Glossary¶

The paper this site accompanies is written for specialists. This page is the opposite: it assumes you know nothing about faults, and defines the terms and abbreviations used across this site in plain language. Nothing here is needed to look at the dashboards — but it should make them mean something.

Two shortcuts

Acronyms across the site carry a tooltip — DZW, FDHI, DEM and the rest appear dotted-underlined, and hovering or focusing one shows its expansion without leaving the page. And the search box (top right) covers every term defined below.

The short version¶

When an earthquake happens on certain kinds of fault, the ground doesn't just shake — it can break and step, leaving a visible ridge or slope at the surface called a scarp. That matters for anything built across it: roads, pipelines, power lines. Almost everything on this site is a measurement of a scarp, or a comparison between scarps.

The study behind this site asks which conditions control what that scarp looks like — how deep the sediment is, how strong it is, how steeply the fault is tilted, how far it slips. It answers that with simulations: 3,434 computer experiments in which a modelled fault is pushed until the ground above it deforms, measured automatically at 346,834 separate moments as the slip accumulates.¹ It then checks those simulations against field measurements made by geologists who walked real ruptures after real earthquakes, and suggests the resulting dataset can help forecast ground deformation in future earthquakes.¹

Everything below is the vocabulary needed to read that.

Abbreviations at a glance¶

Short	Full	What it is
DEM	Distinct Element Method	The simulation technique — explained below. Not "digital elevation model", a different thing entirely.
CV	Computer Vision	The machine-learning model that measures each simulated scarp automatically.
DZW	Deformation Zone Width	How wide the disturbed ground is, in the simulations.
FZW	Fault Zone Width	The field record's width measurement.
VS	Vertical Separation	The field record's vertical-offset measurement.
FNC	Fault-Normal Component	Displacement measured perpendicular to the fault trace.
SH	Scarp Height	Height of the step at the surface.
Us	—	Scarp height, in the paper's notation.
Ud	—	Vertical uplift on the fault at depth. The dataset column `VD_HW` holds the same quantity.
Us − Ud	—	"Additional uplift" — see below.
FDHI	Fault Displacement Hazards Initiative	A published compilation of field measurements.
SURE	the name of a database of surface ruptures	A second published field compilation — see below.
IQR	Interquartile Range	A spread measure — see statistics.
OLS	Ordinary Least Squares	The standard way of fitting a straight line to data.
SDC	Surface Deformation Characteristics	The authors' umbrella term for the measured surface quantities: scarp height, DZW and scarp dip.

The simulations¶

Distinct element method (DEM): A way of simulating rock and sediment as a large collection of individual particles that can press against each other, stick together and break apart, rather than as one continuous solid. Deformation is not prescribed — faults, folds and collapses emerge from the particles' interactions. That is what makes the technique suited to this question: you can watch a rupture find its own way to the surface instead of telling it where to go.
Experiment vs model stage: An experiment is one complete simulation run with a fixed set of conditions — a given sediment depth, density, strength, fault dip. A model stage is a single snapshot within that run, taken every 0.05 m as the slip accumulates. Hence 3,434 experiments but 346,834 stages.¹ A row in the data is a stage, not an experiment.
Fault seed: A modelling device, not a real-world feature: a built-in plane of weakness at the intended fault dip, at the base of the model. It makes the simulated fault start where the experiment intends and avoids edge-of-model artefacts. Crucially it does not dictate what happens near the surface — the paper is explicit that there is no preferred slip surface up there, which is exactly what leaves the surface rupture free to emerge.³

Faults, in plain terms¶

Fault: A crack in the Earth's crust where two blocks of rock can slide past each other. An earthquake is that slip happening suddenly.
Thrust and reverse faults: Faults where the crust is being squeezed, so one block is pushed up and over the other. The two words describe the same motion at different steepnesses — thrust faults are the shallower-dipping ones (conventionally under about 45°), reverse faults the steeper. This study covers only these; sideways-sliding faults like the San Andreas are out of scope. The motivation is practical: this kind of rupture damages infrastructure, and field measurements of it are comparatively scarce.²
Hanging wall / footwall: The two sides of a tilted fault. The hanging wall sits above the fault plane — the block pushed upward here. The footwall is below it, and stays put. The names come from mining: a miner in a tunnel along the fault would hang a lamp on one wall and stand on the other.
Fault dip: How steeply the fault plane is tilted, in degrees from horizontal. 20° is gently inclined; 70° is close to vertical. The simulations cover 20, 30, 40, 45, 50, 60 and 70 degrees.
Slip: How far the two blocks moved past each other along the fault. This is what the simulations drive: slip is increased step by step, and the ground surface re-measured at every 0.05 m.¹
Coseismic: "During the earthquake" — as opposed to movement that accumulates slowly between earthquakes.
Scarp: The step, slope or ridge left at the ground surface once slip reaches it. The thing all of this ultimately measures.

