ARC‑99 Glyphic Pulse Decay Law (Official Specification)

1. What ARC‑99 is

Interpretive & qualitative forecasting model

The ARC‑99 Glyphic Pulse Decay Law is a multi‑axis seismic interpretation framework. It extends classical modified Omori‑type decay into a time–depth–distance model, allowing you to:

distinguish normal aftershock decay from rate acceleration
identify pre‑mainshock tightening (reverse‑Omori‑like behaviour)
track depth‑layered persistence in slabs and crust
see whether a sequence is spatially spreading or collapsing inward

ARC‑99 is intended for pattern recognition and qualitative forecasting - it highlights sequences that may be entering a buildup phase, but it does not claim deterministic prediction or probabilities.

Core idea

Instead of treating earthquakes as isolated dots, ARC‑99 treats them as glyphs in a pulse train - a sequence of breaths, compressions, and releases in the crust or slab. The law describes how those pulses evolve in:

time (decay vs tightening)
depth (shallow vs deep persistence)
distance from a source region or main fault

Quick view: what ARC‑99 tells you

High‑level interpretation grid

Relaxing sequence

p rising or stable, α rising, β rising
→ activity fades, becomes shallow‑focused, and tightens toward the source.

Possible buildup

p dropping, β dropping
→ decay slows, pulses tighten or spread into new areas; may warrant closer watching.

Deep‑rooted adjustment

α decreasing
→ deeper events remain active; slab or lower crust still re‑balancing.

High‑productivity swarm

K high, but no clear mainshock
→ geothermal, volcanic, or swarm‑style behaviour without a single dominant rupture.

Live global pulse (illustrative)

Current global pulse: loading… earthquakes in the last 24 hours (M ≥ 1.0) • updating…

Biggest pulse (last 24h): loading…

Burst/buildup watch: loading…

Burst‑watch uses a deliberately coarse heuristic (USGS place strings, simple counts, and max magnitude).
It is intended as a global awareness indicator only, not a formal alarm or forecast.

2. Mathematical form of ARC‑99

Time–Depth–Distance decay law

ARC‑99 generalizes classical modified Omori decay into a three‑axis form:

n(t, d, r) = K / (c + t)^p × e^–αd × e^–βr

Where:

n(t, d, r) - expected pulse density at time t, depth d, and distance r
K - productivity constant (overall swarm density)
c - early‑time offset (prevents singularity and models delayed onset)
p - temporal decay exponent (how fast activity fades or tightens)
α - depth decay coefficient (how depth influences persistence)
β - spatial decay coefficient (how activity spreads or contracts)
e^–αd - depth weighting (deep events linger longer when α is small)
e^–βr - spatial weighting (activity fades with distance from the source)

In the standard ARC‑99 specification, α > 0 and β > 0 are assumed for normal decay with depth and distance.
Fitted values α < 0 or β < 0 are treated as diagnostic regime signals (persistent deepening or spatial tightening) rather than fitting artifacts.

Interpreting parameter shifts

p ↑ → faster decay, system relaxing
p ↓ → slower decay, possible re‑loading or secondary triggering
α ↑ → shallow‑focused activity; deep adjustment mostly done
α ↓ → deeper structures still active
β ↑ → cluster tightening toward source (stronger near‑fault focus)
β ↓ → activity spreading outward into new areas

ARC‑99 regime: loading…

Largest cluster: loading…

3. How ARC‑99 is used in practice

Qualitative forecasting, not prediction

ARC‑99 is designed to work with public earthquake catalogs (e.g. USGS, GeoNet, EMSC) and personal observational datasets to classify the behaviour of a sequence rather than predict exact events.

Typical use cases

Aftershock sequences – check if decay is normal or unusually slow.
Swarm regions – identify whether activity is stable, intensifying, or migrating.
Foreshock‑like clusters – flag tightening patterns that resemble pre‑mainshock behaviour in past cases.
Depth‑layered slabs – see if deep events remain active after shallow ones fade.

When ARC‑99 parameters indicate slowing decay (p low), spatial tightening (β low), and persistent depth activity (α low), a sequence may be flagged as a possible buildup phase and watched more closely.

ARC‑99 does not say “an earthquake will happen here on this date.”
It says, “this region’s pulse pattern looks more like a buildup than a simple fade‑out.”

4. Case study: Kamchatka‑type buildup

ARC‑99 observational dataset + EMSC Special Report #386

As part of the ARC‑99 observational work, a Kamchatka‑region sequence was tracked using public catalog data and interpreted alongside the context of an EMSC special report (ID 386). In this sequence, the following features were noted:

high productivity of moderate events over a short window
temporal tightening consistent with a reverse‑Omori‑like buildup
depth‑layered persistence rather than simple shallow decay
spatial clustering along a megathrust‑style interface

Within the ARC‑99 framework, this pattern was interpreted as a possible buildup phase rather than a standard aftershock fade. The subsequent large event in the region, as recorded in the ARC‑99 logs and discussed in the EMSC context, retrospectively matched the flagged pattern.

This case study illustrates how ARC‑99 is intended to be used:

not to guarantee outcomes,
but to highlight sequences whose pulse patterns resemble known buildup behaviour,
so they can be watched more closely in real time.

