The second set of studies would be concerned with what happens to the seismic waves that are emitted from the source into the surrounding environment. Different properties of the medium along the path of wave propagation such as the velocities, the genetics of.
DESCRIPTION OF THE IMPERIAL FAULT
Map (after Richter, 1958) showing the location of the Imperial Fault and the epicenter of the main shock. EPICENTER OF THE MAINSHOCK AND AFTERSHOCKS Because all nearby stations were on one side of the epicenter.
EPICENTER OF THE MAIN SHOCK AND AFTERSHOCKS Because all close stations were on one side of the epicenter of
INTERPRETATION OF THE EL CENTRO STRONG MOTION RECORD
El CENTRO ACCELEROGRAM
ANALYSIS OF DISTANT RECORDS
The Tinemaha EW components of the Wood-Anderson records of both the Brawley event (Figure 1. 7) and the main sequence (Figure. Comparison of the Fourier amplitude spectra for the Brawley event (Figure 1.5a, Figure 1.5b) and the main sequence sequence (Figure 1.4a and 1.
FIELD OBSERVATIONS OF FAULT OFFSET
5 MILES
DISTANCE ALONG IMPERIAL FAULT
COMPUTATION OF SOURCE MOM.ENT USING SEISMI C WAVES S e ismi c mom e nt was c a lculated using r e lations from Ben-
Menahem and Harkrider (1964) for a vertical strike-slip surface error and including a correction for the directivity function, i.e. To take into account the attenuation of the waves due to scattering and anelasticity (along with other sources of energy loss), and to correcting for the angle 5 of the EW component with respect to the direction, the following expression can be written:.
- COMPUTATION OF MOMENT FROM FIELD OBSERVATIONS The computation of the moment from field observations was
- MAGNITUDE AND MOMENT
- CONCLUSIONS
From field evidence, the average displacement along the full length of the fault measured at the ground surface was 1. The magnitude calculated from the moment (long-period waves) will tend to be larger than the magnitude determined from the wave record. with a short period. The interval between relatively large events during the last 5 minutes was on the order of 1 minute.
The natural period of vibration of most buildings will fall in the range of T = o. So £or most buildings excited by a series of events similar to the Imperial Valley earthquake, the vibration will almost die out between most of the individual events. Most of the energy and seismic moment was produced in the main sequence of about 4 events that occurred in the first 15 seconds and were distributed over the same section of the fault.
Two lines of evidence indicate that the seismic energy released in the first 15 seconds was generated by a series of events propagating south from the vicinity of the initial epicenter along a 25 km fault section.
CHAPTER II
MODEL WITH HORIZONTALLY PROPAGATING ENERGY Most of the past theoretical work to determine the effects of
Studies were made of the amplification of the wave amplitudes due to successive reflections and refractions through one or more layers. The rationale for using such a model was that waves at distant stations essentially propagate vertically due to the decreasing speed of wave propagation towards the earth's surface. The motion close to the source of the energy release cannot be described by the above simple wave groups.
It is composed of essentially the same four basic types of waves, but often not clearly separated due to source proximity. Also - source size in relation to the distance to the station, the spatial and temporal distribution of the pattern of. In order to study the movement of strong earthquakes close to the source of the energy release, it is proposed here to consider a model in which seismic energy is propagated along the surface of .
Rayleigh surface waves can also exist in the absence of a surface layer, i.e. along the surface of the infinite uniform half-space, and in that case there is no dispersion of the waveform.
LINE SOURCE IN THE LAYER
LAYER
LINE SOURCE IN THE INFINITE MEDIUM
2 are the velocities of the SH ·waves in the layer and in the infinite medium. Their contribution to the total amplitude of ground motion at the surface will tend to zero as the distance from the source increases to infinity. Many destructive, powerful earthquake motions on Earth are generated near fault systems that often extend to the Earth's surface.
P waves on the strong movement record can be recognized by clear high frequency pulses on the vertical component of the instrument record. The duration of P and S groups on the strong-motion accelerator, close to the source, will be of the order of a few seconds each, depending on the source mechanism. Strong earthquake ground movement, as already mentioned, occurs near the locus of the energy release, which is often a surface fault.
Similarly, it was observed for earthquakes originating north of the Imperial Valley that the intensity of shaking rapidly decays south of the valley (Richter, 1958).
INTENSITY OF SHAKING
DECREASING
FAULT
EARTHQUAKE
B ROCK
ALLUVIUM VALLEY
ON THE SIGNIFICANCE OF THE EXISTENCE OF THE LOW VELOCITY SURF ACE LA YER ON THE
An important problem is how the intensity of the shaking of the soil depends on the properties of the underlying soil. 1 is the speed of propagation of SH waves in layer I (U the circular frequency, cy I e the angle of incidence and. The number of zeros in the mode shape is given by n, period of the vibration 2tr /w, and the speed of the.
The physical significance of the imposed limiting values of rr/2 and a will be shown later. At that point, the effect of the surface layer on the behavior of waves propagating with speed C almost equal to (3. 5 shows the behavior of the normalized ratio r / £ 2 as a function of a and for the first six modes.
