Earthquake Models

Why Earthquake Is Uniquely Challenging

Of all the natural perils modelled by the insurance industry, earthquake stands apart in several important ways. It strikes without warning — there is no forecast track, no days of preparation time, no gradual buildup. The physical processes governing where, when, and how severely an earthquake will strike are governed by geological forces that operate over centuries and millennia, yet release their energy in seconds. And the damage an earthquake causes depends on a complex interaction between the source of the rupture, the geological materials through which waves travel, and the local soil and building conditions at each specific site — conditions that can vary enormously within a single city block.

Understanding earthquake risk is therefore not simply a matter of knowing where faults are. It requires integrating seismology, geology, geotechnical engineering, structural engineering, and financial analysis into a coherent probabilistic framework. This lesson takes you through that framework step by step.

The Physics of an Earthquake

Before examining how earthquake models work, it is essential to understand what an earthquake actually is. The Earth's outer shell is divided into tectonic plates that move relative to one another, driven by convection currents in the mantle below. At plate boundaries and within plates, rocks accumulate elastic strain as tectonic forces build over decades to centuries. When the accumulated stress exceeds the frictional resistance along a fault plane, the fault ruptures — releasing stored elastic energy in the form of seismic waves that radiate outward in all directions from the rupture zone.

The point on the fault where rupture initiates is the hypocenter (or focus), which lies at depth within the crust. The point on the Earth's surface directly above the hypocenter is the epicenter. For large earthquakes, the rupture does not occur at a single point — it propagates along a fault segment that may extend for tens to hundreds of kilometres. The geometry, direction, and speed of this rupture propagation all influence the ground motion produced.

Earthquake Magnitude

Earthquake magnitude measures the total energy released by the rupture. The Moment Magnitude Scale (Mw) is the standard used in modern seismology and catastrophe modelling. It is derived from the seismic moment — a function of the fault area that ruptured, the average slip across the fault, and the rigidity of the rock. The scale is logarithmic: each unit increase in magnitude corresponds to approximately 32 times greater energy release. A magnitude 7 earthquake releases roughly 1,000 times more energy than a magnitude 5.

Fault Types and Their Importance

Faults are classified by their geometry and the direction of relative movement across the fault plane. The three primary types have meaningfully different implications for ground motion:

• Strike-slip faults: The two sides of the fault move horizontally past each other. The San Andreas Fault in California is the world's most famous example. Strike-slip faults tend to produce moderate ground motion levels relative to their magnitude.
• Thrust and reverse faults: One side of the fault is pushed up and over the other. Thrust faults are associated with mountain-building and subduction zones. They generally produce higher ground motion than strike-slip faults at the same magnitude and distance — making them particularly damaging. The Northridge (1994) earthquake was a blind thrust fault (one with no surface expression), which caught many by surprise.
• Normal faults: The crust is being pulled apart, and one side drops relative to the other. Normal faults are associated with rift zones and generally produce lower ground motion levels.

Seismic Source Modelling

The foundation of any earthquake cat model is the seismic source model — a comprehensive representation of all earthquake sources that could affect the modelled area, including their locations, geometries, and rates of activity. Building this model is a major scientific undertaking, integrating multiple data types:

Historical Seismicity Catalogs

The starting point is the historical earthquake record — the catalog of past events with their locations, depths, magnitudes, and dates. Instrumental records (from seismographs) provide precise data back to the early 20th century. Pre-instrumental historical records, derived from accounts of damage and felt reports, extend the catalog further back but with greater uncertainty. The challenge is that historical records are short relative to the recurrence intervals of large earthquakes — a fault with a 500-year recurrence interval may have no events in the instrumental catalog at all.

Fault Mapping

Active faults are identified and mapped through a combination of techniques: surface expression visible in aerial photography and satellite imagery, field mapping and fault trenching, and inference from historical seismicity patterns. In well-studied regions like California, fault databases are highly detailed. In less-studied regions — much of Asia, Africa, and South America — significant fault systems remain unmapped or poorly characterised, representing a major source of model uncertainty.

Paleoseismology

Paleoseismology is the study of prehistoric earthquakes using geological evidence. By excavating trenches across fault zones, scientists can identify offset layers, sand boils from liquefaction, and other evidence of past ruptures, and use radiocarbon dating to estimate when they occurred. This allows modellers to estimate recurrence intervals for large earthquakes even on faults with no historical record. Paleoseismic studies have been particularly important in regions like the Pacific Northwest of the United States, where the Cascadia Subduction Zone has been shown to generate magnitude 8–9 megathrust earthquakes approximately every 200–500 years — with the last occurring in January 1700.

Geodetic Data

Networks of GPS receivers now continuously monitor the movement of the Earth's surface, revealing the accumulation of crustal strain across fault systems. Regions with high strain accumulation rates are generating stress that must eventually be released seismically. Geodetic data is increasingly incorporated into seismic hazard models to constrain slip rates on faults and identify regions of strain accumulation not obviously associated with mapped faults.