What gets measured¶

The simulations measure five things about each scarp: scarp height (Us), vertical uplift on the fault at depth (Ud), additional uplift (Us − Ud), deformation zone width, and scarp dip.⁴ (The paper's abstract lists four, counting Us and Ud together as "uplift".)

   hanging wall                                  footwall
   (lifted by the fault)                         (stays put)

   ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾\                         ─┬─
                             \                        │
                              \___                    │  scarp height
                                  \____                │
                                       \______________─┴─

   ├────── deformation zone width (DZW) ──────┤
   ↑                                          ↑
   first ground disturbance          base of the scarp
   (on the hanging wall)              (on the footwall)

Rough schematic only, and only one of the three scarp shapes. The paper's Figure 5 is the real thing — see The paper.

Scarp height (Us): The total height of the scarp, measured from the top of the undeformed footwall.⁴ Where a pressure ridge forms it can exceed the undeformed hanging-wall surface, because folding and secondary faults add height on top of the fault's own movement.⁴
Deformation zone width (DZW): Measured from the first sign of vertical movement on the hanging wall — uplift, cracking, or collapse — across to the base of the scarp on the footwall side.⁵ It is a width spanning the disturbed ground, not a distance out from the fault line. A wide DZW means the deformation was spread out; a narrow one means it was concentrated.
Scarp dip: The steepness of the scarp face itself, from the top of the scarp to its toe, as an angle from horizontal.⁵ Not the same as the fault dip underground.
Vertical displacement of the hanging wall (VD_HW): How far the upthrown side of the fault actually rose. It is the same quantity the paper calls Ud, and it is what the slip regression plots against slip. VD_HW is the column name it carries in the project's data.
Vertical uplift at depth (Ud) and additional uplift (Us − Ud): Ud is how far the fault itself lifted the hanging wall. Us − Ud is everything else that added height at the surface — folding, secondary faulting — beyond the fault's own throw.⁴ It is near zero for simple scarps and positive for pressure ridges, which is what makes it diagnostic of scarp shape.

The sediment conditions¶

These are the experiment settings, and they appear as dashboard controls.

Sediment depth: How thick the layer of loose material above the fault is.
Density and sediment strength: How tightly packed the sediment is, and how well it resists being pulled apart. Strength is the parameter that most changes which scarp shape forms — weak sediment slumps, strong sediment holds a steep face.
Set — homogeneous or heterogeneous: Whether the sediment is one uniform material top to bottom (homogeneous), or layered with different strengths (heterogeneous, for example a cohesive crust over weaker material).
Cohesion: How strongly the simulated particles are bonded to one another — the model's handle on sediment strength.
Unruptured sediment above the fault tip: How much undisturbed material sits between the top of the fault and the ground surface before slip begins. More of it means the rupture has further to travel before it shows.

The field counterparts¶

Field geologists measured real ruptures with their own conventions, which do not map one-to-one onto the simulations'.

Fault zone width (FZW): The width of the zone of surface rupture recorded in the field compilation, measured across the disturbed ground much as DZW is. The paper treats the principal, central FZW as its DZW equivalent.
Vertical separation (VS): The vertical offset across a rupture measured in the field — how much higher one side ended up than the other.
Fault-normal component (FNC): The horizontal part of the displacement, measured perpendicular to the line of the fault at the surface — how much the two sides moved apart or together rather than up. Recorded by the SURE compilation, and the subject of one panel on the per-event boxplots.

Simulation	Field record	Relationship
Deformation zone width (DZW)	Fault zone width (FZW)	Treated as equivalent.
Scarp height (Us)	Vertical separation (VS)	Assumed comparable, not identical.

That second row deserves emphasis, because the paper is explicit about it: the field compilation contains no measurements of both scarp height and fault zone width for individual thrust and reverse events, so the study assumes measured vertical separation is "similar enough to the scarp heights to foster these comparisons", citing the compilation's own report in support.⁶ The overlay on Model vs reality rests on that assumption.

Principal rupture: The field compilation's label for movement on the main fault trace, as opposed to distributed or secondary breaks nearby. Several panels here keep only principal measurements.

Scarp classes¶

The simulations produce three basic shapes, each of which can additionally be modified by hanging wall collapse.⁷ That gives the six labels you will see in the dashboards' colour legends and axes:

Dashboard label	Shape
`Monoclinal`	inclined slope
`Monoclinal Collapse`	the same, after collapse
`Pressure Ridge`	raised ridge
`Pressure Ridge Collapse`	the same, after collapse
`Simple`	direct offset
`Simple Collapse`	the same, after collapse

Field measurements carry no scarp class — it is a classification of the simulated shapes — so on plots that mix the two, the field points fall outside these categories.

