**Open**-Source **S**eismic **H**azard **A**nalysis (**OpenSHA**)

The following is a list of terms commonly used in OpenSHA and in seismic hazard analysis in general.

- Attenuation Relationship
- Distance
- Earthquake Rupture
- Earthquake Rupture Forecast (ERF)
- Epsilon
- Fault
- Frankel Fault Surface
- Gridded Surface
- Ground Motion Prediction Equation (GMPE)
- Hanging Wall & Foot Wall
- Hazard Data
- Intensity Measure (IM)
- Intensity Measure Relationship (IMR)
- Intensity Measure Type (IMT)
- Magnitude
- Magnitude Frequency Distribution (MFD)
- Magnitude Scaling Relationship
- NGA Models
- Probabilistic Earthquake Source
- Rupture Surface
- Shaking Component
- Shear Wave Velocity (Vs)
- Sigma Truncation
- Simple Fault
- Site
- Standard Deviation
- Stirling Fault Surface
- Strike, Dip, & Rake (Focal Mechanism)
- Wills Site Classification

An **Attenuation Relationship** is a type of Intensity Measure Relationship (IMR) that assumes the Intensity Measure Level (IML) (or logarithm thereof) is both a scalar and exhibits a Gaussian distribution. The mean and standard deviation of the Gaussian distribution (and exceedance probabilities derived therefrom) are computed from various parameters, the types of which are discussed below. Of course by virtue of being an Intensity Measure Relationship (IMR), the mean and standard deviation can also be computed from a given Site and Earthquake Rupture. Attenuation relationships are sometimes referred to as Ground Motion Prediction Equations (GMPEs). There are no limits on what types of parameters an attenuation-relationship author can choose to make their model depend upon. However, the following gives the various categories these parameters must fall under, as well as a few common examples for each:

These parameters are obtained or computed from a given Earthquake Rupture and include:

- Magnitude(M
_{W}) - Average Rake
- Average Dip
- Rupture Top Depth

Site-specific parameters that may include:

These parameters are computed from a given Site and Earthquake Rupture and may include:

- Distance
- Hanging-Wall Data
- Directivity Data

Parameters common to many attenuation relationships that don’t fall into the categories above:

- Component (e.g., Avg. Horizontal, GMRotI50, Vertical, Random Horizontal, Greater of Two Horizontal)
- Standard Deviation Type (e.g., Total, Inter-Event, Intra-Event, Zero)
- Sigma Truncation Type (e.g., None, One-Sided, Two-Sided)
- Sigma Truncation Level

Parameter values are numeric unless otherwise indicated with options.

In OpenSHA, **Distance** refers to the distance between an Earthquake Rupture and a Site. However, many Attenuation Relationships use different criteria to define distance. These are the currently supported definitions:

The shortest distance from a site to a *rupture surface*.

The shortest distance from a site to a point on a *rupture surface* that is deeper than some minimum *seismogenic depth*.

The Joyner-Boore distance defined as the shortest distance from a site to the surface projection of the *rupture surface*.

The shortest horizontal distance from a Site to a line defined by extending the *fault trace* (or the top edge of the rupture) to infinity in both directions. Values on the *hanging-wall* are positive and those on the *foot-wall* are negative.

The difference between *DistanceRup* and *DistanceJB* (normalized by *DistanceRup*).

The difference between *DistanceRup* and *DistanceX* (normalized by *DistanceRup*).

See entry on Earthquake Rupture for definition of terms: *rupture surface, seismogenic depth, fault trace, hanging-wall, foot-wall*

In OpenSHA, an **Earthquake Rupture** refers to an event that generates seismic energy as a result of slip on a fault. For large and relatively well-studied events, a rupture may be represented as a portion of a fault that slips during the event. For smaller and less well-studied events, a rupture may be represented simply as a point source. An Earthquake Rupture is defined by a:

- Magnitude(M
_{W}) - Average Rake
- Rupture Surface
- Hypocenter (optional)

A location on a Rupture Surface that marks where earthquake slip nucleates.

An **Earthquake Rupture** with an associated probability of occurrence. See also Probabilisitic Earthquake Source.

An **Earthquake Rupture Forecast (ERF)** is one of the two main modeling components in OpenSHA, the other being an Intensity Measure Relationship (IMR). An **ERF** gives a forecast of all possible Earthquake Ruptures) as their probability of occurrence over a specified **Time Span**. In OpensSHA, an ERF is given as a list of Probabilistic Earthquake Sourcess) and includes information on its region of applicability.

