Spatial Computing Report: The Anatomy of an Earthquake

Executive Summary

This essay presents a new view of earthquakes. They are not represented as sudden events but as four-dimensional events occurring in time and space. Instead of considering the earthquake as an event that can be described by a certain magnitude number or peak acceleration readings, the paper argues that traditional seismology’s scalar summary obliterates precisely those features that determine the amount of damage inflicted by the earthquake.

Built on basic seismic theories such as the elastic rebound theory, seismic moment, and moment magnitude calculations and backed with decades of engineering research, the essay suggests that duration, direction of the rupture propagation, and geology can be as important for the destructive effects of seismic waves as the magnitude itself. Two earthquakes of the same magnitude can have disastrous consequences depending on shaking duration but also soil type and rock characteristics under the buildings.

Next, this essay examines the failure mechanisms from the perspective of wave physics and moves on to the mechanisms, including liquefaction of soil, resonance of objects, and landslides, that will be demonstrated in five case studies of Valdivia in 1960, Sumatra in 2004, Tōhoku in 2011, Turkey and Syria in 2023, and Venezuela in 2026. Each case illustrates a distinct aspect of four-dimensional actors eminent in the seismic event process, such as the resonance at the planetary level or the failure of infrastructure.

The report’s core idea states that spatial computing technologies like the modeling of tsunami waves, lag effects in soil liquefaction, and sway of buildings bring about a new understanding of earthquakes, which are four-dimensional processes that evolve in time and space. The report finishes with the vision of real-time four-dimensional models as a basis for prediction of future earthquakes and urban resilience planning in general.

Mechanics of Planetary Energy Release

An earthquake is not a mechanical event but a very critical moment in a long-running process that starts decades or centuries in advance. During these long-time tectonic forces put stress on the Earth’s crust, accumulating elastic energy in the rocks that will behave as a spring. Harry Reid’s elastic rebound theory distinguishes between the type of fault known to be locking, accumulating stress, and freeing itself as soon as the resolved shear stress exceeds the friction. At this moment, both halves of the earthquake make their way back to the original state, discharging latent energy in the form of seismic waves. This straightforward in its essence, scheme (load, lock, rupture, rebound) served as the basis for all subsequent works in the sphere of earthquake physics.

Determining the magnitude of a seismic event is another way of saying, “How big a shock is needed,” and is essential in using an objective measure that relies on physics rather than on the characteristics of the measuring devices. The seismic moment, which is defined by M₀ = μ·A·D (where the rigidity of the Earth’s crust, the size of the rupture, and the average displacement), establishes a connection between the seismic magnitude and the features of faulting (Kanamori, 1977). The moment magnitude scale, Mw = (2/3)log₁₀M₀ − 10.7, was created to find a solution to the problem of saturation, which made the previous amplitude-dark scales useless in measuring the strongest events (Hanks & Kanamori, 1979). Because M₀ depends on the characteristics of ruptures, and the total size of the rupture increases with the size cubed, moving from M7 to M9 increases the radiated energy by one thousand times. Thus, the distinction between a damaging local earthquake and a powerful megathrust event is not based on the idea of intensity but rather on the idea of the earthquake type.

In addition, the present moment formula allows us to separate the size of the event from the saturation problems of previous scales. Since M₀ is calculated based on the information from long-term asymptotes, it continues growing with the actual event even though surface- and body-wave magnitudes remain the same when the magnitude exceeds M8 (Hanks & Kanamori, 1979). In this respect, the analysis of the events under consideration can be called a prerequisite for making valid comparisons between the earthquake cases described in this report.

However, magnitude alone is a poor predictor of how much damage a structure sustains. Duration is an important parameter that is often overlooked. Two earthquakes could have the same peak ground acceleration (PGA) and yet produce totally different amounts of damage depending on whether one lasts for six seconds and the other for ninety seconds.

Duration enhances the effect of seismic loading,, as structural failure involves a low-cycle fatigue and energy dissipation problem: each cycle of shaking leads to destruction of stiffness, crack opening, and hysteretic resistance of a structural member, which means that total demand and not peak becomes crucial for collapse (Trifunac & Brady, 1975). A big earthquake is dangerous not because it shakes well, but because it shakes for a long time, which is associated with the length of propagation of the rupture front along the fault.

