Intensity Lab
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Why a Simulation Can Differ from What Was Filmed

A simulated seismogram is one plausible version of an earthquake, not a recording of it.

What to expect

We show camera footage of real earthquakes beside animations driven by simulated ground motion for the same earthquake. When the two look different, that is usually not a fault in either one. Simulated shaking at a single place can be off by a factor of two or more, which is roughly one intensity level, and occasionally by more. The reasons fall into five groups: the earthquake source, the model of the crust, the ground under the site, the frequencies that make up the motion, and the limits of the observation it is compared with.

None of these is unique to our pipeline. They are the standing limitations of ground-motion simulation, and they are why seismologists judge a method by its average fit over many recordings, never by one site.

1. The source: how the fault actually broke

A real rupture slips unevenly. Some patches slip several metres and others barely move, the rupture front speeds up and slows down, and the shaking it sends toward a site depends on all of it. Waves pile up ahead of a rupture running toward a site (directivity) and spread out behind it. A simulation cannot know these details for a given earthquake in advance. It builds the fault from a few published numbers:

  • Size from the magnitude, using the Wells and Coppersmith (1994) scaling relations.
  • Orientation from the USGS moment tensor. A moment tensor gives two possible fault planes that fit equally well; we use the one that matches the USGS finite-fault model or the ShakeMap rupture, and fall back to the first plane only when neither is published. The other plane produces different waveforms.
  • Position centred on the epicentre, with the hypocentre halfway down the fault.
  • Slip and rupture speed drawn at random by the simulation method, within ranges calibrated on past earthquakes.

That last point matters most for a comparison. Each animation is driven by one realization: one random draw of how the fault might have slipped. A second draw with a different random seed gives a different seismogram. In measured runs, peak response at a single site changed by under 1% at one site and by about 16% at another between two draws that differed only in the seed. One realization is one sample, not an estimate of the expected shaking.

For large earthquakes, a site close to one end of a long rupture can be shaken mostly by the part of the fault nearest it. A fault built around the epicentre can put the strongest slip in the wrong place for that site.

2. The velocity model: what the waves travel through

Seismic waves speed up, slow down, reflect and focus as they pass through rock of different stiffness. The Broadband Platform describes the crust with a regional one-dimensional model: a stack of flat layers, the same everywhere in the region (Los Angeles Basin, Northern California, Central California, Mojave and others). The real crust is three-dimensional.

  • Sedimentary basins are not represented. Basins such as Los Angeles, San Bernardino and the Santa Clara Valley trap waves and lengthen and amplify shaking at periods of one to several seconds. A layered model cannot produce that trapping, so it tends to underpredict long-period shaking in a basin and can overpredict it on hard rock if the layers are soft.
  • One profile serves the whole region. A hard-rock desert site and a soft valley site in the same region are given the same crust.
  • An earthquake outside every model uses the nearest one. For an event outside all the installed regions, we use the geographically nearest model and label the result approximate. El Mayor-Cucapah (2010, Baja California) is one such event.

Our own checks against recordings found the simulations about 2.6 to 2.9 times too strong at a period of one second for the 2019 Ridgecrest earthquakes. The velocity model is the leading candidate for that, and the question is still open. We publish the measurement rather than leave it out.

3. Site effects: the ground and the building under the camera

The top few tens of metres of soil can double or halve the shaking. The simulation accounts for that through one number, Vs30, the average shear-wave speed in the top 30 m.

  • Vs30 is mapped, not measured. In California it comes from geologic maps (one value per geologic unit), elsewhere from topographic slope. Two neighbouring sites on the same unit get the same value even if their soils differ.
  • 760 m/s means two things. It is a real value for firm rock, and it is also the default we use when no map value is available. A site at 760 m/s may be on rock, or may simply be unmapped.
  • Not modelled: the depth of the soil column, hills and ridges (which can focus shaking at their crests), and the softening of soil in very strong shaking.

Most clips are filmed inside a building, often above the ground floor. A building is not the ground: it filters out some frequencies and amplifies others, especially near its own natural period (roughly 0.1 s per storey). An upper floor can sway far more than the ground under it. Our animated scenes sit on the ground, so a room filmed on the fourth floor can shake visibly harder than an animation of the same ground motion.

4. Frequency content: which shaking the eye sees

Ground motion is a mixture of fast and slow vibrations, and different things respond to different parts of it.

  • Two methods joined at about 1 Hz. The simulation method we use (Graves and Pitarka) computes slow motion, below about 1 Hz, from wave physics, and fast motion, above it, from a calibrated random model. The fast half is right on average, not wave for wave. Rattling, toppling and falling objects respond mostly to the fast half.
  • Long periods move water. A swimming pool sloshes at periods of several seconds and can slosh strongly in shaking that is otherwise light, especially far from a large earthquake. A jug on a table sloshes in a fraction of a second. A pool and a jug side by side respond to different parts of the same ground motion.
  • Our processing. We remove motion slower than 0.1 Hz (periods over ten seconds) before animating, as we do for real recordings, so that integrating acceleration to displacement does not drift. That also removes the permanent offset of the ground right beside a fault.

When no simulation is available for an event, the animation is driven by synthetic motion fitted to the ShakeMap peak acceleration. Its amplitude then matches ShakeMap by construction, but its waveform is a generic one, not a model of that rupture. Every animation is labelled with the motion it used.

5. The observation it is compared with

The clip is not a precise measurement either.

  • A clip reading is good to about one intensity level. A camera shows a few effects, not all of them, and neighbouring levels differ by only a step in their effects. See how clips are rated.
  • The camera's location is often known only to the nearest town. Each comparison says whether the simulation is at the camera, at the town it was filmed in, or at another place in the same earthquake, and how far apart they are.
  • ShakeMap at the camera is itself an estimate, interpolated between seismic stations and reports, with its own uncertainty of about a level away from stations.

What agreement and disagreement tell you

A close match in one clip does not show that the simulation is right, and a mismatch does not show that it is wrong. With one realization, one site and one camera, a difference of a level is within what the five groups above allow. A simulation method is judged by comparing it with many recordings and looking at the average and spread of the misfit, as the validation runs of the simulation service do.

What the comparisons do show well is the character of shaking at a given intensity: how long it lasts, how it builds, and what moves first. That is what they are for. Simulated motions on this site are visualizations, not engineering ground-motion estimates.

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