Given an earthquake with a specified magnitude and distance from a site of interest, Epsilon is a measure of how ground motion deviates from the expected mean. In most cases, one is interested in a ground motion that has a probability of being exceeded over some time period. This is often quite different than the most likely (or mean) ground motion that would be experienced if the event were to occur at any time and epsilon characterizes this variability. Please see the USGS Deaggregation site for more detailed information and references

In the context of OpenSHA, a fault is a relatively planar surface or discontinuity in the earth that can accomodate slip that manifests as earthquakes (see Wikipedia for more info on faults). OpenSHA describes fault geometries in several ways:

The most common type of fault representation in OpenSHA is that of a Simple Fault. A Simple Fault encapsulates the basic information required to define a fault geometry and is one possible basis for Gridded Surfaces such as the Frankel and Stirling Fault Surfaces.

OpenSHA can accomodate these additional fault types:

- Subduction Zones (see the USGS SLAB project)
- Listric Faults

These other fault types may also be gridded.

A **Frankel Fault Surface** is one representation of a Gridded Surface that was created by Arthur Frankel for use in the 1996 and 2002 USGS National Seismic Hazard Maps. See also Earthquake Rupture. In OpenSHA, the trace and average dip of a Simple Fault are used to create rectangular surfaces where the dip direction of each rectangle is perpendicular to the strike of its local segment. The resulting surface is then gridded (discretized) according to whatever interval is specified. Compare to a Stirling Fault Surface.

To facilitate modeling larger earthquakes of various sizes, OpenSHA treats fault and rupture surfaces as gridded surfaces. Gridding makes it easier to both represent arbitrary degrees of surface complexity, and to reference a subset of a larger surface (e.g., for when an Earthquake Rupture occurs on only part of a fault). Depending on the type of Fault being gridded, OpenSHA can accomodate evenly discretized grids (e.g. the fault surface definitions of Frankel and Stirling) or approximately uniformely spaced grids (e.g., for subduction zones).

This is synonymous with Attenuation Relationship (OpenSHA uses the latter).

For a dipping fault, the **Hanging Wall** is the block positioned over the fault, the **Foot Wall** is the block positioned under it. See the cross-sections below and the Wikipedia entry on faults for more information.

More information related to faults can be found in the Rupture Surface and Strike Dip, & Rake glossary entries.

Output from seismic hazard calculations generally takes two forms:

A plot of the probability of exceedance versus an Intensity Measure Level (IML) for a specified Intensity Measure Type (IMT).

A map view of the probability that an IMT will exceed a specified IML, or the IML that has a specified probability of being exceeded (the former is actually the correct definition, but the latter is commonly used as well).

An **Intensity Measure** is an attribute of earthquake shaking that is useful for predicting damage or loss. It is defined by an:

An IMT specifies the particular type of Intensity Measure. IMTs currently implemented in OpenSHA include:

- Peak Ground Acceleration (PGA)
- Peak Ground Velocity (PGV)
- Peak Ground Displacement (PGD)
- Spectral Acceleration (SA)
- Modified Mercalli Intensity (MMI)

OpenSHA was designed so that virtually any other IMT may be defined and implemented. For example, a new IMT might be composed of a vector of traditional IMTs.

An IML specifies the level, or value, of the IMT that one is concerned about exceeding. For example, one might want to know that probability that Peak Ground Velocity (the IMT) will exceed a level of 100 cm/sec (the IML).

An **Intensity Measure Relationship (IMR)** is one of the two main modeling components in OpenSHA, the other being an Earthquake Rupture Forecast (ERF). An **IMR** gives the probability of exceeding some Intensity Measure Level (IML) of a specified Intensity Measure Type (IMT) given a Site of interest and an Earthquake Rupture.

Note that no presumptions are made with respect to how probabilities are computed, leaving the possibility of using full waveform modeling from first principles of physics. At present most IMRs implemented in OpenSHA constitute empirical Attenuation Relationships, although waveform modeling is being implemented in collaboration with the SCEC CyberShake project. See the figure at right for information on other potential types of IMRs.

The **Intensity Measure Types** supported in OpenSHA include:

The peak ground acceleration during an earthquake measured in units of ‘g’ (gravity).

The peak ground velocity during an earthquake measured in units of ‘cm/sec’ (cgs)

The peak ground displacement during an earthquake measured in units of ‘cm’ (cgs).

