Seismic site effects are related to the amplification of
seismic waves
A seismic wave is a wave of acoustic energy that travels through the Earth. It can result from an earthquake, volcanic eruption, magma movement, a large landslide, and a large man-made explosion that produces low-frequency acoustic energy. ...
in superficial geological layers.
[Semblat J.F., Pecker A. (2009) ''Waves and vibrations in soils: earthquakes, traffic, shocks, construction works'', IUSS Press, Pavia, Italy, 499p.] The surface
ground motion
Ground motion is the movement of the earth's surface from earthquakes or explosions. Ground motion is produced by seismic waves that are generated by sudden slip on a fault or sudden pressure at the explosive source and travel through the earth a ...
may be strongly amplified if the geological conditions are unfavorable (e.g. sediments). Therefore, the study of local site effects is an important part of the assessment of
strong ground motion
In seismology, strong ground motion is the strong earthquake shaking that occurs close to (less than about 50 km from) a causative fault. The strength of the shaking involved in strong ground motion usually overwhelms a seismometer, forci ...
s,
seismic hazard
A seismic hazard is the probability that an earthquake will occur in a given geographic area, within a given window of time, and with ground motion intensity exceeding a given threshold. With a hazard thus estimated, risk can be assessed and incl ...
and
engineering seismology
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...
in general. Damage due to an
earthquake
An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in intensity, fr ...
may thus be aggravated as in the case of the
1985 Mexico City earthquake
The 1985 Mexico City earthquake struck in the early morning of 19 September at 07:17:50 (CST) with a moment magnitude of 8.0 and a maximal Mercalli intensity of IX (''Violent''). The event caused serious damage to the Greater Mexico City area ...
. For
alluvial basins, we may shake
bowl of jellyto model the phenomenon at a small scale.
This article defines site effects first, presents the 1985 Mexico City earthquake, describes the theoretical analysis of the phenomenon (through
mechanical waves) and details several research results on seismic site effects in
Caracas.
Definition of the phenomenon
When propagating, the
seismic waves
A seismic wave is a wave of acoustic energy that travels through the Earth. It can result from an earthquake, volcanic eruption, magma movement, a large landslide, and a large man-made explosion that produces low-frequency acoustic energy. ...
are reflected and refracted at the interface between the various geological layers (Fig.1).
The example of Figure 1 depicts the seismic wave amplification in horizontal geological layers. We consider a homogeneous
elastic
Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics.
Elastic may also refer to:
Alternative name
* Rubber band, ring-shaped band of rubber used to hold objects togeth ...
half-space (in green) over which an
elastic
Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics.
Elastic may also refer to:
Alternative name
* Rubber band, ring-shaped band of rubber used to hold objects togeth ...
alluvial layer of constant thickness
is located (in gray). A
shear wave
__NOTOC__
In seismology and other areas involving elastic waves, S waves, secondary waves, or shear waves (sometimes called elastic S waves) are a type of elastic wave and are one of the two main types of elastic body waves, so named because th ...
(
) of amplitude
reaches the interface between the half-space and the alluvial layer with an incidence
. It thus generates:
* a
reflected wave in the half-space with amplitude
and incidence
* a
refracted wave
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
in the superficial layer with amplitude
and incidence
The refracted wave originates a reflected wave when reaching the free surface; its amplitude and incidence are denoted
and
respectively. This latter wave will be reflected and refracted several times at the base and the top of the surficial layer. If the layer is softer than the half-space, the surface motion amplitude can be larger than
thus leading to the ''amplification of
seismic waves
A seismic wave is a wave of acoustic energy that travels through the Earth. It can result from an earthquake, volcanic eruption, magma movement, a large landslide, and a large man-made explosion that produces low-frequency acoustic energy. ...
'' or ''seismic site effects''. When the geological interfaces are not horizontal, it also possible to study seismic site effects by considering the ''
basin effects'' due to the complex geometry of the alluvial filling
[Bard P.Y., Bouchon M. (1985). The two dimensional resonance of sediment filled valleys, ''Bulletin of the Seismological Society of America'', 75, pp.519-541.] For small inclinations of the subsurface layers and/or low impedance contrasts, the assumption of horizontal layering (i.e. the 1D assumption) can still be used to predict site response.
