Cross-spatial correlation model

Inter-IM and intra-IM spatial correlation models for several IMs (PGA, PGV, Sa(T) at periods between 0.01–5.0 s, Saavg2(T), Saavg3(T), and FIV3(T) at periods between 0.1–2.0, 0.1-3.0, and 0.1-4.0s, respectively), using principal component analysis (PCA) and geostatistical tools. Additional figures, beyond those presented in the paper, are provided in the folder Data_Resources.

Reference

Monteiro, V.A, Aristeidou, S. and O’Reilly, G.J. (2026) ‘Spatial cross-correlation models for next-generation amplitude and cumulative intensity measures’, Earthquake Spectra, https://doi.org/10.1002/esp4.70076

How to use

Use the pairwise model to calculate spatial correlation. See pairwise_model_example.py:

"""
---------------  MAO2026 function  ---------------
Arguments:
    IM1 (float): First intensity measure.
    IM2 (float): Second intensity measure.
    h (float): 
    cluster (int, optional): Clustering flag. Defaults to 0.
        - 0 → use "non_cluster" database (ignores vs30).
        - 1 → use "cluster" database (requires vs30).
    vs30 (int, optional): Site condition index. Used only if cluster=1.
        - 1 → low Vs30 (soft soil).
        - 2 → high Vs30 (stiff soil).
        If cluster=0, this is ignored.
Returns:
    corr (float): Correlation value retrieved from the chosen database,
                    for the given IM1, IM2, and distance h.
                    
IMs available are 'Sa', 'Saavg2', 'Saavg3', 'FIV3', 'PGA', and 'PGV'.
For Sa the range of periods is [0.01, 5.0]s
For Saavg2 the range of periods is [0.1, 3.0]s
For Saavg3 the range of periods is [0.1, 2.0]s
For FIV3 the range of periods is [0.1, 4.0]s
"""

from GetSpatialCorrelation import MAO2026

# Example
IM1 = "FIV3(1.5)"
IM2 = "Sa(0.1)"
h_distance = 20 #km
corr = MAO2026(IM1, IM2, h_distance, cluster=1, vs30=2)

print(f'Spatial Correlation between {IM1} and {IM2} at {h_distance} km is: {corr:.4f}')

Use the global model to calculate spatial correlation. See global_model_example.py:

"""
---------------  MAO2026 function  ---------------

Arguments:
    IM1 (float): First intensity measure (e.g., ground motion parameter).
    IM2 (float): Second intensity measure.
    h (float): Depth or scaling parameter.
Returns:
    corr (float): Correlation value retrieved for the given IM1, IM2, and distance h.
                    
                    
IMs available are 'Sa', 'Saavg2', 'Saavg3', 'FIV3', 'PGA', and 'PGV'.
For Sa, Saavg2, Saavg3 and FIV3 the range of periods is [0.1, 3.0]s
"""


from GlobalModelMAO26 import GlobalMAO26

# Example
IM1 = "FIV3(0.6)"
IM2 = "Saavg2(1.0)"
import numpy as np
h_distance = np.linspace(0,150,151) #km
for h in h_distance:
    corr = GlobalMAO26(IM1, IM2, h, npcs=3)
    print(corr)

print(f'Spatial Correlation between {IM1} and {IM2} at {h_distance} km is: {corr:.4f}')