GaMMA Associator Library
What is GaMMA?
GaMMA is an earthquake phase association algorithm that treats association as an unsupervised clustering problem. It uses multivariate Gaussian distribution to model the collection of phase picks of an event, and uses Expectation-Maximization to carry out pick assignment and estimate source parameters i.e., earthquake location, origin time, and magnitude.
GaMMA is a python library implementing the algorithm. For the input earthquake traces, this library assumes P/S wave picks have already been extracted. We provide documentation of its core API.
Zhu, W., McBrearty, I. W., Mousavi, S. M., Ellsworth, W. L., & Beroza, G. C. (2022). Earthquake phase association using a Bayesian Gaussian mixture model. Journal of Geophysical Research: Solid Earth, 127(5).
The skill is a derivative of the repo https://github.com/AI4EPS/GaMMA
Installing GaMMA
pip install git+https://github.com/wayneweiqiang/GaMMA.git
GaMMA core API
association
Function Signature
def association(picks, stations, config, event_idx0=0, method="BGMM", **kwargs)
Purpose
Associates seismic phase picks (P and S waves) to earthquake events using Bayesian or standard Gaussian Mixture Models. It clusters picks based on arrival time and amplitude information, then fits GMMs to estimate earthquake locations, times, and magnitudes.
1. Input Parameters
| Parameter | Type | Default | Description |
|---|
picks | DataFrame | required | Seismic phase pick data |
stations | DataFrame | required | Station metadata with locations |
config | dict | required | Configuration parameters |
event_idx0 | int | 0 | Starting event index for numbering |
|
2. Required DataFrame Columns
picks DataFrame
| Column | Type | Description | Example |
|---|
id | str | Station identifier (must match stations) | network.station. or network.station.location.channel |
timestamp | datetime/str | Pick arrival time (ISO format or datetime) | "2019-07-04T22:00:06.084" |
type |
Notes:
- Timestamps must be in UTC or converted to UTC
- Phase types are forced to lowercase internally
- Picks with
amp == 0 or amp == -1 are filtered when use_amplitude=True
- The DataFrame index is used to track pick identities in the output
stations DataFrame
| Column | Type | Description | Example |
|---|
id | str | Station identifier | "CI.CCC..BH" |
x(km) | float | X coordinate in km (projected) | -35.6 |
y(km) | float | Y coordinate in km (projected) | 45.2 |
z(km) |
Notes:
- Coordinates should be in a projected local coordinate system (e.g., you can use the
pyproj package)
- The
id column must match the id values in the picks DataFrame (e.g., network.station. or network.station.location.channel)
- Group stations by unique
id, identical attribute are collapsed to a single value and conflicting metadata are preseved as a sorted list.
3. Config Dictionary Keys
Required Keys
| Key | Type | Description | Example |
|---|
dims | list[str] | Location dimensions to solve for | ["x(km)", "y(km)", "z(km)"] |
min_picks_per_eq | int | Minimum picks required per earthquake | 5 |
max_sigma11 | float | Maximum allowed time residual in seconds | 2.0 |
|
Notes on dims:
- Options:
["x(km)", "y(km)", "z(km)"], ["x(km)", "y(km)"], or ["x(km)"]
Notes on bfgs_bounds:
- Format:
((x_min, x_max), (y_min, y_max), (z_min, z_max), (None, None))
- The last tuple is for time (unbounded)
Velocity Model Keys
| Key | Type | Default | Description |
|---|
vel | dict | {"p": 6.0, "s": 3.47} | Uniform velocity model (km/s) |
eikonal | dict/None | None | 1D velocity model for travel times |
DBSCAN Pre-clustering Keys (Optional)
| Key | Type | Default | Description |
|---|
use_dbscan | bool | True | Enable DBSCAN pre-clustering |
dbscan_eps | float | 25 | Max time between picks (seconds) |
dbscan_min_samples | int | 3 | Min samples in DBSCAN neighborhood |
dbscan_min_cluster_size |
dbscan_eps is obtained from estimate_eps Function
Filtering Keys (Optional)
| Key | Type | Default | Description |
|-----|------|-------------|
| max_sigma22 | float | 1.0 | Max phase amplitude residual in log scale (required if use_amplitude=True) |
| max_sigma12 | float | 1.0 | Max covariance |
| max_sigma11 | float | 2.0 | Max phase time residual (s) |
| min_p_picks_per_eq | int | 0 | Min P-phase picks per event |
| min_s_picks_per_eq | int | 0 |Min S-phase picks per event |
| min_stations | int | |Min unique stations per event |
Other Optional Keys
| Key | Type | Default | Description |
|---|
covariance_prior | list[float] | auto | Prior for covariance [time, amp] |
ncpu | int | auto | Number of CPUs for parallel processing |
4. Return Values
Returns a tuple (events, assignments):
events (list[dict])
List of dictionaries, each representing an associated earthquake:
| Key | Type | Description |
|---|
time | str | Origin time (ISO 8601 with milliseconds) |
magnitude | float | Estimated magnitude (999 if use_amplitude=False) |
sigma_time | float | Time uncertainty (seconds) |
sigma_amp | float | Amplitude uncertainty (log10 scale) |
cov_time_amp | float |
assignments (list[tuple])
List of tuples (pick_index, event_index, gamma_score):
pick_index: Index in the original picks DataFrameevent_index: Associated event indexgamma_score: Probability/confidence of assignment
estimate_eps Function Documentation
Function Signature
def estimate_eps(stations, vp, sigma=2.0)
Purpose
Estimates an appropriate DBSCAN epsilon (eps) parameter for clustering seismic phase picks based on station spacing. The eps parameter controls the maximum time distance between picks that should be considered neighbors in the DBSCAN clustering algorithm.
1. Input Parameters
| Parameter | Type | Default | Description |
|---|
stations | DataFrame | required | Station metadata with 3D coordinates |
vp | float | required | P-wave velocity in km/s |
sigma | float | 2.0 | Number of standard deviations above the mean |
2. Required DataFrame Columns
stations DataFrame
| Column | Type | Description | Example |
|---|
x(km) | float | X coordinate in km | -35.6 |
y(km) | float | Y coordinate in km | 45.2 |
z(km) | float | Z coordinate in km | -0.67 |
3. Return Value
| Type | Description |
|---|
| float | Epsilon value in seconds for use with DBSCAN clustering |
4. Example Usage
from gamma.utils import estimate_eps
# Assuming stations DataFrame is already prepared with x(km), y(km), z(km) columns
vp = 6.0 # P-wave velocity in km/s
# Estimate eps automatically based on station spacing
eps = estimate_eps(stations, vp, sigma=2.0)
# Use in config
config = {
"use_dbscan": True,
"dbscan_eps": eps, # or use estimate_eps(stations, config["vel"]["p"])
"dbscan_min_samples": 3,
# ... other config options
}
Typical Usage Pattern
from gamma.utils import association, estimate_eps
# Automatic eps estimation
config["dbscan_eps"] = estimate_eps(stations, config["vel"]["p"])
# Or manual override (common in practice)
config["dbscan_eps"] = 15 # seconds
5. Practical Notes
- In example notebooks, the function is often commented out in favor of hardcoded values (10-15 seconds)
- Practitioners may prefer manual tuning for specific networks/regions
- Typical output values range from 10-20 seconds depending on station density
- Useful when optimal eps is unknown or when working with new networks
6. Related Configuration
The output is typically used with these config parameters:
config["dbscan_eps"] = estimate_eps(stations, config["vel"]["p"])
config["dbscan_min_samples"] = 3
config["dbscan_min_cluster_size"] = 500
config["dbscan_max_time_space_ratio"] = 10
