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Secondary surface displacement models#

Moss2022SecondaryFD#

class openquake.pfd.secondary_surf_displ.moss2022.Moss2022SecondaryFD[source]#

Bases: BaseSecondarySurfDispl

Distributed (secondary) displacement exceedance model for reverse faults.

Two methods:

  • 'gamma' - Uses the global gamma distribution (Eqs 4.2–4.3) for the d/MD ratio, with its mean rescaled by the distance-dependent envelope (Eq. 5.8). Integrated over MD(M) uncertainty the same way as the primary FD model.

  • 'envelope' - Deterministic: assumes d_secondary = MD × envelope(r), then integrates over MD uncertainty to obtain P(d > d₀).

Distance r is received in km (adapter convention, matching ctx.r). Envelope Eq. 5.8 operates in km directly.

Reference: GIRS-2022-05, Sections 5.3–5.4. DOI: 10.34948/N3F595

Model contract: DISPLACEMENT_DEFINITION = “distributed”, DISPLACEMENT_COMPONENT = “vertical” – distributed reverse-fault displacement normalised by the principal MD/AD, from vertical-offset measurements (GIRS-2022-05 Section 5). No APPLICABILITY_RANGE is declared: the report documents its envelopes per Section 5 without a single distance limit comparable to the Valentini et al. (2025) Table 4 entries (report-specific validity).

Petersen2011SecondaryFD#

class openquake.pfd.secondary_surf_displ.petersen2011.Petersen2011SecondaryFD(pixel_size=None, cell_size=None)[source]#

Bases: BaseSecondarySurfDispl

Distributed fault-displacement model of Petersen et al. (2011) for strike-slip faults.

Petersen, M.D., et al. (2011). Fault displacement hazard for strike-slip faults. Bulletin of the Seismological Society of America, 101(2), 805-825.

Model contract: DISPLACEMENT_DEFINITION = “distributed”, DISPLACEMENT_COMPONENT = “lateral” – distributed displacement of strike-slip earthquakes, measured as the lateral component like the companion principal model (Petersen et al. 2011; Sarmiento et al. 2025 Table 1 component convention as for PEA11). Declared applicability: r up to 2 km from the principal fault – the paper’s distributed dataset is explicitly “limited to 2 km distance from principal fault” (ibid., data description for eq. 18 / Tables 4-5); beyond that the power law extrapolates.

Takao2013SecondaryFD#

class openquake.pfd.secondary_surf_displ.takao2013.Takao2013SecondaryFD(n_sigma=3.0, norm_disp_type=None)[source]#

Bases: BaseSecondarySurfDispl

Distributed fault-displacement model of Takao et al. (2013).

The distributed displacement DD is normalized by the maximum (PMD) or average (PAD) displacement of the principal fault. The 90% non-exceedance level decays exponentially with the closest distance r [km] from the principal fault (paper Eqs. 15-16):

DD/PMD = 0.55 exp(-0.17 r) DD/PAD = 1.9 exp(-0.17 r)

Following Youngs et al. (2003), the conditional distribution of the normalized displacement is a gamma distribution with shape a = 2.5 whose scale b(r) is anchored so its 90th percentile equals the regression above (paper Eq. 17). PMD and PAD follow the paper’s magnitude scaling (Eqs. 9-10), lognormal with the Wells & Coppersmith (1994) sigmas:

log10(PMD) = -5.16 + 0.82 Mw (sigma 0.42) log10(PAD) = -4.80 + 0.69 Mw (sigma 0.36)

The PMD/PAD lognormal is integrated over mean ± n_sigma·sigma (log10 space); n_sigma defaults to 3 and may be overridden from the logic tree via [Takao2013SecondaryFD] n_sigma = <value>.

Model contract: DISPLACEMENT_DEFINITION = “distributed”, DISPLACEMENT_COMPONENT = “net” – distributed displacement normalised by the principal-fault PMD/PAD net-slip scaling (Takao et al. 2013, Eqs. 15-17; component convention per Valentini et al. 2025, Rev. Geophys., Table 4). Declared applicability: r up to 20 km (ibid., dataset range of the Eqs. 15-16 regressions).

Visini2025SecondaryFD#

class openquake.pfd.secondary_surf_displ.visini2025.Visini2025SecondaryFD(n_sigma: float = 3.0, truncation_eps: float = None, style=None, scaling_model=None, tpfm=None, case=None, rupture_traces=None)[source]#

Bases: BaseSecondarySurfDispl

Distributed (secondary) displacement exceedance model (Visini et al., 2025).

This implements the empirical regression for the exceedance probability P(Y > d), assuming a lognormal residual on ln(Y). The regression median uses predictors ln(s), ln(TPFm), Mw, style, footwall/hanging-wall, and combination offset (A/B/C).

Parameters used across methods#

  • d (m): Displacement threshold.

  • mag (Mw): Earthquake magnitude.

  • s (m): Distance to the principal fault trace.

  • rx (m): Signed cross-fault distance (negative on the footwall).

  • X_L_ratio: Normalized along-strike position (0..1).

  • dip (deg): Fault dip angle (affects throw = slip * sin(dip)).

  • tpfm (m): Mean throw on principal fault. If None, computed from scaling.

  • style: ‘normal’ or ‘reverse’.

  • combination: ‘A’, ‘B’, or ‘C’.

  • scaling_model: ‘WC1994’ | ‘THINGBAIJAM2017’ | ‘LEONARD2010’

  • n_sigma: half-width of ln(Y) truncation in σ units (MATLAB scripts use 3).

Model contract: DISPLACEMENT_DEFINITION = “distributed”, DISPLACEMENT_COMPONENT = “vertical” – the predicted quantity Y is the vertical throw of Rank 2 distributed ruptures (Visini et al. 2025; the regression’s TPFm predictor is likewise a throw). Declared applicability (in the model’s own segments-r metric, see MULTIFAULT_REFERENCE_LINE): the paper excludes data closer than 5 m to the principal rupture (Visini et al. 2025, pp. 11, 20 – such near-trace scarps are not distinguishable from principal faulting), so r_min = 5 m; the outer edges are 10 km on the hanging wall and 8 km on the footwall, the dataset range summarised in Valentini et al. (2025, Rev. Geophys., Table 4). The paper further differentiates its recommended ranges per Combination A/B/C (Visini et al. 2025, p. 14 and Conclusion; e.g. Combination B is only meaningful within ~1 km of a declared Rank 1.5 trace, cf. the user-manual model page); the values declared here are the outermost HW/FW envelope, which is what the once-per-run extrapolation warning needs.

Youngs2003SecondaryFD#

class openquake.pfd.secondary_surf_displ.youngs2003.Youngs2003SecondaryFD(percentile=None, style=None)[source]#

Bases: BaseSecondarySurfDispl

Distributed fault-displacement model of Youngs et al. (2003).

Youngs, R.R., et al. (2003). A methodology for probabilistic fault displacement hazard analysis (PFDHA). Earthquake Spectra, 19(1), 191-219.

Model contract: DISPLACEMENT_DEFINITION = “distributed”, DISPLACEMENT_COMPONENT = “vertical” – distributed (off-fault) vertical separation of normal-faulting earthquakes, normalised by the principal maximum displacement (Youngs et al. 2003; Sarmiento et al. 2025 Table 1 component convention as for YEA03). Declared applicability: r up to 15 km from the principal fault (dataset range summarised in Valentini et al. 2025, Rev. Geophys., Table 4).

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