In this article, we propose several examples of seismic site effects (observed or simulated during large earthquakes) as well as a theoretical analysis of the amplification phenomenon.
Example: site effects in Mexico City (1985)
Seismic site effects have been first evidenced during the
1985 Mexico City earthquake
The 1985 Mexico City earthquake struck in the early morning of 19 September at 07:17:50 (CST) with a moment magnitude of 8.0 and a maximal Mercalli intensity of IX (''Violent''). The event caused serious damage to the Greater Mexico City area ...
.
[Singh S.K., Mena E., Castro R. (1988) Some aspects of source characteristics of the 19 September 1985 Michoacan earthquake and ground motion amplification in and near Mexico City from strong motion data, ''Bulletin of the Seismological Society of America'', 78(2), pp.451-477.] The earthquake
epicenter
The epicenter, epicentre () or epicentrum in seismology is the point on the Earth's surface directly above a hypocenter or focus, the point where an earthquake or an underground explosion originates.
Surface damage
Before the instrumental pe ...
was located along the Pacific Coast (several hundreds kilometers from Mexico-City), the
seismic shaking was however extremely strong leading to very large damages.
Figure 2 displays the recordings performed at different distances from the
epicenter
The epicenter, epicentre () or epicentrum in seismology is the point on the Earth's surface directly above a hypocenter or focus, the point where an earthquake or an underground explosion originates.
Surface damage
Before the instrumental pe ...
during the earthquake sequence. The
acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...
amplitude measured at different distances changes drastically:
* ''Campos'' station: this station is located very close to the
epicenter
The epicenter, epicentre () or epicentrum in seismology is the point on the Earth's surface directly above a hypocenter or focus, the point where an earthquake or an underground explosion originates.
Surface damage
Before the instrumental pe ...
and recorded a maximum
acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...
of
,
* ''Teacalco'' station: this station is located at more than 200 km from the
epicenter
The epicenter, epicentre () or epicentrum in seismology is the point on the Earth's surface directly above a hypocenter or focus, the point where an earthquake or an underground explosion originates.
Surface damage
Before the instrumental pe ...
and recorded a much lower
acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...
(about
). This amplitude decay is due to the wave
attenuation
In physics, attenuation (in some contexts, extinction) is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variabl ...
during
the
propagation
Propagation can refer to:
* Chain propagation in a chemical reaction mechanism
*Crack propagation, the growth of a crack during the fracture of materials
* Propaganda, non-objective information used to further an agenda
* Reproduction, and other fo ...
process:
geometrical
attenuation
In physics, attenuation (in some contexts, extinction) is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variabl ...
due to the expansion of the wavefront and material (or intrinsic)
attenuation
In physics, attenuation (in some contexts, extinction) is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variabl ...
due to the energy dissipation within the medium (e.g. grains friction),
* ''UNAM'' station: this station is located at more than 300 km from the
epicenter
The epicenter, epicentre () or epicentrum in seismology is the point on the Earth's surface directly above a hypocenter or focus, the point where an earthquake or an underground explosion originates.
Surface damage
Before the instrumental pe ...
and recorded a maximum
acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...
of
, larger than that recorded at the ''Teacalco'' station,
* ''SCT'' station: this station is located in Mexico City at approximately 400 km from the
epicenter
The epicenter, epicentre () or epicentrum in seismology is the point on the Earth's surface directly above a hypocenter or focus, the point where an earthquake or an underground explosion originates.
Surface damage
Before the instrumental pe ...
and recorded a very strong maximum
acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...
(about
).
We may notice that the acceleration amplitude strongly decreases first and then increases when the seismic waves reach the alluvial deposit on which Mexico City has been founded.