The maximum acceleration of a damped, single-degree-of-freedom harmonic oscillator, measured in units of ‘g’ (gravity). Spectral acceleration is an approximate measure of what is experienced by a building during an earthquake and is further specified by:

*Spectral Period:*the natural period (seconds) of the oscillator*Spectral Damping:*the degree of damping for the oscillator (usually 5%)

More information on SA is available at the USGS.

A Roman numeral describing the severity of an earthquake in terms of its effects on the earth’s surface and on humans and their structures (see also Wikipedia).

See also Intensity Measure

In OpenSHA “Magnitude” is synonymous with “Moment Magnitude” (in keeping with the USGS Earthquake Magnitude Policy). Moment Magnitude = (log(Seismic Moment) - 9.05)/1.5 where Seismic Moment is given in SI units (Newton-meters).

A **Magnitude Frequency Distribution** is a function that describes the rate (per year) of earthquakes across all magnitudes. An MFD can have an analytical form or, as in the case of OpenSHA implementations, be described by rates of earthquakes over descrete intervals. In addition to an arbitrary distribution, the following types of distributions are currently supported in OpenSHA:

- Single-Mag Distribution
- Gutenberg-Richter Distribution
- Tapered Gutenberg-Richter Distribution
- Gaussian Distribution
- Youngs and Coppersmith Distribution (AKA the”Characteristic” Distribution)
- Summed Magnitude Frequency Distribution (the sum of other distributions)

One can learn more about these using the *Magnitude-Frequency Distribution Plotter*.

A magnitude-scaling relationship gives mean Magnitude as a function of rupture *area* or *length* (or visa versa), where *length* and *area* are given in units of km and km-sq, respectively. **Currenly Implemented Magnitude-Area Relationships:**

- Wells and Coppersmith (1994,
*Bull. Seism. Soc. Am.*):**Mag = 4.07+0.98*log(**(all rupture types)*Area*)**Mag = 3.98+1.02*log(**(strike slip rupture)*Area*)**Mag = 4.33+0.90*log(**(reverse or thrust rupture)*Area*)**Mag = 3.93+1.02*log(**(normal rupture)*Area*)**Area = 10\^(-3.49+0.91***(all rupture types)*Mag*)**Area = 10\^(-3.42 + 0.90***(strike slip rupture)*Mag*)**Area = 10\^(-3.99 + 0.98***(reverse or thrust rupture)*Mag*)**Area = 10\^(-2.87 + 0.82***(normal rupture)*Mag*)- Uncertainty on
*Mag*is 0.24, 0.23, 0.25, and 0.25 for all, strike slip, reverse, and normal ruptures, respectively. - Uncertainty on log(
*Area*) is 0.24, 0.22, 0.26, and 0.22 for all, strike slip, reverse, and normal ruptures, respectively.

- Hank & Bakun (2002 & 2008,
*Bull. Seism. Soc. Am.*)**Mag = 3.98+log(**(if*Area*)*Area*<= 537)**Mag = 3.07+(4/3)*log(**(if*Area*)*Area*> 537)- These equations are inverted to get
*Area*from*Mag* - No uncertainty estimates given

- Ellsworth (2003, published in Chapter 4 and Appendix D of the 2002 Working Group on California Earthquake Probabilities)
(Equation 4.5a, AKA “Ellsworth A”)*Mag*= 4.1+log(*Area*)(Equation 4.5b, AKA “Ellsworth B”)*Mag*= 4.2+log(*Area*)(Equation 4.5c, AKA “Ellsworth C”)*Mag*= 4.3+log(*Area*)- These equations are inverted to get
*Area*from*Mag* - Uncertainty on
*Mag*is 0.1

**Currenly Implemented Magnitude-Length Relationships:**

- Wells and Coppersmith (1994,
*Bull. Seism. Soc. Am.*):**Mag = 5.08+1.16*log(**(all rupture types)*Length*)**Mag = 5.16+1.12*log(**(strike slip rupture)*Length*)**Mag = 5.00+1.22*log(**(reverse or thrust rupture)*Length*)**Mag = 4.86+1.32*log(**(normal rupture)*Length*)**Length = 10\^(-3.22+0.69***(all rupture types)*Mag*)**Length = 10\^(-3.55+0.74***(strike slip rupture)*Mag*)**Length = 10\^(-2.86+0.63***(reverse or thrust rupture)*Mag*)**Length = 10\^(-2.01+0.50***(normal rupture)*Mag*)- Uncertainty on
*Mag*is 0.28, 0.28, 0.28, and 0.34 for all, strike slip, reverse, and normal ruptures, respectively. - Uncertainty on log(
*Length*) is 0.22, 0.23, 0.20, and 0.21 for all, strike slip, reverse, and normal ruptures, respectively.

