여진 발생 확률 계산기

Calculate the probability and expected number of aftershocks following a mainshock.

Analysis

여진 예측의 과학

여진은 본진 이후 같은 단층 지역에서 발생하는 작은 지진입니다. 지각이 새로운 변형 상태에 적응하면서 파열된 단층 주변의 응력이 재분배되어 발생합니다. 여진은 수주, 수개월, 심지어 수년간 지속될 수 있으며, 2011년 규모 9.1의 도호쿠 지진은 10년 이상 상당한 여진을 계속 발생시켰습니다.

이 계산기는 두 가지 기본 지진학 법칙을 결합한 Reasenberg-Jones(1989) 통계 모델을 사용합니다. 수정 오모리 법칙은 여진 발생률이 거듭제곱 패턴을 따라 시간이 지남에 따라 어떻게 감소하는지를 설명합니다. 여진은 본진 직후 가장 빈번하며 급격히 감소합니다. 바스 법칙은 최대 여진이 통계적으로 본진보다 약 1.2 규모 단위 작다는 추정을 제공합니다. 이 모델들을 함께 사용하면 지진학자들이 주어진 규모 임계값 이상의 여진 확률과 예상 횟수를 예측할 수 있습니다.

여진 과학의 핵심 개념

수정 오모리 법칙(1894): 여진 발생률 n(t) = K / (t + c)^p, 여기서 t는 본진 이후 시간이며 K, c, p는 경험적 상수입니다. 발생률은 대략 1/t로 감소합니다.
바스 법칙(1965): 최대 여진은 통계적으로 본진보다 약 1.2 규모 단위 낮지만, 예외적으로 본진에 가까운 규모의 여진이 발생하기도 합니다.
구텐베르크-리히터 b-값(통상 ~1.0)은 소규모 대비 대규모 여진의 비율을 설명합니다: M5 여진 하나당 대략 10개의 M4 여진이 발생합니다.
여진 구역은 일반적으로 본진의 파열 영역에 해당합니다. 규모 7.0의 지진은 30~50 km 범위에 걸쳐 여진을 발생시킬 수 있습니다.

일반적인 용도

대규모 지진 후 손상된 건물에 재진입해도 안전한지 평가.
지속적인 여진 위험을 인식하며 수색 및 구조 작전을 계획.
교육 또는 연구 목적으로 여진 감소 패턴을 이해.
여진 위험이 높은 본진 이후 기간 동안 보험 노출도를 추정.

How to Use

1
Enter Mainshock Parameters
Input the mainshock magnitude (Mw), date, time, and location. The Omori-Utsu law—the foundation of aftershock forecasting—requires the mainshock time as the reference point (t = 0) for the decay calculation.
2
Set the Forecast Window
Select the forecast time window (1 day, 1 week, 30 days) and the minimum magnitude threshold for the aftershock probability estimate. USGS operational forecasts use M3.0+ as the standard reporting threshold.
3
Review the Aftershock Forecast
See the expected number of aftershocks above your chosen magnitude threshold and the probability of at least one aftershock exceeding specific magnitude levels. Note that the forecast uncertainty increases with time since the mainshock.

About

Aftershock sequences are not random noise following an earthquake—they are systematic, predictable in a statistical sense, and carry important information about fault properties and regional stress fields. The scientific basis for aftershock forecasting traces to the Omori-Utsu law, which holds remarkably across tectonic environments from Japan to California to New Zealand. The ETAS (Epidemic Type Aftershock Sequence) model, developed by Ogata (1988), extends Omori-Utsu to capture the full clustering structure of seismicity: each earthquake (aftershock or mainshock) independently generates its own offspring sequence, creating a branching process. ETAS successfully reproduces the broad statistical features of seismicity catalogs and forms the basis of modern operational forecasting.

The completeness of the post-mainshock earthquake catalog is a critical practical limitation. In the hours immediately following a large earthquake, numerous small-to-moderate aftershocks occur whose seismographic coda overlap in time, preventing individual identification—a problem called 'catalog incompleteness.' The magnitude of completeness Mc rises sharply after a mainshock and decays over days to weeks, depending on network density and analyst processing capacity. This incompleteness affects parameter estimation in Omori-ETAS models and means early forecasts carry larger uncertainty. Modern approaches use template matching—cross-correlating continuous waveform streams with known event templates—to detect small aftershocks hidden within the coda, dramatically lowering Mc in the critical early hours.

