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Ground Motion: Complexity and Scaling in the Near Field of Earthquake Ruptures

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Extreme Environmental Events

Article Outline

Glossary

Definition of the Subject

Introduction

Characterizing Earthquake Source Complexity

Wave Propagation in Complex Media: Path and Site Effects

Ground‐Motion Scaling Relations

Future Directions

Acknowledgments

Bibliography

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Abbreviations

Attenuation relation (ground‐motion prediction equation):

The term “attenuation relation”is a former short-hand notation in earthquake engineering for “empirical ground‐motion attenuation relationship”, now referred to as “ground‐motion prediction equation” (GMPE). Attenuation relations represent empirical scaling equations that relate observed ground‐motion intensity measures to parameters of the earthquake source, the wave propagation from the source to the observer and the site response at the observer location.

Dynamic rupture model :

Dynamic rupture models build a physical understanding of the earthquake rupture based on the material properties around the source volume, and the initial and boundary conditions for the forces/stresses acting on the fault plane. The distribution of on-fault slip-rate vectors and the temporal rupture evolution is obtained by solving the elasto‐dynamic equations of motion under an assumed constitutive law (friction model), considering the energy balance at the crack tip (Chap. 11 in [6]). See also kinematic rupture model.

Ground motion intensity measures :

Earthquake shaking due to seismic waves, observed at recording sites or experienced by people and structures, is commonly reported in terms of various scalar intensity measures that capture parts of the transient wave-field. Seismogram‐based ground‐motion intensity measures are, for instance, peak ground acceleration (PGA) and peak ground velocity (PGV), while the modified Mercalli intensity (MMI) is a damage‐related measure. In earthquake engineering, ground‐motion intensities are often reported as response spectra : the response of an idealized building (modeled as a single‐degree-of‐freedom oscillator) of given eigenperiod T and damping ζ (usually 5%) to a given ground‐motion time series. Spectral acceleration (S A ), spectral velocity (S V ) and spectral displacement (S D ) are analyzed considering the period of the structure.

Ground motion uncertainty :

In ground‐motion prediction for engineering purposes, random (aleatory) variability and scientific (epistemic) uncertainty are distinguished. The latter is due to incomplete knowledge and/or limited data, and is captured by alternative empirical attenuation relations or different ground‐motion simulation strategies. Aleatory variability is quantified in terms of a standard deviation of an attenuation relation or by a large number of model realizations within a particular simulation method. The distinction between aleatory variability and epistemic uncertainty is particularly useful in probabilistic seismic hazard analysis (PSHA) .

Kinematic rupture model :

A kinematic rupture model characterizes the time‐dependent displacement field on the rupture plane without considering the forces or stresses acting on the fault and causing its motion. The rupture process is completely specified by the spatio‐temporal distribution of the slip vector, the local slip‐velocity function on the fault, and the rupture velocity with which the rupture propagates over the fault plane. See also dynamic rupture model.

Path effects :

Seismic waves propagating through the Earth are sensitive to the detailed geologic structure along the wave path, generating pronounced waveform complexities. Considering crust and upper‐mantle structure (relevant for near-field ground motions) three major elements to path effects are distinguished in practice: (a) waves in a flat‐layered attenuating Earth ; (b) basins and other deterministic deviations from a flat‐layered model ; (c) random heterogeneities in the three‐dimensional velocity‐density structure . The distinction between path effects and site effects is often ambiguous.

Rise time :

The rise time (or slip duration) τ r measures how long each point on the fault moves during the rupture process, and must not be confused with the rupture duration. The rise time is related to the slip‐velocity function, and is usually measured as the time it takes to attain 5–95% of the final slip at each point. For simple parametric slip‐functions (e. g. boxcar, isosceles triangle or combinations thereof), the rise time is generally given by the width of this function.

Rupture duration :

The rupture duration characterizes the total time for the earthquake rupture process to complete, starting at the nucleation point (hypocenter) and lasting until the last point on the rupture plane stops sliding. Rupture duration therefore depends on rupture velocity and scales with the size (source dimension) of the earthquake.

