Strong motion data of 10 controlled explosion experiments conducted in 1977 at the Lyaur testing range in the Republic of Tajikistan are revisited. The explosions were detonated in arrays, with time delay between detonation of array lines. Ground accelerations, as large as ~1.6g, were recorded at 4 sites by SMA-1 accelerographs. The records were recently digitized and processed with modern accelerogram data processing software. The amplitude and spectral characteristics of these data are here compared with those of strong earthquake shaking data and other published explosion data. The comparison of the Fourier amplitude spectra with estimates by recent empirical scaling laws for strong ground motion, in the near-field of earthquakes, suggests that such explosions can offer powerful possibilities (at present forgotten and neglected) for testing of almost full scale structures (1/2 to 1/3 scaled models). It is suggested that by going into rather than avoiding the nonlinear zone surrounding the explosions, new testing methods can be developed to simulate near-field nonlinear strong motion of soft soils, found in most metropolitan areas in the seismically active regions.
 

Full-scale experimental measurements of structural response are essential for verification of earthquake resistant design codes and for providing new independent data for development of improved methods of analysis and design. Since the 1933 Long Beach, California, earthquake, many strong motion recordings have been obtained in buildings, bridges, dams and other structures. This data has provided a true representation of how man-made structures behave during actual strong shaking (Kojic et al., 1984; Udwadia and Trifunac, 1974). However, because it is not possible to predict the time and the location of future earthquakes, it is difficult to carry out systematic planned experiments. Consequently the rate of accumulation of data in full-scale structures tends to be slow.

The total energy, E, released by earthquakes with magnitudes M = 5 to 9⁺ is in the range between 10¹⁹ and 10²⁶ ergs (log₁₀ E = 1.5M + 11.8; Gutenberg and Richter, 1956). In the near-field of destructive earthquakes, the total energy which is available locally to shake engineered structures in typically less than 10²³ ergs. The average duration of energy release in seconds is t z 0.01exp[M] (Trifunac and Novikova, 1995). The average stress drops on earthquake faults are of the order of 100 bars, and dislocations spread with velocities, v_d , in the range 1-10 km/s but usually close to 2,500 m/s. Only failures of asperities may experience higher stress drops and higher dislocation velocities (Trifunac, 1994a,b; 1998). "Slow" earthquakes (0.1 < v_d < 1 km/s) may be powerful sources of tsunami waves (Todorovska and Trifunac, 1998), but do not contribute to significant inertial excitation of structures. The fault dimensions can reach hundreds of kilometers, but for determining the strong shaking of man-made structures the fault width is more important. In most shallow seismogenic zones, the width rarely exceeds 20-30 km (Trifunac 1993; 1994a,b; 1995a,b). Because of these physical characteristics, Fourier and Response spectra of earthquakes ground motions contain sinificant energy at intermediate (T > 1 s) and long (T > 10 s) periods. Figure 1 shows Fourier amplitude spectra of earthquakes for M = 1-7, evaluated from statistical regression models where the signal to noise ratio is grater than one (the shaded zone), and extended to longer periods (T > 5 s) and higher frequencies (f > 25 Hz) by models proposed by Trifunac (1993, 1994b). The darker shade (between M = 5.5 and 7) indicates destructive strong motion. Theoretical spectra for magnitudes as small as M = 1 are also shown to help comparison with other small motions, discussed later in the text.

Full-scale tests of structures, soils and of geological strata have been carried out using other than strong motion excitations. When the problem is linear and the nature of incident waves is similar, the results of small amplitude measurements may be extrapolated to predict the characteristics of much larger strong motion waves. One such source of excitations comes from microseisms, which are caused by ocean waves. Noise spectra of microseisms have two characteristic peaks, near 0.14 and 0.07 Hz. The peak at 0.07 Hz occurs at the frequency associated with most ocean waves. The peak at 0.14 Hz (Fig. 1) is caused by standing waves near the coast (Longuet Higgins, 1950). Microtremors and microseisms have been used extensively in the studies of geological and soil layers, aiming to predict amplification of incident strong earthquake wave motion (Kanai, 1983; Nakamura 1989; Ohta et al., 1978; Udwadia and Trifunac, 1973) and for identification of structural properties (Trifunac, 1972; Ivanovic and Trifunac, 1995). For ground motions with peak velocities exceeding 10 to 20 cm/s, and for average shear wave velocities near the surface less than about 300 m/s, the soil response begins to be nonlinear, and the extrapolations based on linear theory of wave amplification progressively cease to be valid (Trifunac and Todorovska, 1996; 1998a,b).

