This thesis describes an investigation into the attenuation of strong earthquake ground motion in the 0. This is attributed to the focus effects of the irregular topography that normally accompanies basement rock outcrops. Since the triggering of rupture depends on details of the mechanism itself, (2) is closely related to (1).
To achieve this, the basic physics of the problem must be considered.
ATTENUATION OF STRONG GROUND MOTION FROM THE SAN FERNANDO EARTHQUAKE
This study will use the corrected accelerograms found in Part II of the series, Strong Motion Earthquake Accelerograms (Hudson, et al., 1971), and Fourier acceleration amplitudes found in Part IV of the series (Hudson, ed. ., 1972). It will be observed in plots of the 16 Hz Fourier amplitude data, where. Digitization noise is seen to dominate the signal at epicentral distances greater than 60 km. Before commencing the large amount of computation required to obtain Fourier transforms of the set of 95 gears, a preliminary study of a smaller group of records was carried out using already available computer data.
In comparison with Figure 3 of Hudson (1972) it can be seen that the range of distribution of peak accelerations in Figure 2.
0 CONST 8
CONST
Surface wave amplitudes at a similar idealized decay in half space relative to the reciprocal of the square root of the distance (see, for example, Bullen, 1963). Because of the amount of scatter in the peak displacement values, it is difficult to say whether or not these are a better fit for the curve whose ordinate is inversely proportional to the epicentral distance, or for that with ordinate proportional to the inverse of the. The general trend in velocity peaks is more clearly proportional to the reciprocal of epicentral.
Surface waves do not dominate peak velocities, and with significant dispersion their amplitude decay is proportional to the inverse epicentral distance.
TRANS
OCMN
The amplitude of the fluctuations appears to be proportional to the amplitude of the underlying smooth function. A third data set was constructed from the Volume IV Fourier amplitudes of the full-length accelerograms. Of the 71 stations in the southern group, three are on basement rocks and the rest are on varying depths of sediments.
The second group is formed from sites north of the epicenter, with source station azimuths in the range 310 to 360 degrees. 9(a), was excluded, or extracted, from the data used in the determination of attenuation parameters and in analyzes of the scattering. Fourier spectra of the horizontal components of record F088, from the Glendale Municipal Services Building, are shown in
The top trace of the fault that caused the San Fernando earthquake is shown in Figure 2. When the results of the experiment are scaled according to the digitization rates of 15 seconds. The period of the actual displacement waveform at the peak displacement was measured between three.
However, even these data (C048 and J145) show no extreme deviations from the behavior of the data set as a whole. The reason for this is found in the least-squares estimation of the attenuation curves obtained by minimizing I:( log k)2.
This observation is confirmed by the statistics of the k-factor distribution for the two components of smoothed, 15-second amplitude data shown in Table 2. For engineering purposes, in view of the much larger uncertainties in the estimation of design earthquakes (for example, in earthquake recurrence and source parameters predicted) these differences are not considered significant. Thus, for a statistical distribution of scattering to be of use in structural design, the smoothing bandwidth used to obtain the statistics must be equal to the range of frequency components that make the main contribution to the response of the structure.
The half-power bandwidth, t:i.f, is a commonly used measure of the bandwidth that makes the most important contribution to the response of a. It is seen from equation (2. 16) that for a given value of (, the half-_Power width increases in direct proportion to natural. 06 7 Hz, the bandwidth resolution of the raw Fourier amplitudes from the 15-second data before smoothing , is also shown in Table 2.
Thus, the scatter distributions found for the smoothed data are useful for structures with 2 to 5% critical damping only at frequencies from about 8 to 16 Hz. The unsmoothed Fourier amplitude data from the southern group of 15-second accelerations are listed in Table A2. The smoothing in the original determination of the noise level leaves too narrow a range for the unsmoothed amplitudes shown in this figure.
Again, the distributions at different frequencies are quite similar, as can be seen from the statistics in Table 2. Given the large number of data, these curves should closely fit the cumulative probability distributions for k corresponding to the two resolution bandwidths.