The Gutenberg-Richter Relationship and Recurrence

For any seismic source zone, the model must define not just where earthquakes occur but how frequently — and at what magnitudes. The empirical Gutenberg-Richter relationship describes the frequency-magnitude distribution of earthquakes in a region:

log₁₀(N) = a − b·M

Where N is the number of earthquakes with magnitude greater than or equal to M per unit time, and a and b are constants derived from the seismicity data. The b-value (typically close to 1.0 globally) describes how rapidly earthquake frequency decreases as magnitude increases — a higher b-value means relatively more small earthquakes and fewer large ones. The a-value reflects the overall level of seismic activity in the region.

For individual well-characterised faults, modellers supplement the Gutenberg-Richter distribution with the concept of the characteristic earthquake — a fault that tends to rupture at fairly regular intervals producing events of similar, maximum magnitude. The two approaches are often combined: characteristic earthquakes at the upper end of the magnitude range, with Gutenberg-Richter distribution for smaller events across the broader source zone.

Ground Motion Prediction Equations (GMPEs)

Once a simulated earthquake is generated with its source parameters, the model must estimate the intensity of ground shaking at every location in the exposure database. This is done using Ground Motion Prediction Equations (GMPEs) — empirical relationships derived from large databases of recorded ground motions that relate shaking intensity to earthquake characteristics and site conditions.

The primary ground motion intensity measures used in earthquake modelling are:

• Peak Ground Acceleration (PGA): The maximum acceleration experienced at a site, expressed as a fraction of gravitational acceleration (g). Correlates well with damage to short-period structures.
• Spectral Acceleration (Sa): The maximum acceleration experienced by a simple oscillator of a given natural period. Different building types respond to different periods of ground motion — taller buildings are more sensitive to long-period (slow) shaking; short buildings to short-period (fast) shaking. Modern cat models use spectral acceleration at multiple periods to capture this.
• Peak Ground Velocity (PGV): The maximum ground velocity, which correlates particularly well with structural damage in certain building types.

Key Factors in GMPEs

GMPEs are region-specific because the properties of the geological crust vary around the world, affecting how seismic waves propagate and attenuate. The key factors a GMPE accounts for include:

• Earthquake magnitude: Larger earthquakes produce more intense shaking at any given distance
• Source-to-site distance: Ground motion generally decreases with distance, though the relationship is non-linear and varies by frequency
• Fault mechanism: Thrust and reverse faults produce systematically higher ground motion than strike-slip or normal faults at the same magnitude and distance
• Depth: Shallow earthquakes (less than 20km) are generally more damaging than deeper events of the same magnitude
• Vs30 (site classification): The average shear-wave velocity in the top 30 metres of soil is the standard measure of local site conditions. Soft soils (low Vs30) amplify ground motion; hard rock (high Vs30) amplifies less

Earthquake Vulnerability — How Buildings Respond

Understanding how buildings behave during earthquakes is fundamental to estimating losses. The response of a building to earthquake ground motion is complex and depends on the building's structural system, materials, height, age, and the frequency content of the ground motion. The key concept is resonance — when the frequency of ground motion matches the natural frequency of a building, the building's response is amplified dramatically.

Structural Damage Mechanisms

Earthquake damage to buildings is primarily driven by lateral forces — the horizontal accelerations imparted to buildings by seismic waves. Buildings are designed to carry vertical loads (gravity) efficiently but are far less efficient at resisting horizontal forces unless specifically engineered to do so. The primary structural damage mechanisms include:

• Soft storey collapse: When one floor of a building is significantly weaker or more flexible than the floors above (often the ground floor due to open parking or commercial space), it concentrates deformation and can collapse. A leading cause of earthquake fatalities.
• Column failure: Inadequately designed concrete columns can fail in shear or develop plastic hinges at the top and bottom (a "short column" failure) leading to storey collapse.
• Unreinforced masonry failure: Brick and stone masonry with no steel reinforcement has very poor lateral resistance. Unreinforced masonry (URM) buildings are among the most vulnerable building types globally — common in older building stock across Europe, the Middle East, and Asia.
• Non-structural damage: Even when structures perform well, non-structural elements — partition walls, suspended ceilings, mechanical and electrical systems, façade cladding — can be severely damaged. Non-structural repair costs can dominate total loss even in buildings with minimal structural damage.

Fragility Curves in Practice

Earthquake vulnerability in cat models is captured through fragility curves — functions that express the probability of reaching or exceeding a given damage state as a function of ground motion intensity. The damage states are typically defined as slight, moderate, extensive, and complete. For each building class, separate fragility curves are developed for the structure, its contents, and the time element (loss of use). The combination of these fragility curves with the probability distribution of ground motion from the hazard module produces the expected loss distribution for each event.