Extrapolations based on linear methods to predict amplification of ground motion by geological and soil conditions at the site have often used recordings of aftershocks of destructive earthquakes (e.g. Field and Hough, 1977; Gao et al., 1996; Hartzell et al., 1996). Aftershock ground motions sample higher frequency range than the destructive strong motion (Fig. 1, Trifunac and Todorovska, 1998b) and are one to two orders of magnitude smaller than the strong motion amplitudes.

Long period strong ground motion can be simulated by numerical methods which model the earthquake source, propagation path and the local geological site conditions (Day et al., 1994; Pitarka and Irikura, 1996). These methods can resolve the strong motion amplitudes only for periods longer than about 1-2 s. This region is indicated by an arrow in Fig. 1.

Recordings from distant nuclear explosions have been used also to study local amplification of incident waves (Rogers et al., 1979; 1984; Borcherdt and Gibbs, 1976). The linear transfer-function methods have been shown to work very well, but only in the linear range of response and outside the zones of damaging motions (Trifunac and Todorovska, 1998b).

A powerful and useful approach for gathering full-scale experimental data is to simulate strong ground motion by explosions. The energy released by nuclear explosions is between 10²² and 10²⁴ ergs, and some research on its destructive power has been carried out (ASCE, 1975; Blume and Skjei, 1973), but following the bans on nuclear testing this work cannot be continued in future. Other man made explosions and impacts, associated with quarries, tunneling, stone crushing, construction of roads and excavation of deep foundations in rock, and demolition are associated with energy, orders of magnitude smaller than for earthquakes or nuclear explosions (Henrych, 1979).

The explosions have more rapid energy release than earthquakes and higher stress changes in a smaller source region. The peak pressures are 10-150 kbars, and propagate as shock waves through the explosive with velocities 2,000-9,000 m/s. Common single explosions rarely exceed 100 m in length and 500 m in depth, and last less than a fraction of a second. Due to these characteristics, the frequencies at which most of the energy is radiated are higher than those for earthquakes. The duration and effective dimensions of the explosive source are determined by the impedance of the explosive relative to the surrounding rock (soil) and the dimensions of the crushed and fractured zones surrounding the explosion. The fraction of the total available energy radiated as seismic waves is typically less than 1%.

It has been of interest to find the relevant scaling parameters so that methods can be developed to simulate strong earthquakes by explosion, for testing of full scale engineered structures (Negmatoullaev, 1986). The intensity of strong motion waves created by explosions as function of epicentral distance, depth and other source characteristics were investigated by Sadovski (1946). Related studies on the effects of the explosion size on response of soils and structures were carried out by Barkan (1945), Kuzmina et al. (1962) and Medvedev (1964). The use of delayed detonations in multiple rows of explosions was described by Mills (1972) and Chrostowski (1979). To simulate broad band earthquake spectra and to lengthen the duration of recorded accelerations, different methods involving multiple explosions have been used. These methods employ multiple changes in two-dimensional arrays, decoupling explosions (to extend duration of the driving function), constructive and destructive interference and sequential firing of changes (Bruce et al., 1979; Higgins and Triandafilidis, 1977; Negmatoullaev, 1986).

For planning future full-scale experiments, it is useful to have data on the expected amplitudes of shaking at the testing site. Since the scaling and attenuation equations depend on the geotechnical and geological characteristics of each site, it is necessary to perform calibration tests and to determine the site properties empirically. This paper describes a set of 10 such calibration tests, performed at the Lyaur testing range in the Republic of Tajikistan. This site was used extensively through the 1970’s and 1980’s for full scale testing of different structures (Negmatoullaev, 1986), and can accommodate many difficult and challenging experiments in the future. The tests described in this paper were carried out in 1977, at the time when little was known about direct empirical scaling of spectra and of peaks of strong ground motion (Trifunac, 1976a,b), and when advanced data processing of strong motion accelerograms was in the early stages of development (Trifunac and Lee, 1973). With the currently available data on near-field destructive strong ground motions and with the current capabilities for automatic data processing (Lee and Trifunac, 1990), it is useful to revive the analyses of such calibration explosions and to provide new quantitative comparisons of their ground motions with those of earthquakes.

