Azimuthal Anisotropy Workflow (BANX)

SeisGo implements the BANX method (Beamforming Azimuthal ANisotropy using noise Cross-correlations) for measuring crustal azimuthal anisotropy from ambient noise data.

Reference: Castellanos et al. (2020), Science Advances, 6(28). https://doi.org/10.1126/sciadv.abb0476

Conceptual overview

Station array (receiver cluster around reference site)
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  Load ZZ xcorr data from each source → receiver-cluster pair
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  SNR quality control + signal windowing
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  Slowness beamforming  (grid search in Ux, Uy space)
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  Extract best phase velocity + back-azimuth per source
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  Fit cos(2θ) anisotropy model → strength (RHO) + fast direction (THETA)

The method treats the dense receiver cluster as a mini-array, steers incoming plane waves across all back-azimuths, and recovers the azimuthal dependence of phase velocity.

Preparing input data

Station dictionary

# Keys are station names; values are [lat, lon]
stationdict = {
    "TA.A25A": [45.12, -120.34],
    "TA.A26A": [45.20, -120.15],
    "TA.B25A": [45.55, -120.40],
    # ... all network stations
}

Cross-correlation data layout

do_BANX expects ASDF files (.h5) named source_receiver*.h5 inside datadir. Each file must contain stacked or raw cross-correlations accessible via noise.extract_corrdata().

Running BANX

from seisgo import anisotropy

beam_results, ani_params = anisotropy.do_BANX(
    stationdict_all=stationdict,
    reference_site="TA.A25A",      # the receiver cluster center
    period_band=[10, 20],          # analysis period band (s)
    reference_velocity=3.2,        # reference phase velocity (km/s)
    datadir="./xcorr_output",
    outdir_root="./banx_results",
    sampling_rate=10,              # target sampling rate (sps)
    min_stations=10,
    min_snr=5,
    cc_comp="ZZ",
    doublesided=True,
    show_fig=False,
    plot_moveout=True,
    plot_beampower=True,
    plot_station_result=True,
    map_engine="cartopy",          # or "gmt"
    verbose=False,
)

Return values

beam_results — pandas.DataFrame with one row per source, columns:

Column	Description
`lat`, `lon`	Cluster centre coordinates
`velocity`	Best-fit phase velocity (km/s)
`baz`	Back-azimuth from cluster to source (°)
`sharpness`	Beam sharpness (max/median power ratio)
`power`	Peak beam power
`radius`	Receiver cluster radius (km)
`num`	Number of traces used

ani_params — pandas.DataFrame (one row) with anisotropy parameters:

Column	Description
`A0`	Isotropic velocity (km/s)
`A1`, `A2`	Anisotropy coefficients
`RHO`	Anisotropy magnitude (%)
`THETA`	Fast-axis direction (° from N)
`lat`, `lon`	Effective measurement location

Geometric helper functions

from seisgo import anisotropy

# Array aperture and centre
radius, center = anisotropy.get_ArrayAttributes(lat_array, lon_array)

# Include UTM coordinates
radius, center, utm_info = anisotropy.get_ArrayAttributes(
    lat_array, lon_array, get_utm=True
)

Anisotropy model

The azimuthal velocity variation is modelled as:

$$v(\theta) = A_0 + A_1 \cos(2\theta) + A_2 \sin(2\theta)$$

from seisgo import anisotropy
import numpy as np

azimuths = np.linspace(0, 360, 180)
v_model  = anisotropy.compute_anisotropy(azimuths, a=3.2, b=0.05, c=0.03)

Key parameters

Parameter	Default	Effect
`min_stations`	10	Minimum receivers in cluster
`min_snr`	5	SNR threshold for trace inclusion
`velocity_perturbation`	0.4	±40% search around reference velocity
`max_slowness`	0.5 s/km	Beamforming grid half-width
`slowness_step`	0.005 s/km	Beamforming grid resolution
`azimuth_step`	6°	Back-azimuth bin width for QC
`min_good_bazbin`	5	Min. bins with ≥`min_baz_measurements` sources
`min_beam_sharpness`	0	Sharpness QC threshold (0 = disabled)

Output files

All output is written under outdir_root/<period_min>_<period_max>/:

<reference_site>_beam.csv — filtered beam results for the reference site
<reference_site>_anisotropy.csv — fitted anisotropy parameters
figures/<reference_site>/ — moveout, beam power, station maps, result plots (PDF)