The multiscale analysis involved in evaluation of the USLE coefficients at a given site combines recurrences for earthquakes obtained from the enclosed areas of different size, in order to get enough statistics on larger magnitude shocks from larger surrounding territories for a reliable confident estimation of scaling.
To obtain a seismic risk evaluation based on the concept of the USLE methodology, the following steps are performed: a) characterisation of seismic sources; b) regional seismic effect modelling; c) providing seismic hazard maps; d) obtaining seismic risk estimations for infrastructure based on seismic hazard maps and the end-user hazard mitigation strategy. The following is a description of the algorithm for each of the above steps.
A preliminary data examination should be provided. It takes into account the representative nature and temporal completeness of the earthquake catalog data, regional patterns of the distribution of active faults, parameters of the algorithm for determining the USLE coefficients and options for processing the system of active faults.
Characterization of seismic sources.
The regional seismic sources are characterised by a finite set of earthquake-prone cells {ci} of linear dimension L with expected annual number of earthquakes N(M, L). Nekrasova et al. (2015) elaborately described the Scaling Coefficients Estimation (SCE) algorithm (Nekrasova and Kossobokov 2002), which is a modified version of its prototype (Kossobokov and Mazhkenov 1988). For each ci , with reliable USLE coefficients estimation of N(M, L) can be obtained as
log 10 N (M, L) = A + B (M0 − M) + Clog10L (1)
where A − corresponds to the logarithmic estimate of seismic activity at magnitude M0, normalized to a unit area of 1° × 1° and a unit time of one year, B − the coefficient of magnitude balance, analogous to the b-value of the classical Gutenberg-Richter relationship (Gutenberg and Richter 1954), and C − the fractal dimension of the carrier of earthquake epicenters.
The USLE coefficients are used for estimation of the maximum magnitude Mmax expected with a p% chance of exceedance in T years following the procedures suggested in (Parvez et al., 2014). Specifically, for each ci we apply formula (1) to calculate the expected numbers of events from magnitude ranges Mk in T-years and then find the magnitude Mmax = max{ Mk | T×N (Mk, L) ≥ p% }.
The achieved values of Mmax at the entire set of grid points { ci } are used to compile a set of pairs { (ci, Mi) } for a design of the expected seismic effect in the region considered in terms of macroseismic intensity.
Seismic effect modelling
To describe the seismic effect from each of the earthquake-prone cells ci, we use a model of anisotropic distribution of the macroseismic intensity outside the earthquake source zone (Nekrasova and Kossobokov 2022). In particular, for each pair (ci, Mi) we estimate an elliptical earthquake source zone with semi-axes A(M) = ½×10 α + βM and B(M) = ½×10 γ + δ M where M = Mi and α, β, γ, δ are the constants characterizing typical length and width of the source zone. The constants should be regional, if available, or determined by independent studies in tectonically similar region elsewhere, e.g., (Wells and Coppersmith 1994). The direction of the elliptical shape angle φ is measured from the dominant strike ψ of active faults in the Earth's crust system, defined for the site around ci.
Following Shebalin (1968) we use here the empirical estimate of macroseismic intensity I at distance Δ from of an earthquake epicenter of magnitude M originated at depth h:
$$I=b \times M - \nu \times {\log _{10}}\sqrt {{\Delta ^2}+{h^2}} +c$$
2
where b, v and c are the empirically estimated regional constants.
We assume that seismic waves propagate uniformly from the boundary of the earthquake source zone, so that outside it, macroseismic intensity follows Eq. (3):
I e (M, Δ, h, φ, α, β, γ, δ) = I(M, A(M) + Δr(M, φ), h) (3),
where Δr(M, φ) is the minimum distance from the point (Δ × cosφ, Δ × sinφ) to the boundary of the source zone, namely, to the ellipse with semi-axes A(Mi) and B(Mi) centered at ci, while within the earthquake source zone -
Ie(Mi, Δ, h, φ, α, β, γ, δ) = RAND(I(Mi, A(M), h), I(Mi, 0, h)) (4)
- is randomly distributed from I(Mi, A(M), h) to I(Mi, 0, h). Note that to comply with a qualitative characterization of macroseismic intensity the value of Ie is rounded to the nearest semi-integer, e.g., 7.36 to VII-VIII, 10.12 to X, etc.
We determine the semi-axis A(Mi) as the large one which holds for magnitudes M ≥ 4.9.
Providing Seismic hazard map(s)
The procedure of macroseismic intensity zoning is performed as a definition of boundaries created by merging all areas with the same semi-integer value of macroseismic intensity propagated from seismic source zones with Mmax. The macroseismic intensity zones from one source are determined using equations (3, 4) described in the previous paragraph.
Providing the seismic risk for infrastructure objects
Any kind of risk estimates results from a convolution of the hazard with the exposed object under consideration along with its vulnerability
R(g) = H(g) ⊗ O(g) ⊗ V(O(g)),
where H(g) is natural hazard at location g, O(g) is the exposure of objects at risk at g, and V(O) is the vulnerability of objects at risk. The location g, convolution operator ⊗ and V(O) concerned depend on each certain risk estimation task determined by the end-user.