Lyaur testing range was established in 1962. It is located 20 km south-west of Dushanbe, the capital of Tajikistan. The site is located in a center of a valley, with average elevation ~820 m above sea level, and covers an area of 25 hectars (1 hectar = 100 x 100 m² = 10^-2 km²). The valley gently slopes towards south, with largest gradients less than 10%. It is composed of loess soils with thickness 175–200 m. The top layer, ~60 m thick, consists of dry homogeneous loess. At greater depths, the loess is mixed with sand and rock fragments. The top layer, with thickness ~20 m, has density 2.67 tons/m³. The weight of the soil is 1.35–1.6 tons/m³, the porosity is 45–50% and the relative moisture is 4–6%. The compressive strength is 2 kg/cm² (=2 x 9.81x10⁴ Pa), and the speed of compressional waves is 600–900 m/s.

Explosions are prepared by first drilling 110 mm diameter cylindrical boreholes with depth h m. A small charge (0.1-1.0 kg) is next exploded at the bottom of each hole to create a cavity which is then filled with explosive. The hole is resealed by loess soil. In this paper, we use the following notation: R-horizontal distance from the explosion in m; W -weight of explosive charges/hole in kg;; W₀- total weight of explosive charges in kg (for multiple explosions). After ignition, the detonation propagates through the explosive with velocity 2,000–9,000 m/s (depending on the type of explosive), higher than the velocity of compressional waves in the loess at Lyaur (600–900 m/s). The pressure of the explosive gasses fractures the surrounding material and creates a zone of highly deformed soil, which at first moves radially and away from the charge, as a shock wave. After termination of the dynamic process, an explosion cavity is formed surrounding the original charge, with radius R = R_vd ~ (0.1 to 0.2) W^1/3 m. Beyond the cavity walls, stable shock waves propagate, creating a zone of crushed soil, opening cracks and forcing the soil into large nonlinear deformations. The radius of this zone is R ~ (0.5 to 0.8) W^1/3 (Vovk et al., 1968). Further away, up to distance R = R_e ~ 2.5W^1/3 is a zone of elasto-plastic deformations, and for R > R_e, the wave motion is linear. The notation for distances R_vd and R_e is same as in Henrych (1979). The above limits are applicable to the loess soil at Lyaur, and will change for other soils and rocks materials and for different site conditions.

The waves leaving the explosion eventually encounter the free surface and reflect, creating additional P, S and Rayleigh waves. With increasing epicentral distance, the wave train is changed mainly by dispersion of the Rayleigh waves and by reflections from the layer interfaces at depth. The amplification of wave motions at the surface tends to extend the above limits in the vicinity of the surface.

Throughout this paper, W is defined in kg (=10^-6 kt) of TNT. Nuclear explosions can be equated to chemical explosions by energy release in terms of TNT equivalent. One kiloton (1 kt) equivalent of nuclear explosion equals 10¹² calories or 4.186x10²² Joules.

3. RESULTS AND ANALYSIS

3.1 Description of 10 Calibration Tests

The ten calibration explosions described in this paper were carried out in the south-western corner of the Lyaur testing range, during late 1977. The general features of the explosions are summarized in Tables 1 and 2. Strong ground motion was recorded by four SMA-1 accelerographs. We will refer to these as stations 1-4. Sketches representing the geometrical arrangement of the individual boreholes with explosives and the stations are shown in Figures 2a-j.

Explosions 1 and 2 consisted of a single explosive source, while 3, 4 and 5 had a single raw of n = 3 or 4 explosive sources, fired simultaneously. Explosions 6, 7 and 8 consisted of three rows, each with n = 3 explosive sources. The explosions were detonated simultaneously in each raw, but the firing of rows was delayed by time Dt = 0.2–0.4 s. The weight of the explosives in each source, W, was approximately the same. Explosions 9 and 10 consisted 20 and 9 rows respectively, each with n = 4 explosive sources per row fired simultaneously, and with delays between firing of rows Dt = 0.24–0.49 s (see Table 2). The firing order for explosions 6, 7 and 8 was row by row, starting from the furthermost row and progressing towards station 3. During explosions 9 and 10, the rows were fired consecutively, towards station 1 (Fig. 2i,j).

