Abstract
A probabilistic ground shaking hazard map integrates the parametric contributions of the source-path-site continuum and portrays the spatial and temporal variations of a ground shaking parameter. Each value of ground shaking depicted at a point on a probabilistic map (such as the peak amplitude of ground acceleration, the value of spectral acceleration at a specific period, or the Modified Mercalli intensity) is calculated by summing the contributions of all the earthquake sources. The value at each location represents a specific exposure time (e.g., 50 years), a specific probability of exceedance (e.g., 2-percent or 10-percent), and a specific site geology (e.g., bedrock, stiff soil, or soft soil). More than one map is required to characterize the ground-shaking hazard completely. Probabilistic ground shaking maps are used in model building codes, disaster scenarios, risk assessments, loss estimation, and seismic zonation.
This section describes probabilistic ground motion maps. A probabilistic map is the best way to integrate the parametric contributions of the source-path-site continuum, a model of the community’s earthquake hazard environment, into a map format. Probabilistic ground shaking hazard maps can be used in model building codes, siting and design criteria, disaster scenarios, risk assessments, loss estimation, and in seismic zonation (Hays, Mohammadioun, and Mohammadioun, 1998),
1.1 Key Words and Concepts
Geologists, seismologists, engineering seismologists, and geotechnical engineers have important roles in the analysis of strong ground motion records and in the construction of probabilistic ground shaking maps. The ground motion recorded on a strong motion instrument is characterized by four parameters, each varying as a function of magnitude, the distance from the causative fault, and local site geology. They are:
Peak amplitude (e.g., peak amplitude of horizontal ground acceleration (PGA), or the maximum value of the spectral acceleration (Sa) for a specific period).
Frequency composition (i.e., as depicted by a Fourier analysis or a response spectra).
Duration.
Energy.
The following parameters are typically mapped:
Modified Mercalli intensity (MMI).
Peak ground acceleration (PGA), focusing mainly on the horizontal component.
Peak ground velocity (PGV), focusing mainly on the horizontal component.
Peak ground displacement (PGD), focusing mainly on the horizontal component.
Spectral acceleration ordinates of the horizontal ground shaking at selected periods (e.g., Sa for 0.2 seconds, Sa for 1.0 second), which are related, respectively, to the fundamental period of vibration of low- and high-rise buildings, or certain types of infrastructure.
The maps are used to establish siting and design criteria, disaster scenarios, as a policy tool in seismic zonation, loss estimates, and risk assessments. They are also an integral part of model building codes (e.g., the NEHRP Recommended Provisions for Seismic Design):
The first step in the construction of a probabilistic ground shaking map is to choose the scale of the map (e.g., 1:1,000,000 or 1:24,000) and to prepare a grid of points for the calculations. A Geographic Information System (GIS) can be used to manage the multiple layers of information, which include:
The geographic boundaries and all cultural features of the region at risk.
The fault systems.
The seismicity.
1.2 What Kinds of Information are Required to Construct Ground Shaking Maps?
A triple integral calling for three different summations is solved numerically to calculate the values of a ground motion parameter at each point on the grid. Although the vertical component of ground shaking is important, the highest priority is given to calculating the horizontal ground shaking because of its greater potential for causing damage. The final result is a map depicting the spatial and temporal variations of the horizontal ground motion parameter being mapped. The following types of calculations are performed.
The first summation captures the contributions of all the active faults, as constrained by the seismicity, in the region to the ground-shaking hazard at each point on the grid.
As noted in Session 2, the length of the fault is directly related to the maximum magnitude of the distribution of earthquakes that can be expected to be generated over time. Therefore, the second summation, as constrained by the maximum magnitudes calculated for each fault, captures the contributions of each earthquake in the distribution,
The third summation captures the distribution of ground motion values at each point on the grid by summing the contributions of the seismic waves, which are attenuated by the earth as they propagate from each causative fault to each point on the grid. The constraints are the seismicity and the maximum magnitudes.
Geologists, seismologists, engineering seismologists, and geotechnical engineers acquire, analyze, and integrate many kinds of information in the construction of a probabilistic ground shaking hazard map. They include:
Location of the active faults. Earthquake sources (i.e., active faults) are identified and characterized on the basis of geologic, geophysical, and instrumental, historical, prehistorical data, and in recent years paleoseismicity data. Each active fault is classified in terms of its mode of rupture (e.g., strike-slip, normal, thrust, blind thrust, and subduction zone) and idealized as a point, line, planar, or volume source. Each type of fault contributes to the signature of the amplitude, frequency composition, and duration of ground shaking at a site. Magnitude is controlled by: the length of the fault, its segmentation, the coupling of the individual fault segments, the dynamics of the fault rupture, and the physical dimensions of the fault rupture surface.
Geometry of the faults. The mode of rupture of faulting (i.e., strike slip, reverse or thrust, and normal) and the fault geometry (i.e., the dip, depth, and source dimensions of the earthquake rupture plane) can affect both the amplitude and the geometric attenuation of earthquake ground motion. The style of faulting affects the radiation pattern of the seismic waves, and together with the geometry of the earthquake rupture plane, controls the rate of azimuthal decay of ground motion with distance from the fault plane.
Regional tectonic setting. It is important that the active faults in the region of interest be classified and mapped in terms of their tectonic environment. The amplitude and geometric attenuation characteristics of strong ground motion vary considerably between earthquakes that occur in interplate (plate-margin regions such as California, Japan, and Oregon) and those that occur in intraplate regions (e.g., Midwestern United States).
