View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Caltech Authors - Main Bulletin of the Seismological Society of America Vol. 65 April 1975 No. 2 ON CORRELATION OF SEISMOSCOPE RESPONSE WITH EARTHQUAKE MAGNITUDE AND MODIFIED MERCALLI INTENSITY BY M. D. TRIFUNACAND A. G. BRADY ABSTRACT A quantitative measure of the Modified Mercalli Intensity Scale for earth- quakes in ~he western United States has been developed by correlating the peak seismoscope relative displacement response, Sd, with the reported site intensity, IMM. This correlation can be approximated by 1 100.288IM M for IMM =< VIII and is characterized by one standard deviation of about 0.7 Sa. The data used in this study do not indicate an obvious type of dependence of Sa on local site conditions. A method for computing the analog of the local earthquake magnitude, Mseismoscope, has been presented for possible use in strong-motion seismol- ogy and for sealing earthquakes by close-in measurements, when other seismo- logical instruments may go off scale. INTRODUCTION Early notable attempts to develop simple strong-motion recording instruments that would provide the structural engineer with information on response spectrum amplitudes have been carried out by Galitzin (1913), Kirkpatrick (1927), Suyehiro (1926), and the U.S. Coast and Geodetic Survey (Ulrich, 1941). Based on these pioneering ideas and motivated by the increasing need for simple and inexpensive strong-motion recorders, the U.S. Coast and Geodetic Survey and the California Institute of Technology devel- oped the modern version of the strong-motion seismoscope (Hudson, 1958). Similar instruments were concurrently developed and deployed in the U.S.S.R. (Medvedev, 1965) and later in India (Krishna and Chandrasekaran, 1965) and several other countries. In 1972, over 1,200 seismoscopes were reported to have been installed in at least 16 countries (Fournier d'Albe, 1973), with the largest concentrations being in the U.S.A. (400), Yugoslavia (320), and the U.S.S.R. (197). During the last 15 years, numerous seismoscopes registered strong ground motion. These measurements were used to infer the overall response spectrum amplitudes (e.g., Cloud and Hudson, 1961), to study the variability of strong ground motion with distance from an earthquake source and site conditions (e.g., Hudson and Cloud, 1967; Hudson, 307 308 M. D. TRIFUNAC AND A. G. BRADY 1971), and to fill in the detailed information on strong ground motion where accelero- graphs malfunctioned (Trifunac and Hudson, 1970) or were not available (Scott, 1973). In the U.S.S.R., seismoscope response has also been used for correlations with and determinations of intensity of ground shaking (Medvedev, 1965). The purpose of this paper is to explore and to suggest the possibility of an extended usage of this simple and rugged instrument. The motivation for our effort results from the fact that the number of installed seismoscopes is already sufficiently large and can pro- vide significant input to the overall problem of scaling and interpreting strong ground motion. We begin by developing correlations of seismoscope response with earthquake magni- tude and local site conditions. We show that on the basis of such correlations seismo- scope records might be used to infer the local earthquake magnitude in the epicentral region where other more sensitive seismological instruments normally go off scale. Subsequently, as proposed by Medvedev (1965), we develop correlations between the local estimates of earthquake intensity and seismoscope peak response, and in this way derive the approximate scaling laws for response spectra and Modified Mercalli intensities. To avoid possible constraints on the above-mentioned correlations that might result from~the limited amplitude range that can be recorded on the standard seismoscope recording glass (S a ~ 7.5 cm) and to increase the number of usable correlation points, we derive all correlations from the computed values of 186 seismoscope responses obtained from recorded strong-motion accelerograms. COMPUTATION OF SEISMOSCOPE RESPONSE The elementary theory of the response and the physical characteristics of the seismo- scope (Figure l) have been presented in previous papers (Hudson, 1958; Cloud and Hudson, 1961; Hudson and Cloud, 1967; Trifunac and Hudson, 1970) and will not be repeated here. Laboratory and field tests have further shown that seismoscope response, for small amplitudes, can be approximated by a system of two uncoupled second-order differential equations, that the effect of vertical accelerations can be neglected, and that the damping can be modeled by a constant equivalent viscous dash-pot (Trifunac and Hudson, 1970). For large deflections of the seismoscope pendulum, however, more refined theory is required, and the Coulomb-type friction between the smoked glass and the recording needle and the effects of vertical accelerations may be considered. If one neglects the contributions of torsional and higher modes to the calculated response, then the non- linear, coupled differential equations for the deflection angles ¢p and ~ (Figure 2) become ~+2on(~b+con 2 sin ~0 cos ~ = -(ogn2/g) (cos ~0~:+sin cp;~) (la) ~/+209n(~ +¢.On2 sin ~ cos cp -- --(O)n2/g) (COS ~by+sin @~). (lb) In these equations con is the natural frequency of the seismoscope pendulum normally equal to 8.38 rad/sec, ( is the fraction of critical damping for equivalent viscously damped systems, and g is the acceleration of gravity. 