Skillsbench gamma-phase-associator

An overview of the python package for running the GaMMA earthquake phase association algorithm. The algorithm expects phase picks data and station data as input and produces (through unsupervised clustering) earthquake events with source information like earthquake location, origin time and magnitude. The skill explains commonly used functions and the expected input/output format.

install

source · Clone the upstream repo

git clone https://github.com/benchflow-ai/skillsbench

Claude Code · Install into ~/.claude/skills/

T=$(mktemp -d) && git clone --depth=1 https://github.com/benchflow-ai/skillsbench "$T" && mkdir -p ~/.claude/skills && cp -r "$T/tasks/earthquake-phase-association/environment/skills/gamma-phase-associator" ~/.claude/skills/benchflow-ai-skillsbench-gamma-phase-associator && rm -rf "$T"

manifest: tasks/earthquake-phase-association/environment/skills/gamma-phase-associator/SKILL.md

source content

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 |

| Min P-phase picks per event | |

min_s_picks_per_eq

| int |

|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	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

Skillsbench gamma-phase-associator

GaMMA Associator Library

What is GaMMA?

Installing GaMMA

GaMMA core API

`association`

Function Signature

Purpose

1. Input Parameters

2. Required DataFrame Columns

`picks`
DataFrame

`stations`
DataFrame

3. Config Dictionary Keys

Required Keys

Velocity Model Keys

DBSCAN Pre-clustering Keys (Optional)

Filtering Keys (Optional)

Other Optional Keys

4. Return Values

`events`
(list[dict])

`assignments`
(list[tuple])

`estimate_eps`
Function Documentation

Function Signature

Purpose

1. Input Parameters

2. Required DataFrame Columns

`stations`
DataFrame

3. Return Value

4. Example Usage

Typical Usage Pattern

5. Practical Notes

6. Related Configuration