Spatial and temporal characteristics of seismicity. Although knowledge of the seismic cycle and clustering of large-magnitude earthquakes is still vague for all but a few well-studied fault systems, integration of the historical seismicity record (i.e., the database consisting of Modified Mercalli intensity data, instrumental data, historical data, and paleoseismicity data) with the geologic database on the earthquake sources is a critical factor for estimating "where," "how big," "how often," "when," and "how likely" future earthquakes will recur. The estimates are more certain when the geologic database includes information on the age of the most recent fault displacements, fault slip rate data, and detailed paleoseismicity investigations of historic and prehistoric surface faulting events.
Rate of decay of seismic energy with distance from the point of fault rupture. Knowledge of the regional attenuation function for the ground motion parameter being mapped is essential in the construction of a ground-shaking map. The greatest uncertainty is knowledge of the attenuation characteristics close to the earthquake source (i.e., within 10 km (6 miles) of the causative fault).
Magnitude, other source parameters, and geologic structure. The magnitude governs the long periods of ground shaking and the stress drop controls the short periods. The shape and amplitude of the source spectrum control the overall amplitude, frequency content, and duration of strong ground motion. Therefore, it is important that the maximum moment magnitude, the stress drop, and shape of the source spectrum be determined, to the extent possible, for all active faults in the region of interest. Also, it is important to identify and map important crustal reflectors (e.g., Mohorovicic discontinuity and other mid-crustal reflectors (e.g., the Conrad discontinuity)) in the vicinity of all active faults in the region of interest.
Site response. The physical properties of shallow, near-surface soils (i.e., to a depth of approximately 30 m (100 feet) have the most important influence on the site response. A soil deposit at a site will cause the amplitude, frequency composition, and duration of shaking to differ from those on bedrock. The presence of sediment-filled basins may further modify site response as a function of the geometry of the basin and the properties of the basin sediments. Local topography (i.e., steep slopes, hills, and valleys) can also influence site response.
Uncertainty in physical parameters. Estimates of the uncertainty of the mean and median values of the above parameters of the source-path-site continuum are needed. Quantification of the uncertainty is typically very difficult due to the lack of data and the incompleteness of databases.
1.3 Interactive Exercise (time permitting): Coping With Earthquakes: Integrating the Community’s Hazard, Built, and Policy Environments
1.4 Background References and Internet Resources for This Session
Algermissen, S. T., and D. M. Perkins, A Probabilistic Estimate of Maximum Acceleration in Rock in the Contiguous United States, U S Geological Survey Open-File Report 76-416, Washington, D. C., 77 p. (1976).
Algermissen, S. T., and others, Probabilistic Ground Motion Hazard Maps of Response Spectral Ordinates for the United States, in Proceedings of Fourth International Conference on Seismic Zonation, Stanford, CA, pp. 687-694, (1991).
Bolt, Bruce A., Estimating Seismic Ground Motions, Earthquake Spectra, v. 15, no. 2, pp. 187-197, (1999).
Frankel, Arthur, Thenhaus, Paul, Perkins, David M., and Leyendecker, E. V., Ground Motion Mapping–Past, Present, and Future: in Seminar on New Developments
in Earthquake Ground Motion Estimation and Implications for Engineering Design
Practice, Proceedings, Applied Technology Council, ATC-35, Redwood City, California,
pp. 7-1-7-40, (1994).
Hays, W. W., Procedures for Estimating Earthquake Ground Motions, U S Geological Survey Professional Paper 1114, Government Printing Office, Washington, D. C., 77 p. (1980).
Hays, W. W., Worldwide Assessment of the Status of Seismic Zonation, Fourth International Forum on Seismic Zonation, Proceedings, U S Geological Survey Open-File Report 94-424, Washington, D. C., 44 p. (1994).
Hays, W. W., B. Mohammadioun, and J. Mohammadioun, Seismic Zonation: A Framework for Linking Earthquake Risk Assessment and Earthquake Risk Management: A Monograph, Ouest Editions—Presses Academiques, Nantes, France, 157 p. (1998)
Internet Resources
The probabilistic maps produced by the United States Geological Survey can be downloaded from the USGS
WEB site: http://earthquake.usgs.gov
1.5 Figures and Questions to illustrate Basic Principles
Figure 1:
Schematic illustration of the source-path-site continuum of a community’s earthquake hazard environment.
Questions:
- Describe the cause and effect relationship for each of the parameters of the source-path-site continuum. [Note: Q is a factor characterizing the specific dissipation of the earth’s crust.]
- Indicate how each parameter is determined and quantified.
- Is uncertainty associated with quantification of these parameters? Which ones? Why? How much?
Figure 2: Schematic illustration of the steps involved in the construction of a probabilistic map of horizontal ground shaking.
Questions:
- Describe the consequences of uncertainty on the final map value for each step of the process involving characterization of the local and regional earthquake sources, the regional seismicity, and the regional seismic wave attenuation functions.
- Give three reasons for constructing probabilistic ground shaking hazard maps instead of deterministic ground shaking hazard maps.
- Give three reasons for constructing deterministic ground shaking hazard maps instead of probabilistic ground shaking hazard maps.
Figure 3: Probabilistic map of peak horizontal bedrock ground acceleration, coterminous United States. The map is for a 5-percent probability of exceedance in a 50-year exposure time. [Note: Updated maps are available on the USGS’s WEB site.]
Figure 4: Probabilistic map of peak horizontal bedrock ground acceleration, Central United States. The map is for a 10-percent probability of exceedance in a 50-year exposure time.
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