The Classical Probabilistic Seismic Hazard Analysis (cPSHA) approach allows calculation of hazard curves and hazard maps following the classical integration procedure (Cornell , McGuire ) as formulated by Field et al. .
Hazard Curves are discrete functions which describe probability of ground motion exceedance in a given time frame. Hazard curves are composed of several key elements:
For a given calculation, hazard curves are computed for each logic tree realization, each IMT/IML definition, and each geographical point of interest. (In other words: If a calculation specifies 4 logic tree samples, a geometry with 10 points of interest, and 3 IMT/IML definitions, 120 curves will be computed.)
Another way to put it is:
T = R * P * I
Hazard curves are grouped by IMT and realization (1 group per IMT per realization). Each group includes 1 curve for each point of interest.
Additionally, for each realization a hazard curve container (with output_type equal to hazard_curve_multi) is created. This container output could be used in contexts where you need to identify a whole group of hazard curves sharing the same realization as when you run a risk calculation supporting structure dependent intensity measure types.
The classical hazard calculator is also capable of producing mean and quantile curves. These aggregates are computed from the curves for a given point and IMT over all logic tree realizations.
Similar to hazard curves for individual realizations, statistical hazard curves are grouped by IMT and statistic type. (For quantiles, groups are separated by quantile level.) Each group includes 1 curve for each point of interest.
Mean hazard curves can be computed by specifying mean_hazard_curves = true in the job configuration.
When computing a mean hazard curve for a given point/IMT, there are two possible approaches:
Technically, both approaches are “weighted”. In the first approach, however, the weights are implicit and are taken into account in the process of logic tree sampling. This approach is used in the case of random Monte-Carlo logic tree sampling. The total of number of logic tree samples is defined by the user with the number_of_logic_tree_samples configuration parameter.
In the second approach, the weights are explicit in the caluclation of the mean. This approach is used in the case of end-branch logic tree enumeration, whereby each possible logic tree path is traversed. (Each logic tree path in this case defines a weight.) The total number of logic tree samples in this case is determined by the total number of possible tree paths. (To perform end-branch enumeration, the user must specify number_of_logic_tree_samples = 0 in the job configuration.
The total number of mean curves calculated is
T = P * I
Furthermore, also in that case a hazard curve set grouping all the mean curves is produced (of type hazard_curve_multi).
Quantile hazard curves can be computed by specifying one or more quantile_hazard_curves values (for example, quantile_hazard_curves = 0.15, 0.85) in the job configuration.
Similar to mean curves, quantiles curves can be produced for a given point/IMT/quantile level (in the range [0.0, 1.0]), there are two possible approaches:
As with mean curves, unweighted quantiles are calculated when Monte-Carlo logic tree sampling is used and weighted quantiles are calculated when logic tree end-branch enumeration is used.
The total number of quantile curves calculated is
T = Q * P * I
Moreover, also in that case curves sharing the same quantile are grouped into a virtual output container of type hazard_curve_multi.
Hazard maps are geographical meshes of intensity values. Intensity values are extracted from hazard curve functions by interpolating at a given probability exceedance. To put it another way, hazard maps seek to answer the following question: “At the given level probability, what intensity level is likely to be exceeded at a given geographical points in the next X years?”
The resulting geographical mesh is often depicted graphically, with a color key defining which color to plot at the given location for a given value or range values.
Hazard maps bear the same metadata as hazard curves, with the addition of the probability at which the hazard maps were computed.
For a given calulcation, hazard maps are computed for each hazard curve. Maps can be computed for one or more probabilities of exceedance, so the total number of hazard maps is
T = C * E
Note: This includes mean and quantile maps.
Hazard maps can be produced from any set of hazard curves, including mean and quantile aggregates. There are no special methods required for computing these maps; the process is the same for all hazard map computation.
Uniform Hazard Spectra (UHS) are discrete functions which are essentially derived from hazard maps. Thus, hazard map computation is a prerequisite step in producing UHS. UHS derivation isn’t so much a computation, but rather a special arrangement or “view” of hazard map data.
UHS “curves” are composed of a few key elements:
To construct UHS from a set of hazard maps, one can conceptualize this process as simply extracting from multiple hazard maps all of the intensity measure levels for a given location and arranging values in order of SA period, beginning with the lowest period value. This is done for all locations.
Note: All maps with IMT = SA are considered, in addition to PGA. PGA is equivalent to SA(0.0). Hazard maps with other IMTs (such as PGV or PGD) are ignored.
The example below illustrates extracting the IML values for a given location (indicated by x) from three hazard maps:
Hazard maps PoE: 0.1 /--------------/ / /<-- PGA [equivalent to SA(0.0)] / x /-/ /--------------/ /<-- SA(0.025) / x /-/ /--------------/ /<-- SA(0.1) / x /-/ /--------------/ /<-- SA(0.2) / x / /--------------/
Assuming that the IMLs from the PGA, SA(0.025), SA(0.1), and SA(0.2) maps are 0.3, 0.5, 0.2, and 0.1, respectively, the resulting UHS curve would look like this:
[IML] ^ | 0.5 * | 0.4 | 0.3 * | 0.2 * | 0.1 * | +----|-------|-------|-------|----> [SA Period] 0.0 0.025 0.1 0.2
Uniform Hazard Spectra are grouped into result sets where each result set corresponds to a probability of exceedance and either a logic tree realization or statistical aggregate of realizations. Each result set contains a curve for each geographical point of interest in the calculation.
