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
method	str	"BGMM"	"BGMM" (Bayesian) or "GMM" (standard)

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	str	Phase type: "p" or "s" (lowercase)	"p"
prob	float	Pick probability/weight (0-1)	0.94
amp	float	Amplitude in m/s (required if use_amplitude=True)	0.000017

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)	float	Z coordinate (elevation, typically negative)	-0.67

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
use_amplitude	bool	Whether to use amplitude in clustering	True
bfgs_bounds	tuple	Bounds for BFGS optimization	((-35, 92), (-128, 78), (0, 21), (None, None))
oversample_factor	float	Factor for oversampling initial GMM components	5.0 for BGMM, 1.0 for GMM

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	int	500	Min cluster size for hierarchical splitting
dbscan_max_time_space_ratio	float	10	Max time/space ratio for splitting

• 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 | 5 |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	Time-amplitude covariance
gamma_score	float	Association quality score
num_picks	int	Total picks assigned
num_p_picks	int	P-phase picks assigned
num_s_picks	int	S-phase picks assigned
event_index	int	Unique event index
x(km)	float	X coordinate of hypocenter
y(km)	float	Y coordinate of hypocenter
z(km)	float	Z coordinate (depth)

assignments (list[tuple])

List of tuples (pick_index, event_index, gamma_score):

• pick_index: Index in the original picks DataFrame
• event_index: Associated event index
• gamma_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