Monoclinal: An inclined slope rather than a sharp step, formed by shearing spread through the sediment. Its steepness is limited by the angle of repose — the steepest angle loose material can hold before sliding.⁸
Pressure ridge: A raised ridge, formed by folding and uplift where two fault strands dip towards each other — a forethrust and a backthrust — squeezing the material between them upward. Tends to form above shallowly-dipping faults.⁹
Simple: The ground surface directly offset by the fault plane. The sediment is strong enough to resist collapsing, so the scarp keeps an overhang and its face matches the fault's dip at depth.¹⁰
…Collapse variants: Any of the three where the sediment could not hold the shape: the oversteepened face fails, both by slumping and by tensile cracking that detaches blocks of material into the base of the scarp.¹¹

The datasets¶

DEM model outputs: The 3,434 simulation experiments described above. Detail on the Data page.
FDHI: The Fault Displacement Hazards Initiative compilation — field measurements from many earthquakes, with location and displacement for each.
SURE: "A worldwide and unified database of surface ruptures … for fault displacement hazard analyses" — a public compilation of surface-rupture observations across many historical earthquakes.¹⁷ It is the source of the fault-normal-component and scarp-height panels on the per-event boxplots, and its measurements appear as reference lines on the distributions histograms. Note the database records no earthquake magnitude of its own; the magnitudes on those panels come from a lookup curated inside this project, sourced from the SURE 2.0 data descriptor (Nurminen et al. 2022).
Kern County (1952): A magnitude 7.36 earthquake on the White Wolf fault in California, and one of the best-documented thrust ruptures on record — first surveyed in the field in the 1950s. Sixteen of its vertical-displacement measurements are the project's worked example for running the model backwards, on the slip regression dashboard.

How the quantities relate¶

This is the part that makes the dashboards click.

Vertical displacement = slip × sin(fault dip): The key relationship. If a fault slips one metre along a plane tilted at angle d, the vertical part of that movement is 1 × sin(d). A shallow 20° fault turns only about a third of its slip into uplift; a steep 70° fault turns almost all of it into uplift. Fitting each dip's simulations separately recovers exactly this — fitted slopes of 0.34, 0.50, 0.65, 0.71, 0.77, 0.87 and 0.94 for dips of 20° to 70°, against sines of 0.34, 0.50, 0.64, 0.71, 0.77, 0.87 and 0.94.¹² That is a consistency check rather than a discovery: the simulations drive the hanging wall along a plane at that dip, so the geometry is built in. The paper uses the relationship because it lets model and field be compared directly.¹³
Running it backwards (back-projection): Because the relationship is so tight, it can be inverted: given a vertical displacement measured in the field, estimate the slip that must have produced it — slip = (vertical − intercept) / slope for the fit at the chosen fault dip. The slip regression dashboard does exactly this, and lets you vary the dip. The paper does this for Kern County and arrives at up to about 3 m of near-surface slip, consistent with independent published estimates.¹⁴ One assumption rides along — what is measured in the field is scarp height, and the inversion treats that as equal to vertical displacement.¹⁴ For simple and monoclinal scarps that holds closely; for pressure ridges scarp height runs higher, which is what Us − Ud measures.
Magnitude: A measure of an earthquake's total energy, on a logarithmic scale — each whole number up is roughly 32× more energy. It appears on this site in two unrelated ways. As an event label on the per-event boxplots, it is the real magnitude of a real earthquake. As an x-axis option on the response curves, it is derived from slip by an empirical formula, not something the experiments controlled — the paper works in near-surface slip precisely because earthquakes of a given magnitude produce a whole range of surface displacements.¹⁵ Treat that axis as a relabelling of the slip axis.

Statistics terms¶

Mean and standard deviation (σ): The mean is the average of the measurements; the standard deviation is how far a typical measurement sits from it. The mean ± σ band on either distributions summary panel spans one standard deviation either side of the mean — pooled over all model stages on the first, computed per 0.05 m slip increment on the second.
Histogram: Counts of measurements falling into equal-width bins, drawn as bars — the upper panel of the distributions dashboard, with ¼ m, 1 m and 5° bins for scarp height, deformation zone width and scarp dip.
Median, quartile, interquartile range (IQR): Sort the measurements. The median is the middle one. The quartiles are the values a quarter and three-quarters of the way along, and the IQR is the gap between them — the range the middle half of the data occupies. A box plot draws exactly this: the box is the IQR, the line inside is the median.
Whiskers and outliers: The lines out from the box reach the most extreme measurement still within 1.5 × IQR of it; anything beyond is drawn separately as an outlier. A long whisker means a scattered tail.
Ordinary least squares (OLS), slope, intercept: Fitting the straight line through a scatter of points that makes the total squared vertical error as small as possible. The slope is how much y rises per unit of x; the intercept is where the line crosses x = 0.
r² (goodness of fit): How much of the variation a fitted line explains, from 0 to 1. The per-dip fits here land above 0.997 — an unusually tight fit, as you would expect from simulations obeying a clean geometric relationship. Careful: the DEM dataset also carries a column called R^2 Value which is something else entirely — a measure of ground-surface roughness from fitting the scarp dip.¹⁶
Log scale: An axis where each step is a multiplication rather than an addition (1, 10, 100, 1000…). Used on the width panels of the per-event boxplots because the values there span from centimetres to over a kilometre, which no ordinary axis can show at once.