2, y and ;~ represent the absolute components of acceleration of the pendulum support. For accurate response calculations the ( dependence on the recorded amplitude is as shown in Figure 3. This functional form has been confirmed by many laboratory experiments (Hudson, 1958). It represents a superposition of the viscous amplitude-independent (5 to 7 per cent of critical) damping resulting from the pendulum mass moving in the magnetic field (Figure 1) and the equivalent viscous damping coefficient, which results from Coulomb friction between the glass and the needle, and is inversely proportional to the response amplitude. CORRELATION OF SEISMOSCOPE RESPONSE WITH M AND IMM 309 FIG. 1. Photograph of the Wilrnot seismoscope with protective cover removed. Z (t) Y Y(9 FtG. 2. Coordinates t# and ~ used in describing the relative seismoscope motion. The general motion of the seismoscope support is described by the general displacement x(t), y(t), z(t). z 141 ~ I i I I t t , I T t I I I I I t- E_ <~ a<~j 12 ~ tC cT - O la_ O _ ~ t.U FrO a.k.~ J I I I I r t I I [ I t i t I i i I 0 o.5 1.0 1.5 AMPLITUDE, CENTIMETERS (ON GLASS) FIG. 3. Functional dependence of the fraction of critical damping on the amplitude of the seismoscope response measured on the recording glass. 310 M. D. TRIFUNAC AND A. G. BRADY The distance between the midpoint of the pivot spring suspension and the top surface of the spherical standard watch glass is about 6.00 cm. This distance is required in con- verting the angular deflections of the pendulum into the recorded amplitude on the spherical glass surface. From the analogy of the differential equations describing the relative motion of a single degree-of-freedom viscously damped oscillator which is used in computations of relative displacement response spectra, Sd, and the equations for small amplitude seismoscope response, it can be shown that (Hudson and Cloud, 1967) gT z Sd = ~2 ~.... (2) where Tis the natural period of the seismoscope pendulum, normally 0.75 sec, and where :~.... measured in radians, is the largest angular deflection of the seismoscope pendulum relative to the z axis(Figure 2) during a particular excitation. The value of :t.... can be computed from the time histories (0(t) and 6(t). For large ¢p and ~ when nonlinear terms in equations (la) and (lb) become significant, equation (2), of course, ceases to corre- spond to its linear displacement spectrum analog. Although valid for large pendulum deflections ~0 and 6, equations (la) and (lb) neglect the contributions to the seismoscope response that may result from torsional, second (Scott, 1973), and higher modes of vibration of the seismoscope pendulum. However, in computing the synthetic seismoscope responses in this paper, we shall neglect those torsional and higher mode contributions because the comparison between the calculated and actually recorded seismoscope responses appears to be quite good. This has been demonstrated on several occasions (e.g., Figures 9 and 10 of Hudson and Cloud, 1967) when both a seismoscope and an accelerograph recorded strong ground motion at the same point permitting direct comparison of the recorded and computed seismoscope responses. CORRELATION OF SEISMOSCOPE RESPONSE AND MODIFIED MERCALLI INTENSITY Earthquake intensity scales are of necessity only descriptive and qualitative measures of vibrational effects caused by earthquakes. These scales depend on numerous factors that can change from one area to another. For example, the material and the type of construction used for residential, industrial and public buildings, the type of geological environment, the time of day when the earthquake occurs, public awareness of an existing earthquake hazard, the methods used in collecting and interpreting intensity data (e.g., Lomnitz, 1970), all can result in significant differences of intensity determination in various parts of the world. One possible remedy for these variations would be the estab- lishment of some instrumental basis for intensity determinations. One instrumental basis for the MKS intensity scale, now used in the U.S.S.R., has been proposed by Medvedev (1965). To this end a conical pendulum, with static magni- fication of 1.1, has been developed. This instrument, called an SBM seismometer, is very similar in construction to the Wilmot type seismoscope used in the U.S. (Hudson, 1958). It records on a spherical smoked glass, has a natural period of T = 0.25 sec, and the fraction of critical damping ( = 0.08.