This report considers earthquakes to be four-dimensional phenomena—three dimensions plus one dimension of time—and thus concludes that spatial computing has emerged as the natural diagnostic tool. Traditional seismology reduces a rupture to a set of numbers, i.e., magnitude, focal mechanism, maximum reading at a station, etc. However, the physics of a rupture is basically three-dimensional: slip, wavefront propagation, soil failure sequence, and building resonance. In contrast, immersive 4D simulation allows the analyst to be part of the unfolding situation, not just infer it from a seismogram. In the following technical parts of the report, reference will be made to three simulation tools – the tsunami wavefront model, the red particle sand engine for liquefaction, and the 1:1 Metropolis model of structural resonance—as enormous visual instruments used to visualize events otherwise impossible to imagine. Importantly, it will not be claimed, however, that visualization replaces analysis: seeing the fourth dimension opens new horizons for representatives of different disciplines, such as seismology, geotechnical engineering, and hazard policies.

Micro-to-Macro Dynamics

The energy released during seismic activity breaks up into various types of waves that generate different behaviors that dictate the subsequent movement of the waves. There are two main types of waves: the body waves, which originate from the interior of the Earth, and surface waves. The body waves consist of two types of waves: the compressional P-wave, which is the fastest, and the shear S-wave, which moves at a slower speed. The speed of the body wave is influenced by the material’s density and elastic moduli. The occurrence and propagation of the waves are discussed in detail in seismology (Aki & Richards, 2002). Surface waves are generated by the interaction of body waves at the Earth’s free surface. Surface waves can be divided into two types: Rayleigh waves and Love waves. Note that the speed of transmission of surface waves is considerably lower and may result in longer shaking time during an earthquake (Stein & Wysession, 2003).

At a site, the near-surface material plays a significant role in the transition from source physics to ground motion. While seismic energy travels quickly through strong bedrock, it moves slowly through soft sediments. Thus, as the seismic waves pass into a basin, there is a reduction in velocity and impedance of the wave, which produces amplitude magnification. This effect allows for a possible minor disturbance on strong rock being transformed into a serious disaster when the waves get to soft soils. The empirical and theoretical method for determining ground motion is based on the foregoing stochastic partitioning. In other words, two structures that are 1 km apart might experience different levels of damage even though they are at the same distance from the seismic source (Boore, 2003). This dependence on the geologic environment is not merely linear. The underlying soil behaves in a non-linear way. In fact, as the soil deformation increases, the soil becomes weaker and more absorptive, thereby leading to a decline in its resonant frequency.

Rupture is directional, and the direction is very important. Fault ruptures do not occur everywhere at the same time; they start at the hypocenter and then propagate, either bilaterally or unilaterally. When the rupture reaches a point at a speed close to the speed of shear waves, most of the energy is concentrated into a very short pulse of high amplitude, while the place behind the rupture is getting a low signal. The scaling relation of magnitude with rupture length, width, and displacements that helps with assessing directivity comes from studying data about faults all over the world (Wells & Coppersmith, 1994). It means that a fault with a certain magnitude can be responsible for great damage asymmetrically, which is directly important for the discussion of the Turkey-Syria sequence below.

If there is a rupture underneath the ocean, the vertical movement of the seabed connects the solid-Earth event with the movement of the water column. A megathrust rupture that occurs over large areas of the seabed generates a tsunami since the initial waveform corresponds to the coseismal deformation. The properties that make a subduction earthquake capable of generating a tsunami have been studied in detail by paleoseismic data analyses (Satake & Atwater, 2007). However, not every big earthquake will cause a tsunami; the mechanism of a tsunami earthquake is quite the opposite since, according to it, slow updip slip rocks the seabed but produces few high-frequency signals (Okal & Synolakis, 2004).