Where to go next¶

Model vs reality — the simulations and the field measurements on one plot.
Response curves — how each measured quantity grows as slip accumulates.
Per-event boxplots — how much real measurements vary within a single earthquake.
Slip regression — the slip-to-uplift law per fault dip, run backwards on Kern County.
Distributions — the spread of each output across all simulations, and which input shifts it.
Data — where all four datasets come from.

Please cite as:

Chiama, K., Bednarz, W., Moss, R., Plesch, A., and Shaw, J. H. (2025). "Quantifying relationships between fault parameters and rupture characteristics associated with thrust and reverse fault earthquakes." Earthquake Spectra, 41(5), 3977–4014. DOI: 10.1177/87552930251346434

If you use the underlying data itself, cite the archives it comes from as well — the DEM experiments are deposited open-access on DesignSafe-CI, and the field compilations carry their own citations. The full list, with DOIs, is under How to cite this data.

Any DOI issued for this site or its source code identifies the software and the website, and does not replace the citations above.

Related work, for the wider project's 3D models — not a source for anything shown here:

Chiama, K., Plesch, A., and Shaw, J. H. (2025). "Along-Strike Variability of Surface Deformation on Thrust and Reverse Fault Ruptures: Insights from 3D Distinct Element Method Models." Seismological Research Letters 96(6), 3473–3489. DOI: 10.1785/0220250173

Chiama et al. (2025), abstract — see The paper. ↩↩↩↩
Chiama et al. (2025), introduction: the motivation is the impact of thrust and reverse rupture on the built environment, and the comparative scarcity of measured ground-surface ruptures for these fault types. ↩
Chiama et al. (2025): the fault seed "localizes deformation to the defined slip plane at the base of the model and prevents undesirable boundary condition issues", allowing examination of "how the fault will propagate from a well-defined, weaker fault at depth through overlying sedimentary materials without a preferred slip surface near the surface". ↩
Chiama et al. (2025): the measured characteristics are "scarp height (Us), vertical uplift on the fault at depth (Ud), additional uplift (Us−Ud), DZW, and scarp dip", with Us "measured as the total scarp height from the top of the undeformed footwall block". ↩↩↩↩
Chiama et al. (2025), measurement definitions. ↩↩
Chiama et al. (2025), citing Sarmiento et al. (2021, 2024). ↩
Chiama et al. (2025): monoclinal, pressure ridge and simple scarps, "each of which can be modified by hanging wall collapse". ↩
Chiama et al. (2025): monoclinal scarps "form inclined dip slopes that are limited by the angle of repose of the sediment" and "form through distributed shear of the sediment". ↩
Chiama et al. (2025): pressure ridge scarps "feature folding and uplift due to the presence of both forethrusts and backthrusts" and "generally form above shallowly dipping faults". ↩
Chiama et al. (2025): simple scarps "represent cases in which the ground surface is directly offset by the fault plane", where "the sediment is strong enough to resist gravitational collapse". ↩
Chiama et al. (2025), on collapse-modified scarps — gravitational collapse together with tensile fracturing that detaches colluvium into the base of the scarp. ↩
Computed from the shipped DEM data by the project's own dem_regression view; the coefficients are pinned by subprojects/python/tests/test_regression_views.py in the source repository. ↩
Chiama et al. (2025): Equation 2 "effectively describes the relationship between vertical displacement, slip, and fault dip across all of our DEM models", which "allows us to directly compare the Kern County data and DEM model results". ↩
Chiama et al. (2025): Kern County displacements "yield a near-surface slip of up to 3 m", consistent with independent estimates of 1–3 m and 1–4 m from earlier studies; the relationship uses scarp height "which we assume to equal vertical displacement". ↩↩
Chiama et al. (2025), which focuses on near-surface slip rather than magnitude for this reason. ↩
Chiama et al. (2025): the dataset "reports an R2 value to characterize the ground surface roughness related to the fit of the scarp dip to the rupture". ↩
Baize, S., Nurminen, F., Sarmiento, A., et al. (2019). "A worldwide and unified database of surface ruptures (SURE) for fault displacement hazard analyses." Seismological Research Letters 91: 499–520 — the reference Chiama et al. (2025) cites for this dataset. ↩