These are the Attenuation Relationships developed as part of the PEER “Next Generation Attenuation” (NGA) project.

To provide independent verification of OpenSHA’s implementations of the NGA models, Kenneth Campbell (EQECAT Inc.) computed a suite of test files. These files provide mean and standard-deviation values for a sufficiently wide range of parameter settings to suggest that OpenSHA implementations are correct, or at least consistent with independent computations. The test files and README are available here (2.8 MB .zip file). The tests include ~170,000 test calculations, the results of which all of which match to within 0.05%. Each file has a single-line header to label the columns. The first nine columns represent values of the following parameters:

**Mw**- Magnitude**Rrup**- DistanceRup (km)**Rjb**- DistanceJB (km)**Rx**- DistanceX (km)**Dip**- Average Dip of the rupture plane (degrees)**W**- Down Dip Width of rupture plane (km)**Ztor**- Rupture Top Depth (km)**V**- V_{s}30_{s}30 (m/sec)**Zsed**- Depth 1.0 km/sec or Depth 2.5 km/sec depending on the model (km)

*(note that not all the above are used by each NGA model)* The columns that follow represent the mean or natural-log standard deviation for various spectral periods, SA (g), plus PGA (g) and PGV (cm/s). There are 30 separate files for testing: different NGA models, different focal mechanisms, mean versus standard deviation (sigma), whether sites are on the hanging wall, whether the event is an aftershock, and whether V_{s}30 is measured or inferred/estimated.

A **Probabilistic Earthquake Source** is a list of mutually exclusive Probabilistic Earthquake Ruptures. As an example, a Probabilistic Earthquake Source could be defined for a particular fault as a list of all possible Earthquake Ruptures corresponding to a range of Magnitudes that could occur on the fault or Rupture Surface. A Probabilistic Earthquake Source can also encapsulates the following information:

- Number of Probabilistic Earthquake Ruptures in the list
- Total Probability (sum of those in the list)
- Total Probability above a specified Magnitude
- Whether or not the source is Poisson (if yes, the probability for each Probabilistic Earthquake Rupture is interpreted as the probability of
*one or more*events, otherwise it’s interpreted as the probability of the*next*event)

A Probabilistic Earthquake Source is also always defined in the context of an Earthquake Rupture Forecast (ERF), so the event probabilities are with respect to the Time Span associated with the ERF.

In OpenSHA, a **Rupture Surface** is the surface that slips during an earthquake (see Earthquake Rupture). It may be represented in a variety of ways:

**Point Surface**– Used to represent point-source earthquakes.**Gridded Surface**– Used to represent entire faults (e.g. the uniformely gridded Frankel Fault Surface, Stirling Fault Surface, and Listric Surface. We also have an Approximately Gridded Surface that is used for subduction zones).**Subset Surface**– Used to represent subsets of entire Gridded Surfaces (see figure to right) when modelling earthquakes of different sizes on an individual fault.

A Fault Surface is further defined by a:

The depth (in km) to the shallowest point on an earthquake **Rupture Surface**.

The average width of an **Rupture Surface** measured in the down-dip direction.

The **Component** of shaking of interest for an Intensity Measure (IM). Current options in OpenSHA include:

Usually defined as the geometric average of the maximum of the two horizontal components (which may not occur at the same time).

Because *Average Horizontal*, above, is dependent on seismometer orientation, this was defined by Boore et al. (2006, *Bull. Seism. Soc. Am.* 96, 1502-1511).

A randomly chosen horizontal component.

The vertical component.

The largest value obtained from two perpendicular, horizontal components.

In seismic hazard analysis, the **Shear Wave Velocity** at a Site is of interest because it gives an indication of whether the expected shaking in response to an Earthquake Rupture may be higher. For instance, at a bedrock site (high shear-wave velocity) there will be little amplification of seismic waves, whereas in a sedimentary basin (low shear-wave velocity) one might expect intense amplification. There are several ways that shear-wave velocity data is incorporated into seismic hazard calculations:

The average shear-wave velocity between 0 and 30-meters depth. Some Attenuation Relationships require knowing whether a Vs30 value was *Measured* or *Inferred*. More information is available at the USGS Global Vs30 Map Server site

The depth (km) to where shear-wave velocity = 1.0 km/sec (the first occurrence if more than one depth exists).