Figures 2a-2j also show the recorded waveforms (uncorrected acceleration), except those at station 3 from explosion 4, and at station 1 from explosion 7, which are not available. The accelerographs were always oriented so that their longitudinal sensitivity axes (Todorovska, 1998) coincide with the radial direction from the source. The recorded components are labeled "R", "V" and "T" designating radial (longitudinal), vertical and transverse direction relative to the source. All the waveforms in Figure 2 are plotted on same scale, except those from explosion 9 which are plotted with compressed time scale, to accommodate the longer record length. The distances from the stations to the nearest explosives are 20 and 40 m, except for stations 1 and 2 during experiment 9 (124 and 144 m respectively from the last row; Fig. 2i).

3.2 Data processing

The accelerograms were digitized by a PC and a flat bed scanner with resolution 600 dpi, using the 1998 version of the LeAuto software package for automatic digitization of accelerograms (Lee and Trifunac, 1990). Due to the large amplitudes and high frequencies, for some records, the regions with high frequency and overlapping traces were first photographically enlarged (magnification of 4), then digitized from the enlargement and finally imported into the scanned images and further edited by the LeAuto software.

The small distances between the recording sites and the explosions may have resulted in some nonlinear and permanent displacements contributing to the recorded motions. Broad-band data processing of such accelerograms and estimation of permanent displacement is one of the oldest and most difficult challenges in strong motion data analysis and is beyond the scope of this paper. Here we estimate only the peak amplitudes of the transient components of motion, by band-pass filtering all the digitized records between 2 and 25 Hz (Ormsby filter with up ramp 1.8–2.0 Hz and down ramp 25–27 Hz). The computed peak accelerations, velocities and displacements of the filtered data are summarized in Table 3. In this table, W₀ is the total quantity of explosives and W is the quantity of the explosives for the nearest source to the station (both in kg). The explosion depth, physical distance, R, and the normalized distance, R/W^1/3 , are all in meters. The units for the peak amplitudes are cm and s.

3.3 Peak velocities

Peak ground velocity is one of the most common parameters for quick estimation of the effects of ground shaking on response of structures. It has been used to describe ground motion from explosions (Negmatoullaev, 1986), for rough description of damaging effects of strong earthquake shaking (Trifunac and Todorovska, 1997a) and for estimation of peak strains in the soils (Trifunac and Todorovska, 1997b). In scaling peak amplitudes of motion from explosions, it is common to use normalized distance R/W^1/3, where R is the horizontal distance in m and W is the quantity of explosive in kg. Figure 3 shows peak amplitudes of acceleration, velocity and displacement for the records of the 10 explosions vs. normalized distance, R/W^1/3, for the radial, vertical and transverse components of motion (parts a, b and c respectively). There are two groups of data points (full and open squares), to separate the focusing and directivity effects for line sources and in front of the spreading explosions. We named the data points by the corresponding explosion and station number (e.g., 6–3 stands for record of explosion 6 at station 3). Group 1 (open squares) consists of data points at stations such that their radial (R) axis is parallel to the rows of explosive sources (all points for explosions 1 and 2, and points 3–1, 3–2, 4–1, 4–2, 5–1, 5–2, 6–1, 6–2, 7–2, 8–1 and 8–2). Group 2 (solid squares) consists of data points at stations such that their radial (R) axis is perpendicular to the rows of explosive sources (points 3–3, 3–4, 4–3, 4–4, 5–3, 5–4, 6–3, 6–4, 7–3, 7–4, 8–3 and 8–4). It is seen that the peak amplitudes for group 2 are generally larger than those for group 1. The solid and dashed lines show respectively the least squares fit for the data points shown by solid and open squares. The coefficients for these lines are listed in Table 4. To compute R/W^1/3, we used the representative closest charge, W, listed in Table 3, instead of the total weight of the explosive W₀.