The number of UHS results (each containing curves for all sites) is
Tr = E * (Q + M + R)
The total of UHS curves is
T = Tr * P
The Event-Based Probabilistic Seismic Hazard Analysis (ePSHA) approach allows calculation of ground-motion ﬁelds from stochastic event sets. Eventually, Classical PSHA results - such as hazard curves - can be obtained by post-processing the set of computed ground-motion ﬁelds.
Stochastic Event Sets are collections of ruptures, where each rupture is composed of:
SES results are structured into 3-level hierarchy, consisting of SES “Collections”, SESs, and Ruptures. For each end-branch of a logic tree, 1 SES Collection is produced. For each SES Collection, Stochastic Event Sets are computed in a quantity equal to the calculation parameter ses_per_logic_tree_path. Finally, each SES contains a number of ruptures, but the quantity is more or less random. There are a few factors which determine the production of ruptures:
From a scientific standpoint, the MFD for each seismic source defines the rupture “occurrence rate”. Combined with the investigation time (specified by the investigation_time parameter), these two factors determine the probability of rupture occurrence, and thus determine how many ruptures will occur in a given calculation scenario.
From a software implementation standpoint, the random seed also affects rupture generation. A “base seed” is specified by the user in the calculation configuration file (using the parameter random_seed). When a calculation runs, the total work is divided into small, independent asynchronous tasks. Given the base seed, additional “task seeds” are generated and passed to each task. Each task then uses this seed to control the random sampling which occurs during the SES calculation. Structuring the calculation in this way guarantees consistent, reproducible results regardless of the operating system, task execution order, or architecture (32-bit or 64-bit).
Event-Based hazard calculations always produce SESs and ruptures. The user can choose to perform additional computation and produce Ground Motion Fields from each computed rupture. (In typical use cases, a user of the event-based hazard calculator will want to compute GMFs.)
GMF results are structured into a hierarchy very similar to SESs, consisting of GMF “Collections”, GMF “Sets”, and GMFs. Each GMF Collection is directly associated with an SES Collection, and thus with a logic tree realization. Each GMF Set is associated with an SES. For each rupture in an SES, 1 GMF is calculated for each IMT (Intensity Measure Type). (IMTs are defined by the config parameter intensity_measure_types.) Finally, each GMF consists of multiple “nodes”, where each node is composed of longitude, latitude, and ground motion values (GMV). The sites (lon/lat) of each GMF are defined by the calculation geometry, which is specified by the region or sites configuration parameters. (In other words, if the calculation geometry consists of 10 points/sites, each computed GMF will include 10 nodes, 1 for each location.)
It is possible to produce hazard curves from GMFs (as an alternative to hazard curve calculation method employed in the Classical hazard calculator. The user can activate this calculation option by specifying hazard_curves_from_gmfs = true in the configuration parameters. All hazard curve post-processing options are available as well: mean_hazard_curves, quantile_hazard_curves, and poes (for producing hazard maps).
Hazard curves are computed from GMFs as follows:
As with the Classical calculator, it is possible to produce mean and quantile statistical aggregates of curve results.
The Scenario Siesmic Hazard Analysis (SSHA) approach allows calculation of ground motion ﬁelds from a single earthquake rupture scenario taking into account ground-motion aleatory variability.
The Disaggregation approach allows calculating relative contribution to a seismic hazard level. Contributions are defined in terms of latitude, longitude, magnitude, distance, epsilon, and tectonic region type.
Hazard curve calculation is the first phase in a Disaggregation calculation. This phase computes the hazard for a given location by aggregation contributions from all relevant seismic sources in a given model. (The method for computing these curves is exactly the same as the Classical approach.)
Mean and quantile post-processing options for hazard curves are not enabled for the Disaggregation calculator.
Once hazard curves are computed for all sites and logic tree realizations, the second phase (disaggregation) begins. While the hazard curve calculation phase is concerned with aggregating the hazard contributions from all sources, the disaggregation phase seeks to quantify the contributions from the various ruptures generated by the source model to the hazard level at a given probability of exceedance (for a given geographical point) in terms of:
This analysis, which operates on a single geographical point and all seismic sources for a given logic tree realization, results in a matrix of 6 dimensions. Each axis is divided into multiple bins, the size and quantity of which are determined the calculation inputs. Longitude and latitude bins are determined by the coordinate_bin_width calculation parameter, in units of decimal degrees. Magnitude bins are determined given the mag_bin_width. Distance bins are determined by the distance_bin_width, in units of kilometers. num_epsilon_bins defines the quantity of epsilon bins. truncation_level is taken into account when computing the width of each epsilon bin, and so this is a required parameter. The number of tectonic region type bins is simply determined by the variety of tectonic regions specified in a given seismic source model. (For instance, if a source model defines sources for “Active Shallow Crust” and “Volcanic”, this will result in two bins.)
The final results of a disaggregation calculation are various sub-matrices extracted from the 6-dimensional matrix. These sub-matrices include common combinations of terms, which are as follows:
Each disaggregation result produced by the calculator includes all of these.
The total number of disaggregation results produce by the calculator is
T = E * R * I * P
Note: In order to not waste computation time and storage, if the hazard curve used to a compute disaggregation for a given point and IMT contains all zero probabilities, we do not compute a disagg. matrix for that point.