Response curves¶

The question: how do the measured surface characteristics change as slip accumulates, and which conditions change that relationship?

This dashboard stays inside the simulations — the two-dimensional distinct element method (DEM) experiments — with no field measurements plotted. Each point is one model stage: a snapshot of the modelled ground surface after another 0.05 m of slip. The trend line through them is the relationship you are reading.

Unfamiliar terms?

Slip, fault dip, DZW, Us − Ud, r², and the sediment settings — all defined in the glossary, which also explains why each curve's slope lands near sin(fault dip).

Three controls define the view:

Driver (the x-axis): Slip or Magnitude.
Response (the y-axis): Scarp_Height, DZW, Scarp_Dip, or Us - Ud — the height added at the surface by folding and secondary faulting, over and above what the fault itself lifted.¹
Condition By (the colouring): Scarp_Class (the six shapes — monoclinal, pressure ridge, simple, and each after collapse), Fault_Dip, Cohesion, Set (homogeneous or layered sediment), Density or Sediment_Strength.

Holding the driver fixed and re-colouring by each condition in turn is the fastest way to see which inputs separate the curves and which leave them overlapping. The paper reports that the parameters with most influence on surface rupture patterns are fault displacement, fault dip, sediment depth and sediment strength.¹

The sediment conditions are easier to read as pictures than as labels: Figure 4 shows the six set-ups side by side, and Figure 7 shows how much difference a cohesive top unit makes at the same slip and dip.

Magnitude is a derived axis, not a model input

The experiments are driven by slip, not by magnitude — the paper focuses on near-surface slip rather than magnitude, noting that earthquakes of a given magnitude produce a range of surface displacements.² The Magnitude option on this dashboard is computed from slip through an empirical scaling relation applied in the workbook, so it is a monotone re-labelling of the same axis rather than an independent variable. Read it as a convenience scale, and prefer Slip when the distinction matters.

Open full-size on Tableau Public

Where this comes from¶

This is chart family 2 in the project's inventory, which maps it to the paper's Figure 6 (homogeneous and heterogeneous cases side by side).³ It is the interactive replacement for what the legacy analysis notebooks produced as large static small-multiple grids — in one case 96 separate scatter panels in a single figure, one per material case.³

The underlying data is the DEM experiment set described on the Data page.

Where to go next¶

Model vs reality — put the simulations side by side with measurements from real earthquakes.
Per-event boxplots — how much the field measurements vary within a single earthquake.
Slip regression — that same sin(dip) relationship fitted per dip, then inverted to infer slip from a field measurement.
Glossary — why each curve's slope lands so close to sin(fault dip).

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 — the measured characteristics are scarp height, uplift, deformation zone width and scarp dip. ↩↩
Chiama et al. (2025): the study "focuses on considering the near-surface values of slip on a fault, rather than coseismic slip values at depth", and notes that while it is useful to compare results broadly to event magnitude, they are most appropriately used to estimate deformation for a given local displacement. The derived-axis formula lives in dashboards/tableau/dem-response-curve-public.twb. ↩
notes/chart-families.md in the source repository. ↩↩