The smoothed Fourier amplitudes of the full-length accelerations from the southern sites are listed in Table A2. Q and Ai parameter estimates obtained from the MlOHIV data using the least-squares procedures of Section 2. The scatter in these (Ml OHIV) data is quite similar to that of the smoothed 15-s amplitudes.
An additional record, D056, Castaic, is included in the table and attenuation plots for comparison, but is not used to estimate parameters for the group as it lies in an azimuth well separated from the rest of the group. It is interesting to correlate features of the amplitude spectra from the rotated, 15-second records, shown in Figure 2. Continuing to the next location, 0207, the Fairmont reservoir, is the spectrum of the transverse component.
Since the presence of the fault has created the valley, it is reasonable to assume that the width of the fault zone at Lake Hughes is also in this area. For simplicity, a width equal to the depth of the soft fault zone layer is assumed, i.e. 860 feet. The amplitude spectrum of the N21E accelerogram component, which is approximately across the fault at Lake Hughes, is shown in Figure 2 .
At higher frequencies this is not as apparent, possibly due to greater material attenuation of the high-frequency components (note that f acts as a multiplier in the attenuation exponent of. Due to the small number of data it is difficult to compare the spread with the other area in which several data were obtained from the San Fernando earthquake within a narrow range of the source station azimuths is located southeast of the epicenter.
This added more sites in the easternmost part of the southern group, bring the total number of sites in this.
In this chapter, A(f) is considered in more detail, particularly how observed A(f) agrees with A(f) predicted by simple source models of the San Fernando earthquake. The discussion draws on the results of geophysical studies of earthquake rupture mechanisms, and as some of these are not well known in the engineering literature, a brief summary is considered appropriate. Recent intensive research into the nature of the earthquake source has resulted in several different models that relate the radiated seismic wavefield to details of the rupture mechanism.
In this section you will find some results that provide exact solutions to the hypothesized, and in some cases highly specialized, fracture. Maruyama (1963) and Haskell (1964) have presented exact solutions for the dynamic displacement field resulting from the sudden appearance of a random dislocation in an infinite, homogeneous, iso-. Hanks and Wyss (1972) show that the radiated energy can only be limited if the exponent of f is less than -1.
The data of Thatcher and Hanks (1973) show that frequencies of interest in engineering (e.g., 0.05 to 20 Hz) are close to or, more often, above the angle. Haskell also shows that coherent or uniform fracture propagation results in energy being focused in the direction of fracture propagation, and he offers an alternative derivation from Ben-Menahem's (1961) classic work on this subject. The focusing effect of a propagating fracture is superimposed on the four-lobed radiation pattern, commonly denoted Q.Gcp', expected from a dislocation source, and serves to modify it by increasing the frequency.
LOG10 (f/fo)
In the case of the data used in this study, no well-defined pattern emerged from the plot of individual decay-corrected acceleration Fourier amplitudes from the southern set. Since the exact details of the actual fracture mechanism are not known, assumptions are again necessary:-. Because a detailed understanding of the rupture mechanism is lacking, and because of the complexity of the mathematics involved in exact solutions for the idealized rupture mechanisms discussed above, many
Randall (1973a} notes that the exponent y is related to the nature of the highest-order singularity in the dislocation time function and that, in general, instantaneous relaxation sources should have a value of y = 2. Within the two-parameter model, Hanks and Thatcher (1972) and Thatcher and Hanks (1973) investigate the relationships between M and f in. Fourier displacement amplitudes were considered in the preceding discussion following the convention of seismology.
This essentially empirical nature of the simple model must be kept in mind, especially in the. The error bar at 8 Hz shows the 90% confidence interval for As and is indicative of the large uncertainty in the A(f) determination. Little or no real difference can be found between the amplitudes at basement rock sites and those of the group as a whole, in Figures 2.
Independent estimates of the source parameters of the San Fernando earthquake are available from (a) teleseismic observations, (b) field observations of the surface trace of the rupture, and (c) the. In the case of the southern group, this is a good starting point because the fault maximum is modulated by fault propagation.