The amplitudes of wave motion at the ground surface depend also on the depth of the charges, h. Other tests have shown that the vertical amplitudes of Rayleigh waves in loess are the largest for h ~ (0.5 to 1.0) R_e which gives h ~ (1.2 to 2.5) W^1/3 (R_e ~ 2.5 W^1/3 was defined earlier as the horizontal distance beyond which the soil motion is essentially elastic). This range is illustrated in Fig. 4, which also shows h for the ten explosions (see Table 3). It is seen that h for all the 10 explosions is within the ideal range, producing maximum surface wave amplitudes.

The amplitudes and directivity of motions at the surface also depend on the horizontal separation, l, of the individual charges (three or four per row, in the examples shown in Fig. 2c through 2j). Several other experiments have shown that for loess at the Lyaur site, l should be 1.5 W^1/3 < l < 6 W^1/3 (Negmatullaev, 1986). For l > 6 W^1/3 (= 2.4 R_e), the explosions begin to act as individual sources, and their interaction is essentially lost. For l < 1.5 W^1/3, the nonlinear zones of deformation, surrounding each explosion, begin to interfere destructively and this diminishes the motions on the ground surface. Figure 5 shows l for explosions 3 through 10 (l = 8 m) against the curve l = 1.5 W^1/3. It is seen that all the points are above or close to this curve.

Henrych (1979) gathered data on peak velocities of P-waves, and of normalized vertical peak displacements of P-waves, A_z/W^1/6, from numerous studies, mostly in the former Soviet Union. In Figures 6a and 6b, these data is plotted against the corresponding data analyzed in this paper (the open squares). It is seen that there is a good agreement in amplitudes and continuity in trends with the other data recorded in loess for R/W^1/3 > 10. For smaller R/W^1/3, there is a clear change in slope of amplitude attenuation trends. We interpret this to be associated with the onset of nonlinear strains and permanent displacements for small R/W^1/3.

The values of the peak amplitudes in Fig. 3a,b,c are affected by the band-pass filtering (2-25 Hz was chosen for this analysis). The filtered peak accelerations and peak displacements are reduced, while the peak velocities should be close to their true values (Lee et al., 1995).

The range of the recorded radial peak velocities for the ten explosion tests is 3-20 cm/s. Only for explosion 5 at station 3 (R = 20 m), the peak velocity reached 46 cm/s (this corresponds to R/W^1/3 = 4.04). Velocities equal to 3, 20 and 46 cm/s correspond to average velocities of earthquakes with M = 4.5, 5.5 and 6 respectively, at epicentral distance R = 0, and for average site conditions (Trifunac 1976b; Trifunac and Novikova, 1995).

Visual analysis of the recorded accelerograms (Fig. 2a through 2j) and the foregoing analysis of the trends of the peak amplitudes show that, for the explosions in groups of 3 or 4 per row, the peak amplitudes were governed by the largest explosion. Only for the explosions 9 and 10 the interference among different rows caused some peak amplitudes to be larger (9-1, 9-2) and smaller (9-3, 10-3) than the overall trends.

3.4 Fourier Spectra

Figure 7 shows Fourier amplitude spectra of the processed accelerations, plotted on a common scale, for all the ten explosions, and for the radial, vertical and transverse components of motion. The range of the observed spectral amplitudes is shown by the heavy dashed and continuous lines. The spectra of single explosions and of most other motions generated by various arrays of explosions are peaked between 5 and 10 Hz, and their amplitudes are below the heavy dashed line. Few explosions did provide significant long period amplitudes. For example, explosion 5 at stations 1 and 3. As can be seen from Table 1, this explosion had relatively large quantity of explosive (485.5 kg) and all four sources were fired simultaneously. Fig. 2e shows that the radial components at both stations had a long and large acceleration pulse.

Predominant periods of surface motions in the loess of the Lyaur testing range have been estimated empirically, by visual analysis of analog records, as (Negmatoullaev, 1986)
 
 

Tp = 0.08 W 0.13 R 0.11

(1)

 
where T_p is in seconds, W represents the mass of explosive in kg and R is the horizontal distance in m. For 40 < W < 128 kg and 20 < R < 40 m (see Table 3) the computed T_p is in the range 0.18-0.23 s. The corresponding predominant frequencies are 4.4-5.5 Hz.