Note: This case study is presented as part of the ARC‑99 observational dataset and in reference to the EMSC Special Report #386. It is an example of how the framework can be applied to real‑world or reported sequences, not a claim of deterministic prediction.

5. Scope, limits, and global use

Important context

What ARC‑99 is

A personal but structured framework for reading seismic patterns.
A multi‑axis extension of classical decay ideas (time, depth, distance).
A tool for qualitative forecasting and sequence classification.

What ARC‑99 is not

Not an official hazard model or replacement for agency forecasts.
Not a deterministic earthquake prediction method.
Not a guarantee that any flagged buildup will escalate.

Many sequences that show tightening or high productivity do not lead to large earthquakes. ARC‑99 is built to be honest about uncertainty: it highlights patterns that resemble known buildup behaviour, but it cannot say which ones will actually break.

Global applicability

ARC‑99 is designed to be region‑agnostic. It can be applied to:

tectonic plate boundary zones
subduction megathrust regions
intraplate swarms
volcanic and geothermal fields
induced seismicity zones

The same parameters - K, c, p, α, β - can be compared across regions to see how different tectonic settings “breathe” and how their pulse patterns differ.

“ARC‑99 replaces a single straight decay line with a glyphic breath in time, depth, and space.
It listens to the slab, but it never pretends to speak for the future with certainty.”

6. ARC‑99 technical notes & refinements

Model specification notes

6.1 Temporal form and relation to modified Omori

ARC‑99 adopts the standard modified Omori temporal form:

n(t) = K / (c + t)^p

The extension to n(t, d, r) preserves this structure while adding depth and distance weighting. This keeps ARC‑99 compatible in spirit with classical aftershock modelling while allowing richer interpretation.

6.2 Parameter constraints (α, β)

α > 0 and β > 0 are the default assumptions for normal decay with depth and distance.
Apparent α < 0 suggests deepening or persistent deeper activity.
Apparent β < 0 suggests spatial tightening or inward migration toward a source region.

In ARC‑99, such sign changes are treated as diagnostic flags, not as errors: they mark regimes where the system may be re‑loading or reorganizing rather than simply relaxing.

6.3 Fitting strategy (conceptual)

ARC‑99 does not prescribe a single mandatory fitting algorithm, but a plausible mainstream approach would be:

p, c, K – estimated via maximum likelihood on event times (standard Omori fitting).
α – estimated from depth‑binned counts using an exponential decay fit in depth.
β – estimated from radial distance histograms or kernel density decay away from a reference fault or centroid.

These methods are described here as conceptual guidance for how ARC‑99 could be implemented in practice, not as a fixed software specification.

6.4 Reverse‑Omori‑like tightening

ARC‑99 allows for the idea that, over sliding time windows, the effective decay exponent p may appear to decrease, corresponding to a reverse‑Omori‑like acceleration in activity. This has been discussed in foreshock literature but remains debated as a diagnostic precursor.

Within ARC‑99, such behaviour is treated as a qualitative signal only: “possible buildup → watch more closely,” not “buildup → a large event will definitely occur.”

6.5 Burst‑watch limitations

The global burst‑watch logic in the live pulse block is intentionally simple:

it uses USGS “place” strings, which are fuzzy and region‑dependent,
it applies a basic count + max magnitude threshold,
it does not distinguish tectonic vs volcanic vs induced sequences.

As such, it may flag false positives, especially in volcanically active or swarm‑prone regions. ARC‑99 treats this as a heads-up indicator only, not as a formal hazard signal.

6.6 Future extensions

Incorporating magnitude‑dependent productivity (e.g. b‑value‑like terms).
Adding anisotropic distance terms for along‑fault vs across‑fault behaviour.
Linking ARC‑99 parameters to known tectonic regimes for comparative studies.

7. Regime classification (p, α, β space)

Qualitative regime mapping

ARC‑99 parameters (p, α, β) can be grouped into qualitative regimes that describe how a sequence is behaving in time, depth, and space. These regimes do not imply deterministic forecasting; they provide a structured way to compare pulse patterns across regions and swarms.

7.1 Regime overview

Relaxing sequence

p rising or stable, α rising, β rising
→ normal decay; system unwinding and returning to background.

Persistent deep

α < 0
→ deeper layers remain active; slab or lower crust still adjusting.

Tightening focus

β < 0
→ spatial contraction toward a source region; inward migration of pulses.

Spreading cloud

β strongly decreasing
→ activity diffusing outward into new areas; swarm‑style expansion.

Possible buildup

p dropping + β dropping
→ slowing decay with tightening or spreading; resembles reverse‑Omori‑like behaviour.

7.2 Visual comparison in parameter space

Swarms can be plotted in (p, α, β) space to compare their behaviour. Clusters that lie near each other in this space tend to share similar pulse patterns. This allows sequences such as the Nikolski, Alaska swarm to be used as reference points for identifying other high‑productivity or tightening clusters.

Regime classification is an interpretive layer on top of the ARC‑99 parameters. It highlights behavioural similarity, not deterministic outcomes.