ESTIMATION OF RESPONSE SPECTRA AND PEAK ACCELERATIONS FROM WESTERN NORTH AMERICAN EARTHQUAKES: AN INTERIM REPORT PART 2

We have derived equations for predicting the larger horizontal and the random horizontal component of peak acceleration and of 2-, 5-, 10-, and 20percent-damped pseudovelocity response spectra for 46 periods ranging from 0.1 to 2.0 sec. The equations were obtained by fitting a functional form to empirical data using a two-stage regression method. 271 two-component recordings from 20 earthquakes were used to develop the equations for peak acceleration, and 112 two-component recordings from 14 earthquakes were used for the response spectral equations. The data included a subset of those used in earlier studies by us (Joyner and Boore, 1981, 1982), augmented by data from three recent earthquakes with magnitudes close to 7: 1989 Loma Prieta, 1992 Petrolia, and 1992 Landers. Besides the addition of new data, this study differs from our previous work in several ways: records at distances equal to and greater than the distance to the first record triggered by the 5 wave were not included (this resulted in eliminating 56 records from our previous data set for peak horizontal acceleration and 19 records from our previous data set for response spectra; in addition, 7 records providing peak acceleration values were removed for a variety of other reasons), we used weighted regression in the second stage of the twostage regression, equations were evaluated at many more periods than previously and for four values of damping, and the smoothing of the regression coefficients over period was done by computer rather than by eye. In addition, we changed the way in which geologic conditions beneath the site are classified. Our previous studies used a binary rock/soil classification. In anticipation of future building code classifications, we now divide site geology into four classes, depending on the average shear-wave velocity in the upper 30m. Site class A includes sites where the average shear-wave velocity is greater than 750 m/s; site class B sites where the velocity is between 360 and 750 m/s; site class C sites where the velocity is between 180 and 360 m/s; and site class D sites where the velocity is less than 180 m/s (site class D class was poorly represented in the data set and has not been included in the analysis). Compared to the predictions from our previous equations, the new results have a lower variance and show differences between site classes at all periods, not just at periods longer than about 0.3 sec. At distances within a few tens of kilometers the motions for our new class B and class C are similar to those for our old rock class and soil class respectively; the motions for our new class A are lower than any of our previous predictions. At large distances the new equations predict larger motions, larger at 80 km by a factor of two or more. INTRODUCTION In earlier studies (Joyner and Boore, 1981; Joyner and Boore, 1982; and Joyner and Boore, 1988) we presented equations for peak horizontal acceleration, velocity, and response spectra as a function of earthquake magnitude, the distance from the earthquake source, and the type of geologic material underlying the site. These equations were based on data obtained through 1980, and they used a binary classification ("rock" and "soil") for the geologic materials. Many more data have been collected since 1980. In particular, three earthquakes in California (1989 Loma Prieta, 1992 Petrolia, and 1992 Landers) have provided data for a range of magnitude and distance, critical for engineering design, which was poorly represented in our previous work. Furthermore, it is likely that future editions of national building codes will use at least a four-fold classification of site geology, based on average shear velocity to a depth of about 30 m. Our long-term goal is to develop prediction equations incorporating all of the data recorded since our earlier work and to reprocess all of the data for the sake of uniformity and to extend the period range covered by the equations. We decided, however, that an interim report would be useful at this time. Most of the post-1980 data that we are not including in this interim study are for magnitudes and distances sampled relatively well in our previous studies, and we expect that the results of our final study will not change greatly from those in this interim report. In this report we give only brief discussions of those matters that were explained in our previous reports; we concentrate instead on topics that are new in this study. DATA Ground Motion Data The set of data to be used in the regression was chosen from the data used in our previous studies combined with recordings of the 1989 Loma Prieta, the 1992 Petrolia, and the 1992 Landers earthquakes. Most of the data were collected by the California Division of Mines and Geology's Strong-Motion Instrumention Program and the U.S. Geological Survey's National Strong-Motion Program. As in our previous studies, we used