The frequency of the peak amplitude of smoothed Fourier spectrum of recorded earthquake accelerations, f_p, roughly corresponds to 1/T_p for earthquake ground motions. It is at f_p ~ 1.9, 2.9, 4.2, 6.1 and 9.3 Hz for M = 7, 6, 5, 4 and 3, and R = 10 km (see Fig. 1). The ten explosions described in this paper, according to eqn (1), should have predominant periods of ground motions similar to those for an earthquake with 4 < M < 5. As can be see from Fig. 1, f_p for the radial accelerations is higher and closer to f_p for a M = 4 earthquake. The frequency f_p of course depends on distance (it decreases with distance), but for R comparable to and smaller than the source dimension S (Trifunac and Lee, 1990), it is essentially constant and is equal to the above values.

The solid and dashed borderlines in Fig. 7, for Fourier amplitude spectra of radial acceleration, are reproduced in Fig. 1 for comparison with spectra of strong earthquake shaking. It is seen that for frequencies higher than about 5 Hz, all the explosion spectra exceed the spectra of destructive strong motions. Several of the large explosions did produce Fourier amplitude spectra which have broader frequency content and which are quite similar to spectra of strong earthquake motions. In Fig. 8, Fourier spectra of accelerations recorded at 5-1, 5-3, 2-4 and 2-2 are compared with the average trend of smoothed empirical Fourier amplitude spectra of strong earthquake shaking at epicentral distance of R = 10 km. For example, typical spectra of strong motion accelerations in San Fernando Valley during the 1994 Northridge earthquake would fall between the spectra for M = 6 and 7 in this figure. In view of the damage to structures and soil (Trifunac and Todorovska, 1997a,b), for this area, it is seen that explosion 5 at stations 1 and 3 had equally large spectra.

4. DISCUSSION AND CONCLUSIONS

We reviewed one series of typical explosion calibrating tests at the Lyaur testing range, near Dushanbe, in Tajikistan. These tests were carried out in 1977 at a time when little was known about direct scaling of Fourier amplitude spectra of strong earthquake motions, and so direct comparisons were not possible. The comparisons we presented in this paper confirm the general knowledge that the Fourier spectra of single explosions (1) are peaked at higher frequencies (3 to 4 times) than the spectra of destructive earthquake motions, and (2) have smaller amplitudes of long period motions (T > 0.5 s; see Fig. 1).

Perusal of literature on the general use of explosions (Henrych, 1979) and for testing full scale structures (Negmatoullaev, 1986) will show that, except for excavation applications, explosion waves are studied at distances R > R_e (= 2.5W^1/3, for loess at Lyaur), where the motions are predominantly linear (e.g. see Fig. 6). The recent experience with damaging effects of the Northridge, California earthquake of 1994 shows that the most valuable tests of soils and of structures should in fact be performed in the zone of nonlinear response (for peak ground velocity v_m > 15 to 20 cm/s., and for strain factors v_m /v_s > 10^-3 , where v_s is the average shear wave velocity in the top 30 m of soil; Trifunac et al., 1996). In the near-field of shallow strong earthquakes, linear transfer-function theory cannot be used to predict ground motions (Trifunac and Todorovska, 1998b). To develop new data and understanding of the governing nonlinear processes, for the development of design codes under comparable conditions, the use of controlled explosions may offer powerful and new needed tools. The fact that the explosion spectra peak at 3-4 times higher frequencies than the destructive strong motion may in fact be advantageous, since it should allow almost perfect compliance with all scaling requirements using 1/2 to 1/3 scaled models. In engineering theory of bending, the stiffness is proportional to 1/L (where L, for example, is the length of a column), while the overall structural mass is proportional to Lⁿ where n is between 1 and 2. Therefore the frequency w ~ 1/L^m, where m is 1-1.5. Consequently, 1/2 to 1/3 scaled models excited by near explosions in loess at the Lyaur testing range, should be able to provide data on many different nonlinear response problems in earthquake engineering. For example, it should be possible to test and to extend the empirical scaling laws on strain accompanying strong ground motion for use in the nonlinear response range, to test complicated aspects of nonlinear soil-structure interaction involving pile foundations (e.g. Trifunac et al., 1998), and to simulate the effects of differential ground motion for long foundations (Trifunac, 1997) and for columns of long continuous span bridges (Trifunac and Todorovska, 1997c), for example.