Here the tsunami wavefront model acts as an interpretive tool. Real-time tsunami forecasting requires modeling wavefront propagation from the source based on refraction over ocean floor topography and changes in water depth as the wavefront hits land, a technique tested and verified during real-time tsunami forecasting following major transoceanic tsunamis (Titov et al., 2005). The 4D wavefront model helps to illustrate what tide gauges measure only in the form of a time series coming out from a single point; in fact, the moving and bending wavefront’s energy is either concentrated by undersea ridges or dispersed by deep-sea canyons and reaches coastlines scattered miles apart in time. For the emergency management planner, experiencing this wavefront and ultimately knowing how the ocean floor patterns focus the bore enables the transformation of a theoretical arrival timetable into an effective visual understanding of the possible disaster that may affect communities.

Structural & Geotechnical Failures

When we think of how to transmit energy, we think of waves; when we think of failure, we think of its effects—and there is nothing like the ground itself to experience failure. Soil liquefaction is the ultimate form of geotechnical failure: under cyclical shear loading, cohesionless saturated soils develop high pore water pressure which cannot rapidly dissipate during shaking. An increase in pore pressure causes effective stress, the very stress that is responsible for the shear strength of soils or intergranular contact stress, to drop to the point where the material turns into a liquid. Theory and practice of assessing the hazard of liquefaction are based on the practical work that allowed engineers to quantitatively assess the risk of liquefaction (Seed & Idriss, 1971) and standardize their findings (Youd et al., 2001). The consequences of liquefaction include a loss of bearing capacity, buoyancy of structures below ground level, and lateral movements of the ground (Kramer, 1996).

The anchor for the red particle sand engine addresses exactly this case. The phenomenon of liquefaction is extremely difficult to describe, as the basic governing parameter, effective stress, remains invisible, and the granular mechanics takes place on the micro-scale. A particle-based simulation where individual grains of sand can be observed in the process of losing contact, redistribution of pressure, and flow makes the transition from solid state to liquid visible in a way that the pore-pressure history plot does not. From the perspective of a geotechnical engineer, the ability to visualize the propagation of the effective stress collapse in the modeled deposit connects the previously known and established closed-form cyclic stress formula (Seed & Idriss, 1971; Youd et al., 2001) with the real-life scenario of a building falling on unresolved liquefied fill.

In the air, the most common kind of failure is resonance. All structures have their own natural period of vibration, and all ground motions occur at a certain frequency. The two become coincidental, and the result is a major amplification of the response, which leads to catastrophic failure. It is important to remember that the main point in this case is the connection of the building period with the wave period: short, rigid buildings correspond to waves of high frequency, while tall, flexible buildings resonate with long period waves. It means that a tall building can be put in danger by an earthquake with the epicenter several hundred kilometers from its location. The response-spectrum framework transforms this into the structural engineering language (Chopra, 2012).

To that end, the 1:1 Metropolis Sway experiment aims to achieve this connection. The full-scale representation of an urban street corner experiencing the induced ground shaking reveals the variable responses of buildings based on their size: low-rise buildings rocking back and forth while the skyscrapers sway very slowly and out of sync. This allows for the understanding of the period dependence that accounts for the failure of different components of the city during different events. The accumulation of inter-story drift through every cycle also illustrates the effect of duration discussed in section 1 (Trifunac & Brady, 1975): the model fails not during the first large cycle but at cycle numbers ten or forty, due to the exhaustion of hysteretic capacity, just as the spectral approach indicates (Chopra, 2012). For an engineer or a decision maker, seeing the 1:1 Metropolis sway towards the failure event makes them understand so-called joint demand, comprising amplitude, frequency match, and duration, much easier than just emphasizing spectral acceleration value.

The presence of sloped ground adds the third failure category. Landslides, levee failures, and damage to dams happen due to the force of shaking exceeding the forces of resistance (the resistance to the failure of the sloped ground). Instead of keeping in mind that all failures are binary events, the sliding block principle measures the accumulated irreversible movement every time the force exceeds the threshold required for this failure to happen (Newmark, 1965). This reformulation means that instead of thinking about whether the failure happened, one needs to ask, “How much displacement is there? This point is essential for the seismic design of earth dams, highway embankments, and natural slopes, emphasizing the importance of the duration once again.

In all three categories, we can see the same message: structural and geotechnical failure is the cumulative response of the structure in different space and time instances, and this is exactly the reason why the 4D design is necessary. Each of the three components aims at a different link in this chain of events.