Figure 2a: Shows the effect of resonance: The thickness of the upper geological bed of the modern area of Mexico City is 40 m. The velocity of the shear waves through that layer is 80 m/sec. It means that the natural frequency of that formation is 0.5 Hz (period of 2 seconds). When the shear waves of the same frequency arrived to that area, the resonance was responsible for that huge seismic site effect.
Theoretical analysis of seismic site effects: horizontal layering
In case of horizontal soil layering (constant thickness, cf Fig.1), we may analyze seismic site effects theoretically. One considers a
shear wave
__NOTOC__
In seismology and other areas involving elastic waves, S waves, secondary waves, or shear waves (sometimes called elastic S waves) are a type of elastic wave and are one of the two main types of elastic body waves, so named because th ...
(
) (i.e. polarized perpendicularly to the figure)
reflected and
refracted wave
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
at the interface between both media and
reflected at the free surface.
Considering Fig.1, we may analyze the
propagation of the various waves in the sedimentary layer (
) and in the half-space (
). Assuming both media as linear
elastic
Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics.
Elastic may also refer to:
Alternative name
* Rubber band, ring-shaped band of rubber used to hold objects togeth ...
and writing the continuity conditions at the interface (
displacement
Displacement may refer to:
Physical sciences
Mathematics and Physics
* Displacement (geometry), is the difference between the final and initial position of a point trajectory (for instance, the center of mass of a moving object). The actual path ...
and
traction) as well as the free surface conditions, we may determine the spectral ratio
between the surface motion and the motion at the top of the half-space without any sedimentary layer:
where
;
and :
*
is the layer thickness,
*
is the wave
incidence in layer
,
*
is the
mass density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
in layer
,
*
is the
shear modulus
In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain:
:G \ \stackre ...
in layer
,
*
is the vertical
wave number
In the physical sciences, the wavenumber (also wave number or repetency) is the ''spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temp ...
in layer 1,
*
is the
shear wave velocity
Shear may refer to:
Textile production
*Animal shearing, the collection of wool from various species
**Sheep shearing
*The removal of nap during wool cloth production
Science and technology Engineering
* Shear strength (soil), the shear strengt ...
.
Fig.3 displays the variations of the spectral ratio
with respect to
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
for different mechanical features of the half-space (with
for the sedimentary layer). We notice that the
motion
In physics, motion is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and frame of reference to an observer and m ...
amplification may be very strong at certain
frequencies. The amplification level depends on the
velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...
contrast
and takes the following maximum values:
*
for
(blue curve),
*
for
(green curve),
*
for
(yellow curve).
The red curve corresponds to a large
velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...
contrast between the layer and the half-space (
); the amplification is thus very large. As displayed in Fig.3, the maximum amplification is reached at certain
frequencies corresponding to the
resonance
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...
of the sedimentary layer. The fundamental frequency of the layer (or 1st resonance frequency) may be easily calculated
under the form:
. The fundamental mode thus corresponds to a quarter
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...
resonance
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...
. The "quarter wavelength" approach can be used to estimate site amplifications due to the impedance contrast.
When the sedimentary layers are not horizontal (e.g.
sedimentary basin
Sedimentary basins are region-scale depressions of the Earth's crust where subsidence has occurred and a thick sequence of sediments have accumulated to form a large three-dimensional body of sedimentary rock. They form when long-term subside ...
), the analysis is more complex since
surface waves generated by the lateral heterogeneities (e.g. basin edges) should be accounted for. In such cases, it is possible to perform empirical studies but also theoretical analyses for simple geometries
[Sánchez-Sesma F.J. (1983). Diffraction of elastic waves by three-dimensional surface irregularities, ''Bulletin of the Seismological Society of America'', 73(6), pp.1621-1636.] or numerical simulations for more complex cases.
Seismic site effects in sedimentary basins: the case of Caracas
In
sedimentary basin
Sedimentary basins are region-scale depressions of the Earth's crust where subsidence has occurred and a thick sequence of sediments have accumulated to form a large three-dimensional body of sedimentary rock. They form when long-term subside ...
s, site effects also lead to the generation of
surface waves at the basin edges. This phenomenon may significantly strengthen the amplification of the
seismic motion. The aggravation of the amplification level when compared to the case of horizontal layering may be up to a factor of 5 or 10. It depends on the
velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...
contrast between the layers and the geometry of the basin.