values for peak acceleration scaled directly from accelerograms, rather than the processed, instrument-corrected values.. We did this to avoid bias in the peak values (e.g., Fig. 5 in Boore and Joyner, 1982) from the sparsely sampled older data. This bias is not such a problem with the more densely sampled recent data. With a few exceptions we used response spectra as provided by relevant agencies; the exceptions are the data collected by Southern California Edison Company and by S. Hough of the U.S. Geological Survey, for which we computed response spectra ourselves. (We use the notation psv for response spectra, and all uses of the term "response spectra" refer to pseudo-velocity response spectra, computed by multiplying the relative displacement spectra by the factor 2?r/T, where T is the undamped natural period of the oscillator [the psv provided by the U.S. Geological Survey for the Loma Prieta earthquake used the damped period, but in the worst case (20 percent damping) this amounts to a difference in response spectra of only 2 percent].) As we did previously, to avoid bias due to soil-structure interaction, we did not use data from structures three stories or higher, from dam abutments, or from the base of bridge columns. In addition, we include no more than 1 station with the same site condition within a circle of radius 1 km. In such cases, we generally chose the station with the lowest database code number and excluded the others. The radius of 1 km is a somewhat arbitrary choice. When a strong-motion instrument is triggered by the S wave, the strongest motion may be missed. In this study, unlike previous studies, we made a systematic effort to exclude records from instruments triggered by the S wave. A strong-motion data set will be biased by any circumstance that causes low values of ground motion to be excluded because they are low, as happens when the ground motion is too weak to trigger the strong-motion instrument, when the ground motion is so weak that an instrument triggers on the S wave, or when records are not digitized because their amplitude is low. To avoid a bias toward larger values, we impose a distance cutoff for each earthquake, beyond which we ignore any data available for that earthquake. This cutoff should logically be a function of geologic condition and trigger level of the recording instrument. We have ignored geologic condition in the determination of cutoff distance in this report, but we have partially considered the effect of trigger level by distinguishing between those stations employing a trigger sensitive to horizontal motion and those that were triggered on the vertical component of motion. Potentially, every earthquake could have two cutoff distances, depending on the type of trigger used in the recorder. In fact, this was only necessary for the 1971 San Fernando earthquake, which occurred during the time of transition between older instruments that trigger on horizontal motion and newer instruments that employ vertical triggers. For peak acceleration, the cutoff distance is equal to the lesser of the distance to the first record triggered by the S wave and the closest distance to an operational nontriggered instrument. For response spectra we chose to presume that amplitude is a factor in deciding which records are digitized, and we set the cutoff distance to the lesser of the distance to the first digitized record triggered by the S wave, the distance to the closest non-digitized recording, and the closest distance to an operational nontriggered instrument. The cutoff distances are given in Table 1. In Table 1, the greater-than sign indicates that the cutoff distance is at an unknown distance greater than that indicated. For the Landers earthquake the digitizing of the analog records is in the early stages, and few records from digital instruments have been released. It is likely that the cutoff distance for response spectra for the 1992 Landers earthquake will increase in the future. In our previous studies we ignored the possible bias introduced by including records triggered by the S wave. Using the cutoff distances shown in Table 1 resulted in the elimination of 56 records from the peak acceleration data and 19 records from the peak velocity data set, a significant fraction of the data used in our previous studies. In addition, 7 records were deleted because information was available only for one horizontal component, because the record was obtained on a dam abutment, or because available information indicated that the site was underlain by muskeg or peat. Table 2 contains a listing of the records used in the previous study that were eliminated from the current analysis. Because of the relatively low sampling rate of the older data (unevenly sampled, but usually interpolated to 50 samples/s), the response spectra are not well determined at periods less than 0.1 s. At longer periods, low signal to noise and filter cutoffs employed in the processing limit the generally useful band to periods less than about 2 to 4 s (we