Case Studies

1960 Valdivia (Mw 9.5): The biggest earthquake ever recorded continues to be a crucial reference example because the energy released was so enormous that it caused the entire planet to resonate. The rupture contributed to the Earth’s free oscillations—its normal modes, the frequencies to which the entire planet vibrates—and has led to the situation in which these modes could be detected, with the reevaluation of the records solving the problem of the source and confirming the seismic moment of Mw 9.5 (Cifuentes, 1989). The tsunami caused by the earthquake traveled throughout the Pacific basin and caused deaths in Hawaii and Japan a day after—a clear example of the extent to which the energy of a megathrust can go. The case of Valdivia indicates the upper limit to which the phenomena discussed in this paper are true, as this earthquake is an example of a single fault slipping enough to make an earthquake that is not only local but also global in nature. It shows how useful it is to apply the 4D approach even to pre-digital cases, as free oscillations are the planet’s spatiotemporal response—standing waves whose spatial nodes and temporal periods define the source of the earthquake—and recovering the Mw 9.5 moment from the records of 1960 instrumentation is the evidence of how much information is preserved in the fourth dimension even when the record is very rough (Cifuentes, 1989).

2004 Sumatra-Andaman event (Mw 9.1-9.3): Sumatra may serve as a unique case to fully support the 4D model because of its specific characteristic of having an exceptional spatial and temporal extension of the rupture. Slip experienced a propagation in a northern direction across approximately 1,300 kilometers of the Sunda megathrust within 8-10 minutes, which is unusually long for a rupture, but this was well based on the clear and direct seismological observation conducted by scientists in the earthquake. Thanks to high-frequency back projection technology, the processes of the rupture eruption could be tracked, thus allowing seismologists to produce a 4D visual film of an earthquake. The reason behind this effect is the huge amount of moment released, which led to the re-excitation of the Earth’s normal modes, as evident from the elevated total moment calculated in the process (Park et al., 2005). As far as the consequences of the Sumatra earthquake are considered, it caused the deaths of about 230,000 people due to a lack of a tsunami warning system around the area (Synolakis & Bernard, 2006).

2011 Tōhoku (Mw 9.1): The Tōhoku earthquake is regarded as the most well-instrumented major earthquake. It is particularly known for the lessons related to system failures through this earthquake. The rupture of this earthquake caused enormous slip (up to about fifty meters) on the shallow up-dip part of the subduction zone over about six minutes. The slip distribution was obtained because of a tsunami model inversion as well as by performing extensive geodetic measurements onshore and offshore (Fujii et al., 2011; Simons et al., 2011). Surprisingly, this shallow slip is the type of slip described in this paper in Section II since it caused maximum uplift of the sea bed, thus causing a tsunami that surpassed the seawalls that were designed for smaller earthquakes. As for the greatest effect caused by this flooding, it is connected to a cascade of disasters starting from flooding of the backup power supply systems of the Fukushima Nuclear Power Plant. The Tōhoku earthquake proves that an earthquake cannot be understood only in its geological context but must be studied in the context of its interaction with modern infrastructure. Geodesy is another landmark technology demonstrated in the Tōhoku earthquake: geodetic measurements were performed using dense GPS networks and seafloor instruments and allowed registering the coseismic displacement with such a level of detail that it was possible to determine the slip distribution directly instead of evaluating it from data of stations spread over a large area in this version of technology (Fujii et al., 2011; Simons et al., 2011).

The Turkey-Syria earthquake in 2023 (Mw 7.8 and Mw 7.5) makes a contrast to the megathrust cases in terms of its magnitude: it is lower in the moment but devastatingly harmful due to shallow crustal ruptures, high peak ground acceleration, and the multi-fault geometry discussed in the second section of the paper. The event of Mw 7.8 first ruptured the East Anatolian Fault, followed by another earthquake of magnitude Mw 7.5, which occurred on a new fault branching from the first fault—the multi-fault cascade, which was basically unilateral and resulted in devastating movement in a populated area (Melgar et al, 2023). The ruptures are characterized by shallow strike-slip earthquakes, which caused high surface acceleration in cities, with a failure mode being collapse of non-ductile concrete construction frames experienced by structural failure as described in Section III and caused by failure to follow seismic codes (Dal Zilio & Ampuero, 2023). The case of Turkey-Syria proves that lethality depends not only on the magnitude but also on the depth of the source, site conditions, and quality of construction.