Rupture velocity :

Earthquake ruptures, either modeled as propagating cracks or slip‐pulses, expand over the fault plane at rupture speeds (v r ) close to the local shear-wave velocity (v S ), typically in the range \({0.5 \cdot v_s \leq v_r \leq 0.9 \cdot v_S}\), or about 1.0–\({{3.5}\,\mathrm{km/sec}}\) for crustal earthquakes. However, the crack tip, the transition region from unbroken, intact rock to the currently slipping zone, does not necessarily travel at constant rupture speed. Rupture velocity may locally slow down or accelerate, even to super-shear velocities (in which case the crack front travels at speeds faster than the local shear-wave velocity), depending on the initial and boundary conditions that govern the dynamic rupture process.

Site effects :

Site effects refer to wave‐propagation effects in the immediate proximity to the observation point; they are distinguished from path effects which comprise the complete path from the source to the receiver (although the boundary between these two is often ill defined). The local sedimentary cover , topography , strong geologic contrasts or water-table variations may contribute to site effects that modify the incoming “bedrock” seismic motions.

Slip distribution :

The slip distribution represents the cumulative slip on each point on the fault acquired during the co‐seismic rupture process (i. e. small contributions from post‐seismic slip episodes are ignored). A slip distribution for an earthquake is computed from the space-time integration of slip‐velocity functions on the rupture plane.

Slip‐velocity function (Slip-rate function) :

Each point participating in the rupture process experiences a time‐dependent slip history during which the two sides of the fault go through a stage of acceleration, stable sliding, deceleration, and final stopping. This local displacement trajectory is often represented in terms of a slip‐velocity function (or slip function) whose details depend on the dynamic rupture process and the constitutive behavior of the host rock. Slip-rate functions are often modeled using simple parametric functions.

Source effects:

Amplitudes and waveform character of seismic waves are strongly affected by source effects, i. e. by the details of the earthquake rupture process . Far-field signals carry the signature of the overall “point‐source” earthquake source mechanism; near-field recordings are very sensitive to the spatio‐temporal details of the rupture process, characterized in a finite‐fault source model either as kinematic or dynamic rupture model.

Static stress drop :

The static stress drop \({\Delta\sigma}\) represents the difference between the initial and final stress across the fault before and after an earthquake, and is related to slip on the fault. It is defined, based on a shear crack with uniform stress drop, as \({\Delta\sigma = C\cdot\mu\cdot D / L_c}\), where μ is the shear‐modulus, D the mean slip over the fault, L c a characteristic length scale (usually the smallest dimension of the rupturing fault), and C a constant of order unity which depends on the source geometry. Using the fault width W as characteristic length, static stress drop is related to the seismic moment, \({M_o = \mu\cdot L\cdot W\cdot D = C\cdot \Delta\sigma \cdot A^{3/2}}\), where A is fault area, and L is fault length. Inferred values of static stress drop are in the range of 0.1–10 MPa, independent of seismic moment , leading to the generally assumed self‐similar constant stress‐drop scaling (see Earthquake Scaling Laws). The static stress drop must not be confused with the dynamic stress drop  [164] which captures the time‐dependent stress change on a point of the fault during the dynamic faulting event, and may be significantly higher or lower than the static stress drop.

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Acknowledgments

I am indebted to J. Bühler for generating several figures for this article. J. Ripperger provided simulation data for Fig. 5. Thanks to P. Spudich for computing isochrone quantities and synthetics shown in Fig. 11. Strong‐motion data were taken from the COSMOS strong‐motion database (http://db.cosmos-eq.org). Critical comments and helpful suggestions by J. Clinton, G. Cua, and S. Jonsson greatly improved the article. I am also grateful for constructive reviews by R. Harris and Y. Ben-Zion. Parts of this work was supported by the Southern California Earthquake Center; SCEC is funded by NSF Cooperative Agreement EAR‐0106924 and USGS Cooperative Agreement 02HQAG0008. This is SCEC contribution number 1154.

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  1. Swiss Seismological Service, Institute of Geophysics, ETH, Zürich, Switzerland

    P. Martin Mai

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    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Mai, P.M. (2011). Ground Motion: Complexity and Scaling in the Near Field of Earthquake Ruptures. In: Meyers, R. (eds) Extreme Environmental Events. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7695-6_34

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