Secondary Perils — Often Overlooked, Sometimes Dominant

Earthquakes are not a single hazard — they are a trigger for multiple secondary processes that can cause losses comparable to or exceeding direct shaking damage. Comprehensive earthquake cat models attempt to capture these secondary perils, though with varying levels of sophistication.

Liquefaction

Liquefaction occurs when water-saturated, loosely packed soils lose their strength and stiffness during earthquake shaking and temporarily behave like a viscous liquid. Buildings can sink, tilt, or lose foundation support. Underground utilities can rupture. The 2010–2011 Canterbury earthquake sequence in New Zealand — centred near Christchurch — produced extensive liquefaction across the city, generating losses that significantly exceeded what shaking-based models alone would have predicted. Liquefaction susceptibility depends on soil type (loose, saturated sand is most vulnerable), depth to groundwater, and shaking intensity.

Landslides and Slope Failure

Earthquake shaking can destabilise slopes, triggering landslides that destroy buildings, block roads, and disrupt lifelines. In mountainous regions — the Himalayas, the Andes, the mountains of Japan and Taiwan — earthquake-triggered landslides can cause losses far from the primary rupture zone and make emergency response and reconstruction far more difficult and expensive.

Tsunami

Submarine earthquakes — particularly along subduction zones where one tectonic plate dives beneath another — can displace large volumes of water and generate tsunamis. The 2004 Indian Ocean tsunami (triggered by an M9.1 earthquake off Sumatra) killed over 225,000 people across 14 countries. The 2011 Tōhoku tsunami devastated Japan's northeastern coastline and triggered the Fukushima nuclear accident. For insured losses, the tsunami component of the 2011 Japan event dominated over direct shaking losses — dramatically different from any previous earthquake modelling assumption. This event forced a fundamental revision of how earthquake models handle tsunami risk for subduction zone events.

Fire Following Earthquake

Fire following earthquake (FFE) is a secondary peril with a well-documented history of causing significant additional losses. The 1906 San Francisco earthquake caused relatively modest shaking damage, but the fires that followed — ignited by broken gas lines and spread unchecked because the water mains had ruptured — destroyed most of the city. Modern estimates suggest that FFE could contribute 10–20% of total insured losses in a major urban California earthquake. FFE models must account for fire ignition probability (as a function of shaking intensity and building density), fire spread (influenced by building density, wind conditions, and access by fire services), and suppression capacity (degraded by broken water mains and inaccessible roads).

The Insurance Landscape for Earthquake

Earthquake insurance market structures vary significantly around the world, and understanding this context is important for cat modellers working in different regions:

• United States: Earthquake is excluded from standard homeowners policies. Separate earthquake endorsements or policies are available but take-up rates are very low even in high-risk areas like California — estimated at 10–13% of homeowners. The California Earthquake Authority (CEA) is a publicly managed, privately funded insurer that provides the majority of residential earthquake coverage in the state.
• Japan: Residential earthquake insurance is sold as an endorsement to fire policies, with premiums set by the government and reinsurance provided partly by the state. The Japan Earthquake Reinsurance Company (JER) provides the core reinsurance mechanism. Take-up rates have increased significantly since the 1995 Kobe earthquake, reaching approximately 35% of households.
• New Zealand: The Earthquake Commission (EQC) provides the first layer of residential earthquake cover, with private insurers providing cover above the EQC cap. The Canterbury earthquake sequence (2010–2011) tested this model severely and led to significant reforms.
• Turkey and developing world: Many countries with high earthquake exposure have very low insurance penetration, creating enormous protection gaps. The 1999 Marmara earthquake in Turkey killed 17,000 people and caused USD 12 billion in economic losses with negligible insured losses.

Key Earthquake Regions for the Insurance Industry

Cat modellers working in earthquake need to be familiar with the major seismically active regions and their specific characteristics:

• California (USA): The San Andreas Fault system dominates, with Los Angeles and San Francisco at risk from multiple fault sources. The largest modelled scenario is often a major San Andreas rupture (the "Big One") estimated at M7.8–8.0.
• Pacific Northwest (USA/Canada): The Cascadia Subduction Zone poses risk of M8–9 megathrust events with potential for devastating tsunami impacts on Seattle, Portland, and Vancouver.
• Japan: One of the world's most seismically active countries, with subduction zones on multiple sides. The 2011 Tōhoku event demonstrated the potential for M9 megathrust earthquakes even in one of the world's best-prepared nations.
• Turkey: The North Anatolian Fault — a major right-lateral strike-slip fault — has produced a sequence of large earthquakes moving westward through the 20th century, raising concern about a major event near Istanbul, a city of 15 million people.
• New Zealand: The Alpine Fault on the South Island is capable of M8+ earthquakes. The Canterbury sequence demonstrated the complexity of aftershock sequences and the insurance loss amplification from repeated moderate events.