Social communication of aftershock probabilities presents persistent challenges. Research by social scientists (e.g., Becker et al., 2019, GeoJournal) shows that probabilistic formats ('35% chance of M5+') are frequently misinterpreted by the public as certainties or dismissals. Newer guidance from USGS and GNS Science emphasizes communicating aftershock information in terms of what people should do, not just probabilities: inspect your home before re-entering; assume any aftershock large enough to feel is large enough to collapse weakened structures; follow official guidance rather than individual seismicity monitoring apps whose algorithms and parameters may not align with operational systems.

FAQ

What is the Omori-Utsu law?

The Omori-Utsu law is an empirical relation describing the temporal decay of aftershock rates following a mainshock. Original formulation by Fusakichi Omori (1894) expressed aftershock rate as K/(t + c), where t is time after the mainshock and K and c are constants. Tokuji Utsu (1961) modified it to K/(t + c)^p, where the exponent p typically ranges from 0.9 to 1.5 across different tectonic environments. A p-value of 1.0 means that if 100 aftershocks occur on day 1, about 50 will occur on day 2, 33 on day 3, and so on. The law applies over remarkable time scales—years to decades—and is the foundation of the Epidemic Type Aftershock Sequence (ETAS) model used in operational aftershock forecasting by USGS, GNS Science, and other agencies.

How long do aftershocks typically last?

Aftershock sequences decay according to the Omori-Utsu law but have no strict termination point—they asymptotically approach background seismicity rates over time. As a practical rule, for a M7.0 mainshock, notable aftershocks (M3.0+) may continue at elevated rates for 6–12 months; for a M8.0, 2–5 years; for a M9.0, decades. The 2011 Tohoku earthquake's aftershock sequence remained elevated above background rates for at least 3 years afterward. The Kaikoura M7.8 earthquake (New Zealand, 2016) produced productive aftershock sequences on multiple fault strands lasting years. Aftershocks that themselves generate sub-sequences are properly called 'secondary aftershocks' and are handled by the stochastic branching structure of the ETAS model.

Can an aftershock be larger than the mainshock?

By definition, the mainshock is the largest earthquake in a sequence, so an aftershock cannot retrospectively exceed the mainshock—if a larger event occurs, it is reclassified as the new mainshock and all preceding earthquakes (including the former 'mainshock') become foreshocks. In approximately 5–10% of earthquake sequences, the initial large event is followed within days by a still-larger event. This is known as the 'foreshock problem' and creates practical challenges for official communication. The Omori-Utsu aftershock model cannot be unambiguously distinguished from a foreshock-mainshock sequence in real time. USGS operational forecasts acknowledge this explicitly: after a significant earthquake, there is always a non-trivial probability (typically 5–10% for M ≥ 5 mainshock, decreasing rapidly with time) that a larger event will follow.

What is the Bath's Law?

Båth's Law (Markus Båth, 1965) states that the largest aftershock in a sequence is typically about 1.2 magnitude units smaller than the mainshock, regardless of mainshock magnitude. This empirical observation means a M7.0 earthquake can be expected to produce a largest aftershock around M5.8; a M8.0 around M6.8. The rule has important practical implications: a M6.8 aftershock following a M8.0 mainshock can itself cause significant additional damage and is within the range that could kill people and damage weakened structures. Båth's Law is incorporated into USGS operational aftershock forecasts and into the ETAS model's magnitude-frequency parameters. The largest aftershock does not always occur on the first day—for the 2010 Darfield M7.1 earthquake, the largest aftershock (M6.3 Christchurch, February 2011) occurred 5 months later and caused 185 deaths.

How do operational aftershock forecasts work?

The USGS Operational Aftershock Forecast System (OAF), deployed following significant US earthquakes, uses the Epidemic Type Aftershock Sequence (ETAS) model and the Reasenberg-Jones model in parallel to produce probabilistic forecasts. The forecasts are updated continuously as new aftershocks occur and refine parameter estimates. A typical OAF statement specifies: the probability of one or more M5.0+ aftershocks in the next day (e.g., 35%), the expected number of M3.0+ aftershocks in the next week (e.g., 8–20), and the probability of an event exceeding the mainshock magnitude (e.g., 2%). The GNS Science aftershock forecasting system in New Zealand and the JMA aftershock probability system in Japan follow similar Omori-ETAS frameworks. All systems stress that aftershock forecasts are probabilistic, not deterministic, and uncertainty bounds are wide particularly in the hours immediately after a mainshock when the seismicity catalog is incomplete due to coda interference.