# Attenuation Relationship

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