2026 Offshore Venezuela (Mw 7.2 + Mw 7.5 doublet ~10 km deep): The most recent case in the study is beyond primary literature, and we approach it in all honesty based on the reconnaissance reports and leading news and agency sources. The characteristic feature was the doublet nature of the events. The Mw 7.2 shock occurred first, followed by Mw 7.5 on the same offshore fault system at about a depth of 10 km, which stands for a foreshock-mainshock pair with no significant time difference between the two events, which has an analogy to the clustering of events observed in Kahramanmaraş. In contradiction to early expectations that severe liquefaction and underwater landslides occurred, now we know that the major hazard in Caracas was soft-basin site amplification, which is responsible for the amplified long-period ground motion due to sedimentary deposits in the city. Tsunami alerts after the offshore events were eventually canceled due to the nature of source geometry related to the strike-slip mechanism, which moved little water. The Venezuela doublet is brought into the case study as an illustration of intellectual honesty in approaches to events not covered in the traditional literature.

Intraplate and regional vulnerability: Though the previous case studies concentrated on plate boundaries, it is important to note that the biggest earthquakes are not necessarily the most fatal ones and that vulnerability can significantly vary in terms of geography, as probabilistic frameworks indicate. Intraplate areas experience earthquakes seldom; however, the impact of such earthquakes on the population and infrastructure can be devastating, given the fact that people are not prepared to face such events (Bilham, 2019). Measuring this requires creating an appropriate probabilistic model of seismic hazard, which requires taking the process of recurrence and attenuation of ground motion into consideration (Cornell, 1968). The above-mentioned model is based on the empirical evidence that for any magnitude-frequency relation, small earthquakes occur frequently, while large earthquakes occur rarely (Gutenberg & Richter, 1954). Thus, this shows that hazard is determined not only by the possible occurrence of an earthquake but also by the possible preparedness of the society to cope with the earthquake.

Spatial Computing as Seismological Vanguard

The message of this essay is that since earthquakes are four-dimensional phenomena, their destructive effects arise from the way they traverse across time and space—rupture propagation, wavefront passing, sequential ground failures, and developing stresses on buildings. But traditional methods disregard important aspects of this situation. Damage is proportional to the time factor (Trifunac & Brady, 1975), and directivity helps converge damage in one area (Wells & Coppersmith, 1994), whereas the basin effect concentrates damage in a particular direction (Boore, 2003). One maximum magnitude alone cannot explain any of these factors.

This is the reason that spatial computing has the potential to become a leader in seismology. The three anchors of simulation that have been discussed throughout this report—the tsunami wavefront, the red particle sand engine, and the 1:1 Metropolis—are not simply illustrations of completed findings but rather tools for thinking about phenomena whose driving components are theoretical or hidden: energy propagation (Titov et al., 2005), the loss of effective stress (Seed & Idriss, 1971; Youd et al., 2001), and periodic resonance that determines whether any buildings can fall (Chopra, 2012). Using these models brings a unique benefit that cannot be obtained through a seismogram — the ability to familiarize oneself with the fourth dimension of the incident.

The practical results pertain to various readerships of this bulletin. In the realm of preparedness and communication, an immersive wavefront or a swaying city communicates danger more simply than the tables of arrival times or frequency diagrams do, even for specialists preparing briefings for decision-makers. In terms of city planning, there is a possibility of transforming hazard maps into theories about the site using models of site amplification linked to objectively existing buildings, as illustrated by the example of the Caracas basin. In construction, models based on particle theory and full-scale simulations for the building process make it possible to connect analytical algorithms for computer-aided design with the reality of construction failure.

The future holds the 4D dynamic twin. This is a constantly evolving physics-based model of a city and its base, provided by a dense network of devices that helps predict tremors, liquefaction, land flooding, and the possibility of leaks during early-warning system operation. The feature of such twins is that they combine the probabilistic hazard framework (Cornell, 1968) with the dynamics of rupture, as was first analyzed at Sumatra (Ishii et al., 2005). Thus, it becomes possible to merge the theory with practice.