"Tajikvzrivprom" company assisted in carrying out the explosion tests. The recording instruments were provided by USGS. We thank Prof. V.W. Lee from USC for his help in modifying the LeAuto software to handle some difficult records, and Dr. Anatoli Ischuk from Tajik Institute of Earthquake Engineering and Seismology for his help with Russian-English translation. The records were digitized during the summer of 1998 while the first author and Dr. Ischuk were visiting the Univ. of Southern California. Their visit was supported by a grant from the National Science Foundation, Div. of International Programs. We thank Casandra Dudka and Cliff Astill from NSF for their interest to support their visit.

1. American Society of Civil Engineers Research Council (1975). ‘Structural response to explosion-induced ground motions, a comparative study,’ ASCE project 210.03/17-2.72-3.
2. Barkan, D.D. (1945) ‘Seismovzrivnie volni i deistvie ih na sooruzheniya,’ Stroiizdat, Moscow.
3. Borcherdt, R.D. and J.F. Gibs (1976). ‘Effects of local Geological Conditions in the San Francisco Bay Region on Ground Motions and the intensities of the 1906 Earthquake,’ Bull. Seism. Soc. Amer., 66(2), 407-500.
4. Blume, J.A. and R.E. Skjei (1973). ‘Structural response to seismic motions generated by underground nuclear explosions,’ The Military Engineer, 65, 423, 30-32.
5. Bruce, J.R. H.E. Lindberg and G.R. Abrahamson (1979). ‘Simulation of strong earthquake motion with contained explosive line source arrays,’ Proc. U.S. National Conf. Earthquake Eng., 1134-1143.
6. Chrostowski, I. (1979). ‘Simulating strong motion earthquake effects on nuclear power plants using explosive blasts,’ Report No. UCLA-Eng-7119, Nuclear Energy Lab., Univ. of California, Los Angeles.
7. Day, S.M., H. Magistrale, K.L. McLaughlin and B. Shkoller (1994). ‘Three-dimensional Strong Motion Finite Difference Simulations of the Northridge Earthquake,’ EOS, 75, 168-168.
8. Field, E.H., and S.H. Hough (1997). ‘The variability of PSV response spectra across a dense array deployed during the Northridge aftershock sequence,’ Earthquake Spectra, 13(2), 243-257.
9. Gao, S., H. Liu, P.M. Davis and L. Knopoff (1996). ‘Localized amplification of seismic waves and correlation with damage due to the Northridge earthquake: evidence for focusing in Santa Monica,’ Bull. Seism. Soc. Amer., 86(1B), S209-S230.
10. Gutenberg, B. and C.F. Richter (1936). ‘Magnitude and energy of earthquakes,’ Annali di Geofisica, 9, 1-15.
11. Hartzell, S., A. Leeds, A. Frankel and J. Michael (1996). ‘Site response for urban Los Angeles using aftershocks of the Northridge earthquake,’ Bull. Seism. Soc. Amer., 86(1B), S168-S192.
12. Henrych, J. (1979). ‘The dynamics of explosion and its use,’ Elsevier Publ., Amsterdam.
13. Higgins, C.J. and G.E. Triandafilidis (1977). ‘The simulation of earthquake ground motions with high explosives,’ Proc. Sixth World Conf. Earthquake Eng., N. Delhi, India, 2-155-160.
14. Ivanovic, S.S. and M.D. Trifunac (1995). ‘Ambient Vibration Survey of Full Scale Structures Using Personal Computers,’ Rep. 95-05, Dept. Civil Eng., Univ. of Southern California, Los Angeles, California.
15. Kanai, K. (1983). ‘Engineering Seismology,’ Univ. of Tokyo Press.
16. Kojic, S., M.D. Trifunac and J.C. Anderson (1984). ‘Post Earthquake Response Analysis of the Imperial County Services Building,’ Rep. No. 84-02, Dept. Civil Eng., Univ. of Southern California.
17. Kuzmina, N.V., A.N. Romashev and B.G. Rulev (1962). ‘Seismicheski effect vzrivov na vibros v neskalnih svyaznih gruntah,’ Trudi I.F.Z., AN SSSR. No. 21 (188), 3-72.