This is of course true if the source of energy release generates the same amount of energy in all directions in the xz plane.
The only nonzero component of the ground motion is v in the y direction, which is parallel to the shear vector of the SH waves. The amplitudes of the waves to be analyzed depend only on the x and z coordinates. In particular, the behavior of the wave amplitudes along the surface of the layer is studied as a function of the layer thickness.
In principle, such a problem can only be solved by numerical integration of the differential equation. The function Z(x,z) describes the change in amplitude of particle motion in the right y direction. After determining the form of the solution of equation (3), it is useful to consider some requirements that are necessary for the existence of Love waves in the surface layer.
The normal to the plane front of the SH waves indicates a path of part of the long plane wave front that jumps in the layer.
INCIDENT \
WAVE
INFINITE MEDIUM
By definition, the rate at which that point propagates in the positive x-direction is given by C. From the simple geometry of the ray paths it can therefore be deduced that if any successive reflection is to be realized in the layer, which in turn will lead to a conservation of energy in the layer, the phase velocity C must lie in the interval f31 < c < !32 which is equivalent to the statement e c < e < 1T' /2. There therefore exists a wave in the infinite medium which is not confined to the vicinity of the layer and the fourth boundary condition (6d) is violated.
The requirement that the ray bounding in the layer along etc. interfere constructively may be related to the distance along the ray path from, for example, G to K (Figure 2.6), and the phase shifts experienced at points 1 and 6. 2 This leads to the period equation for love waves (see for example Ewing, Jardetsky and Press, 1957) in the surface layer with a constant thickness H. Because the phase velocity plays an important role in the variation of the amplitude of love waves along the x-direction (see (19)), diagrams showing the phase velocity dependence of the material. properties expressed by the ratios £ and x, and the.
Phase (l\ /C) and group velocity {{3 . 1 /U) curves corresponding to the fundamental state of love waves in the individual surface layer for different conditions x.
LOVE WAVE DISPERSION FOR FIRST MODE
VARIATIONS OF LOVE WAVE AMPLITUDES CAUSED BY CHANGING THICKNESS OF THE LAYER
One of the main objectives of this work is to understand at least qualitatively the relationship between surface wave amplitudes and layer thickness. The importance of the existence of the surface layer has already been considered and has been. This means that as the thickness of the layer increases, the amplitude of the Love waves decreases.
Most of the surface wave energy is probably contained in the fundamental vibrational mode, and it can therefore be tentatively concluded that even in the case where all modes are considered the total resulting change in spectrum amplitudes, even for significant changes in layer thickness, will be of the order of 1. Moreover, gradients along the free surface and lower boundaries of the layer are often smoothly and slowly changing functions for many actual geologic conditions. Up to this point, the treatment of the variation of wave amplitudes has been formal and derived as a consequence of the properties of the period equation and the amplitude of the solution X(x) satisfy.
This is true if the layer thickness is a continuous and smoothly varying function of x, and if the slopes of the layer interfaces are uniformly small, continuous and slowly varying along x.
For example, a variable thickness of the layers underlying the stations, treated from the point of view of a model with vertically incoming shear waves, can be considered. Since T (t} is found to be sinusoidal, one can think of X(x)Z(z) as an amplitude function of the wave motion that describes the behavior of the wave envelope in the xz plane when waves propagate in the x .The behavior of this function along the x-direction will now be investigated for a layer of constant thickness H.
011, so that 11 will be dimensionless measure of distance along x in terms of the layer thickness H. Because the amplitude of the final surface motion is obtained by multiplying X(x) by T(t) and since T(t) is also a sinusoidal function with amplitude equal to unity, in the spectrum calculation, amplitude variations along the x-direction are observed as a variation of the absolute value of the X(x) function. The relative velocity response spectrum represents by definition the maximum amplitude of the velocity response of a viscously damped one degree of freedom system during the time of the earthquake excitation.
It can be shown that there is a close similarity in the shape of the zero-damped relative velocity response spectrum and the Fourier amplitude spectrum of the excitation function (D. E. Hudson, 1962) and that one can be used approximately. - partner representation of the other.
CONCLUSIONS
The constructive interference of SH waves bouncing into the surface layer will introduce the following features into the Fourier amplitude spectrum for the motion at the surface of the layer. Here the term (~)( l+x) is explicitly left in the order term in (51), just to illustrate the x-dependence of the error. Substituting the assumed solution v(x, z, t)=X(x)Z(x, z)T(t) into the differential equation (3) (Part C) yields (omitting the arguments in the functions) .
For the layer of uniform thickness in the x direction, the second term in the brackets in equation (12) would vanish due to the fact that. Since the layer medium is uniform, this change can only occur at the layer boundary. The error analysis so far has focused only on the part of the solution v(x, z, t) in the surface layer, i.e.
0 indicates that the error must also be continuous and of exactly the same order as (34) near the boundary a.(x)H.
