NACB", "TW.YHNB"),
    ("TW.SSLB", "TW.TPUB"),
    ("TW.TPUB", "TW.YULB"),
    ("TW.NACB", "TW.SSLB"),
    ("TW.NACB", "TW.YULB"),
    ("TW.SSLB", "TW.YHNB"),
    ("TW.SSLB", "TW.TWGB"),
    ("TW.NACB", "TW.TPUB"),
]

starttime = UTCDateTime("2020-01-01")
endtime = UTCDateTime("2020-01-02")

plt.figure(figsize=(10, 7))
for s1, s2 in pairs:
    lags, ccf, dist = download_and_correlate(s1, s2, starttime, endtime)
    n1, n2 = s1.split(".")[1], s2.split(".")[1]
    plt.plot(lags, ccf * 3 * dist + dist, label=f"{n1}–{n2}")

# Reference moveout lines for surface wave speeds
t = np.linspace(-100, 100, 500)
plt.plot(t, np.abs(3.0 * t), 'k--', lw=1, label='3.0 km/s')
plt.plot(t, np.abs(2.0 * t), 'k-', lw=1, label='2.0 km/s')

plt.title('Cross-Correlation Functions vs. Distance')
plt.xlabel('Lag time (seconds)')
plt.ylabel('Distance (km)')
plt.text(-95, 5, r'$\leftarrow$ Sta 2 to Sta 1', fontsize=9, ha='left')
plt.text(95, 5, r'Sta 1 to Sta 2 $\rightarrow$', fontsize=9, ha='right')
plt.xlim(-100, 100)
plt.ylim(0, 160)
plt.grid(True, alpha=0.3)
plt.legend(loc='lower right', ncol=2, fontsize=8)
plt.tight_layout()
plt.show()

# Station pairs at various distances pairs = [ ("TW.NACB", "TW.YHNB"), ("TW.SSLB", "TW.TPUB"), ("TW.TPUB", "TW.YULB"), ("TW.NACB", "TW.SSLB"), ("TW.NACB", "TW.YULB"), ("TW.SSLB", "TW.YHNB"), ("TW.SSLB", "TW.TWGB"), ("TW.NACB", "TW.TPUB"), ] starttime = UTCDateTime("2020-01-01") endtime = UTCDateTime("2020-01-02") plt.figure(figsize=(10, 7)) for s1, s2 in pairs: lags, ccf, dist = download_and_correlate(s1, s2, starttime, endtime) n1, n2 = s1.split(".")[1], s2.split(".")[1] plt.plot(lags, ccf * 3 * dist + dist, label=f"{n1}–{n2}") # Reference moveout lines for surface wave speeds t = np.linspace(-100, 100, 500) plt.plot(t, np.abs(3.0 * t), 'k--', lw=1, label='3.0 km/s') plt.plot(t, np.abs(2.0 * t), 'k-', lw=1, label='2.0 km/s') plt.title('Cross-Correlation Functions vs. Distance') plt.xlabel('Lag time (seconds)') plt.ylabel('Distance (km)') plt.text(-95, 5, r'$\leftarrow$ Sta 2 to Sta 1', fontsize=9, ha='left') plt.text(95, 5, r'Sta 1 to Sta 2 $\rightarrow$', fontsize=9, ha='right') plt.xlim(-100, 100) plt.ylim(0, 160) plt.grid(True, alpha=0.3) plt.legend(loc='lower right', ncol=2, fontsize=8) plt.tight_layout() plt.show()

6. How CCFs Change with Time¶

Let's split the day into overlapping 3-hour windows and compute a CCF for each one. Individual windows are noisy, but the surface wave signal is visible in most of them. Stacking many windows would improve the signal — this is why ambient noise studies typically use weeks to months of data. (One day is enough for a demo, but published studies often stack 6–12 months for high-quality measurements.)

What do you think drives the differences between windows? Try changing the window length — how does that affect the results?

In [11]:

sta1, sta2 = "TW.NACB", "TW.YHNB"
starttime = UTCDateTime("2020-01-01")
window_length = 10800  # 3 hours (seconds)
n_windows = 10

plt.figure(figsize=(8, 10))
for i in range(n_windows):
    t1 = starttime + i * window_length // 4  # 75% overlap
    t2 = t1 + window_length

    lags, ccf, dist = download_and_correlate(sta1, sta2, t1, t2)
    plt.plot(lags, ccf * 10 + i, label=t1.strftime("%H:%M"))

plt.title(f'CCF Time Evolution: {sta1} \u2013 {sta2}')
plt.xlabel('Lag time (seconds)')
plt.ylabel('Time window')
plt.xlim(-100, 100)
plt.grid(True, alpha=0.3)
plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left', fontsize=8)
plt.tight_layout()
plt.show()

sta1, sta2 = "TW.NACB", "TW.YHNB" starttime = UTCDateTime("2020-01-01") window_length = 10800 # 3 hours (seconds) n_windows = 10 plt.figure(figsize=(8, 10)) for i in range(n_windows): t1 = starttime + i * window_length // 4 # 75% overlap t2 = t1 + window_length lags, ccf, dist = download_and_correlate(sta1, sta2, t1, t2) plt.plot(lags, ccf * 10 + i, label=t1.strftime("%H:%M")) plt.title(f'CCF Time Evolution: {sta1} \u2013 {sta2}') plt.xlabel('Lag time (seconds)') plt.ylabel('Time window') plt.xlim(-100, 100) plt.grid(True, alpha=0.3) plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left', fontsize=8) plt.tight_layout() plt.show()

---

Summary¶

Key takeaways:

1. Ambient noise is not random — it contains coherent surface waves generated by ocean waves, wind, and human activity.

2. Cross-correlation recovers surface waves — by cross-correlating noise between two stations, we extract the surface wave Green's function, as if one station were a seismic source.

3. Arrival time scales with distance — the signal arrives at lag time $\tau \approx D/c$, where $D$ is the inter-station distance and $c \approx 2$–$4$ km/s for surface waves.

4. Longer stacking improves signal — individual short-window CCFs are noisy, but stacking over days to months produces clear, stable signals.

5. Asymmetry reveals noise source direction — if noise comes mainly from one direction, the CCF is stronger on one side (causal vs. acausal).

Connection to other topics: The surface wave travel times from ambient noise CCFs can be used for seismic tomography — mapping the velocity structure of the crust and upper mantle without needing earthquakes.