Scenarios

Windows come in 38 scenarios, so you can see where a method breaks. Each scenario answers three questions:

• Which earthquakes: at random, a sequence (aftershocks, foreshocks: close in space and time) or outside the network (large azimuthal gap).

• How many in a window: sparse 1–2, low 3–5, med 6–10, high 11–20.

• How much noise, in noise picks per real pick: none 0, low 0.1, med 0.3, high 1, extreme 3.

Which earthquakes	How many	Noise	Scenarios	Name, e.g.
Random: anywhere, any time	sparse, low, med, high	all 5 levels	4 × 5 = 20	ev-med__noise-high
Sequence: aftershocks, foreshocks	low, med, high	all 5 levels	3 × 5 = 15	seq-med__noise-high
Outside the network: gap 0–90°, 90–180°, 180–270°	low	med	3	gap-090-180
			38

Every scenario has the same number of windows: 600 train, 120 val and 60 test per network. The three answers are columns of the windows table (selection, n_events_level, noise_level), so you can choose windows without reading names:

import bepad

rel = bepad.open(bepad.download(splits=()))          # small files only
w = rel.table("test", "windows", networks=["tx"])
seq = w[(w.selection == "sequence") & (w.noise_level == "none")]
test = bepad.load("test", window_ids=list(seq.window_id[:20]))

Random earthquakes

The earthquakes of a window are drawn at random from one network, within a year of each other (so the same stations existed), and placed at random times in the window.

Local network (Texas). Left to right: more earthquakes at once. Top to bottom: more noise. Each panel shows its window_id (bottom right): load it again with bepad.load("test", window_ids=[...]).

Regional network (Colombia).

Global network. Windows last tens of minutes and distances reach 10,000 km.

Code for these figures

import bepad
from bepad.plots import plot_scenario_grid

for net in ["tx", "CM", "R08"]:
    test = bepad.load("test", networks=[net])
    plot_scenario_grid(test, net, save_path=f"scenarios_{net}.png")

Sequences

Earthquakes close in space and time, as after a large earthquake or in a swarm: the hardest case for association, because their picks arrive together at the same stations.

A sequence is an earthquake and its nearest earthquakes in 3D (same network and split, within a year). Each window has one of four types, drawn at random:

Type	In the window
Mainshock first	The mainshock early in the window, then its aftershocks.
Foreshocks	A few foreshocks, more and more frequent, the mainshock in the middle, then aftershocks.
Late in a sequence	Aftershocks only: the mainshock was long before the window (1–100 window lengths).
Two sequences	A first mainshock early with its aftershocks, a second mainshock later in another place (farther than twice the size of the first sequence) with its own aftershocks.

The rules, the same for every network:

• The mainshock is among the largest 25 % of the network’s earthquakes and larger than every earthquake of its sequence. Size is the magnitude; in a network without usable magnitudes (fewer than half the earthquakes with one, or fewer than 5 distinct values, e.g. R07), it is the number of stations that recorded the earthquake.

• Timing: after a mainshock the rate of aftershocks decays as 1 / (t + c), with c = 5 % of the window (Omori’s law); foreshocks follow the same law backwards, towards the mainshock.

• 0–2 background earthquakes (independent, at random times) are added, so not every earthquake belongs to the sequence.

• A window that a network cannot make (not enough nearby earthquakes) is left out, as in every scenario.

How tight a sequence is depends on the catalog: within a few kilometres in dense local and microseismic networks (e.g. tx, CM, R05), tens to hundreds of kilometres in global catalogs. The windows table gives sequence_radius_km (distance from the mainshock to its farthest earthquake) to choose tight sequences; the events table gives each earthquake’s sequence and role (mainshock, foreshock, aftershock, background).

Texas, one window of each type (6–10 earthquakes, little noise). Large stars: mainshocks. Each panel shows its window_id.

Regional network (Colombia).

Code for these figures

import bepad
from bepad.plots import plot_sequence_types

for net in ["tx", "CM", "R08"]:
    test = bepad.load("test", networks=[net], scenarios=["seq-med__noise-low"])
    plot_sequence_types(test, net, save_path=f"sequences_{net}.png")

Earthquakes outside the network

Three more scenarios select earthquakes by their azimuthal gap, the largest angle around the epicentre without a station. A large gap means the earthquake is at the edge of the network or outside it, which is harder to associate.

Gap 0–90°, 90–180° and 180–270° (3–5 earthquakes, noise 0.3). Networks with few far-away earthquakes may have fewer earthquakes per window in the 180–270° scenario. The window_id of each window is at the bottom right of its panel.

Code for this figure

import bepad
from bepad.plots import plot_gap_sweep

for net in ["tx", "CM", "R08"]:
    test = bepad.load("test", networks=[net])
    plot_gap_sweep(test, net, save_path=f"gap_sweep_{net}.png")

How hard is it?

Test split; “seq” are the sequence scenarios. (a) Earthquakes active at the same time. (b) Share of real picks that arrive while another earthquake is also active. (c) Time between the two closest origins. (d) Picks per window by noise level. (e) prob of real and generated picks. (f) Distance from each pick to the nearest earthquake: noise is found at the same distances as real picks.

Code for this figure

import bepad
from bepad.plots import plot_difficulty

test = bepad.load("test")                  # all networks
plot_difficulty(test, save_path="difficulty.png")

What easy and hard look like:

An easy, a typical and a hard window (10th, 50th and 90th percentile of the number of earthquakes active at once) for a local, a regional and a global network. Each panel shows its window_id.

Code for this figure

import bepad
from bepad.plots import plot_representative_windows

test = bepad.load("test")
# easy / typical / hard = 10th / 50th / 90th percentile of the number of earthquakes active at once
plot_representative_windows(test, by="max_concurrent_events", save_path="stats_representative_windows.png")

Statistics of the earthquakes, stations and picks: Dataset statistics.

More figures, each with its code: Figure gallery.