The depth (km) to where shear-wave velocity = 2.5 km/sec (the first occurrence if more than one depth exists).

The **Truncation** of a Gaussian distribution applied when computing probabilities. A Sigma Truncation must also specify a *Truncation Level* (in units of sigma). Current options in OpenSHA include:

No truncation.

Truncation of upper side of distribution only.

Truncation of both upper and lower sides of distribution.

The geometry of a **Simple Fault**, the most common fault type used in OpenSHA, is described by the fault’s **Trace**, **Average Dip** and **Upper** and **Lower Seismogenic Depths**. This is the minimum information required to define surfaces on which slip associated with earthquakes occurs. Simple Faults may be gridded according to different algorithms (e.g. see the Frankel and Stirling Fault Surface definitions).

A line marking the intersection of a fault (rupture) surface with the surface of the earth. In OpenSHA a Fault Trace is represented with a list of locations (latitude, longitude, depth).

The average dip (angle between the earth’s surface and fault plane) along the length of the fault.

The depth (in km) of the lower limit of seismogenic rupture. This depth is generally based on the maximum depths of microsesmicity in a given region.

The depth (in km) of the upper limit of seismogenic rupture. This depth is generally applied regionally to reduce near surface seismic energy (moment) release in hazard models (to match observations).

A **Site** is any location where one is interested in knowing the seismic hazard or risk. Site-specific effects, such as varying shear-wave speed as a function of changing geology, may modulate any computation of hazard.

See also V_{s}30

The type of **Standard Deviation** used in an Attenuation Relationship calculation. Current options in OpenSHA include:

The total variability.

The variability from one event to the next.

The variability among observations within an event.

Assumes no variability.

A **Stirling Fault Surface** is one representation of a Gridded Surface as defined by Mark Stirling (and perhaps others). See also Earthquake Rupture. In OpenSHA, the trace and average dip of a Simple Fault are used to create a corrugated surface by translating the Fault Trace down dip, perpendicular to the average fault strike. The resulting surface is then gridded (discretized) according to whatever interval specified is specified. Compare to a Frankel Fault Surface.

OpenSHA defines strike, dip and rake according to the conventions set forth by Aki and Richards (1980), *Quantitative Seismology*, Vol. 1. In OpenSHA, as elsewhere, strike, dip, and rake are used to describe earthquake **Focal Mechanisms**. Please see the USGS and Wikipedia entries on focal mechanisms for more information.

Fault strike is the direction of a line created by the intersection of a fault plane and a horizontal surface, 0° to 360°, relative to North. Strike is always defined such that a fault dips to the right side of the trace when moving along the trace in the strike direction. The hanging-wall block of a fault is therefore always to the right, and the footwall block on the left. This is important because rake (which gives the slip direction) is defined as the movement of the hanging wall relative to the footwall block.

Fault dip is the angle between the fault and a horizontal plane, 0° to 90°.

Rake is the direction a hanging wall block moves during rupture, as measured on the plane of the fault. It is measured relative to fault strike, ±180°. For an observer standing on a fault and looking in the strike direction, a rake of 0° means the hanging wall, or the right side of a vertical fault, moved away from the observer in the strike direction (left lateral motion). A rake of ±180° means the hanging wall moved toward the observer (right lateral motion). For any rake>0, the hanging wall moved up, indicating thrust or reverse motion on the fault; for any rake<0° the hanging wall moved down, indicating normal motion on the fault.

```
Dip = 90° Rake = 0° :: left-lateral strike-slip
Dip = 90° Rake = 180° :: right lateral strike slip
Dip = 45° Rake = 90° :: reverse fault
Dip = 45° Rake = -90° :: normal fault
```

See also the Wikipedia and USGS entries on strike and dip.

This is the site-type classification scheme developed by Wills et al. (2000, *Bull. Seism. Soc. Am.*, vol. 90, p. 187-208). The categories and their **Vs30** equivalents are:

Site Class | Vs30 range (m/sec) |
---|---|

B | >760 |

BC | 555-1000 |

C | 360-760 |

CD | 270-555 |

D | 180-360 |

DE | 90-270 |

E | <180 |

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