Such phenomena are named ''basin effects'' and we may consider the analogy with the vibrations in
bowl of jelly
The theoretical analysis of site effects in canyons or semi-circular sedimentary basins has been performed through semi-analytical methods in the early 80's.
Recent numerical simulations
allowed the analysis of site effects in ellipsoidal sedimentary basins. Depending on the basin geometry, the aggravation of site effects is different from that of the horizontally layered case.
When the mechanical properties of the
sedimentary basin
Sedimentary basins are region-scale depressions of the Earth's crust where subsidence has occurred and a thick sequence of sediments have accumulated to form a large three-dimensional body of sedimentary rock. They form when long-term subside ...
are known, we may simulate site effects numerically. Figure 4 depicts the amplification phenomenon for the city of
Caracas.
[Duval A.M., Méneroud J.P., Vidal S., Bard P.Y. (1998). Relation between curves
obtained from microtremor and site effects observed after Caracas 1967 earthquake, ''11th European Conference on Earthquake Engineering'', Paris, France.][Papageorgiou A.S., Kim J. (1991). Study of the propagation and amplification of seismic waves in Caracas Valley with reference to the 29 July 1967 earthquake: SH waves, ''Bulletin of the Seismological Society of America'', 81(6), pp.2214-2233] The amplification level of a
plane wave
In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space.
For any position \vec x in space and any time t, ...
(
) is computed by the
Boundary Element Method
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in ''boundary integral'' form), including fluid mechanics, acoustics, el ...
in the
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
domain.
Each color map displays the amplification level
at a given frequency
:
* top:
. Site effects due to the topography clearly occur at the top of the hill (right). Nevertheless, site effects due to the sedimentary basin lead to a larger amplification.
* middle:
. Topographical site effects are negligible when compared to that due to the basin (4 times larger than at 0.3 Hz).
* bottom:
. Site effects in the basin are of the same order than at 0.4 Hz but we notice a much shorter wavelength.
Numerous geological sites have been investigated by various researchers for weak
earthquakes as well as for strong ones (cf synthesis
). In the latter case, it is necessary to account for the
nonlinear behavior of the soil under large loading
or even the
soil liquefaction which may lead to the
soil failure.
References
{{reflist
See also
*
Earthquakes
*
Earthquake engineering
*
Plate tectonics
Plate tectonics (from the la, label=Late Latin, tectonicus, from the grc, τεκτονικός, lit=pertaining to building) is the generally accepted scientific theory that considers the Earth's lithosphere to comprise a number of large ...
*
Seismic hazard
A seismic hazard is the probability that an earthquake will occur in a given geographic area, within a given window of time, and with ground motion intensity exceeding a given threshold. With a hazard thus estimated, risk can be assessed and incl ...
*
Seismic intensity scales
Seismic intensity scales categorize the intensity or severity of ground shaking (quaking) at a given location, such as resulting from an earthquake. They are distinguished from seismic magnitude scales, which measure the magnitude or overall stren ...
*
Seismic magnitude scales
Seismic magnitude scales are used to describe the overall strength or "size" of an earthquake. These are distinguished from seismic intensity scales that categorize the intensity or severity of ground shaking (quaking) caused by an earthquake at ...
*
Seismic risk
Seismic risk refers to the risk of damage from earthquake to a building, system, or other entity. Seismic risk has been defined, for most management purposes, as the potential economic, social and environmental consequences of hazardous events th ...
*
Seismic waves
A seismic wave is a wave of acoustic energy that travels through the Earth. It can result from an earthquake, volcanic eruption, magma movement, a large landslide, and a large man-made explosion that produces low-frequency acoustic energy. ...
*
Seismology
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...
*
Near-surface geophysics
Earthquakes