18. Lee, V.W. and M.D. Trifunac (1990). ‘Automatic digitization and processing of accelerograms using PC,’ Rep. No. 90-03, Dept. Civil Eng., Univ. of Southern California, Los Angeles, California.
19. Lee, V.W., M.D. Trifunac, M.I. Todorovska and E.I. Novikova (1995). ‘Empirical equations describing attenuation of the peaks of strong ground motion in terms of magnitude, distance, path effects and site conditions,’ Rep. No. 95-02, Dept. Civil Eng., Univ. of Southern California, Los Angeles, California.
20. Longuet-Higgins, MS. (1950). ‘A theory of the origin of microseisms,’ Philosophical Transactions of the Royal Society of London, A243a:, 1-35.
21. Medvedev, S.V.(1964). ‘Seismika gornih vzrivov,’ Nauka, Moscow.
22. Mills, P.H.(1972). ‘Blast Dynamics of a model structure,’ Master Thesis, School of Enginering and Applied Science, U. of California, Los Angeles.
23. Nakamura, Y. (1989). ‘A method for dynamic characteristics estimation of subsurface using microtremor on the ground surface,’ QR Railway Tech. Res. Inst. 30, 1, 25-33.
24. Negmatullaev, S.Kh. (1986). ‘Imitaciya seismicheskogo vozdeistviya s cilju ispitaniya zdani i soruzenii na seizmostoikost,’ Inst. Seism. Stroitelstva i Seizmologi Akademii Hauk Tadzitskoi SSR., Izd. Donish, Dushanbe.
25. Ohta, Y., H. Kagami, N. Goto, and K. Kudo (1978). ‘Observation of 1- to 5-second microtremors and their application to earthquake engineering. Part I: Comparison with long period accelerations at the Tokachi-Oki earthquake of 1968,’ Bull Seism. Soc. Amer., 68, 767-779.
26. Pitarka, A. and K. Irikura (1996). ‘Basin structure effects on long-period strong motion in the San Fernando valley and the Los Angeles basin from the 1994 Northridge earthquake and an aftershock,’ Bull. Seism. Soc. Amer., 86(lB), S126-S137.
27. Rogers, A. M., J. C. Tinsley, W. W. Hays, and K. W. King (1979). ‘Evaluation of the relation between near-surface geological units and ground response in the vicinity of Long Beach, California,’ Bull Seism. Soc. Am., 69, 1603-1622.
28. Rogers, A.M., R.D. Borcherdt, P.A. Covington, and D.M. Perkins (1984). ‘A comparative ground motion study near Los Angeles using recordings of Nevada nuclear tests and the 1971 San Fernando earthquake,’ Bull. Seism. Soc. Amer., 74(5), 1925-1949.
29. Sadovski, M.A.(1946). ‘Prosteishie priemi opredeleniya seismicheskoi opasnosti masovih vzrivov,’ Izd. A.N.S.S.R.
30. Todorovska, M.I. (1998). ‘Cross-axis sensitivity of accelerographs with pendulum like transducers: mathematical model and the inverse problem,’ Earthquake Eng. and Struc. Dynam., (in press)
31. Todorovska, M.I. and M.D. Trifunac (1998). ‘Generation of tsunamis by slow earthquakes,’ (submitted for publication).
32. Trifunac, M.D. (1972). ‘Comparison between ambient and forced vibration experiments,’ Earthquake Eng. and Struct. Dynam., 1,133-150.
33. Trifunac, M.D. (1976a). ‘Preliminary empirical model for scaling Fourier amplitude spectra of strong ground acceleration in terms of earthquake magnitude, source to station distance and recording site conditions,’ Bull. Seism. Soc. Amer., 66, 1343-1373.
34. Trifunac, M.D. (1976b). ‘Preliminary analysis of the peaks of strong earthquake ground motion–dependence of peaks on earthquake magnitude, epicentral distance and the recording site conditions,’ Bull. Seism. Soc. Amer., 66, 189-219.
35. Trifunac, M.D. (1993). ‘Long period Fourier amplitude spectra of strong motion acceleration,’ Soil Dynam. and Earthquake Eng., 12(6), 363-382.
36. Trifunac, M.D. (1994a). ‘Similarity of strong motion earthquakes in California,’ Europ. Earthquake Eng., Vol. VIII-n.1, 38-48.
37. Trifunac, M.D. (1994b). ‘Q and high frequency strong motion spectra,’ Soil Dynam. and Earthquake Eng., 13(3), 149-161.
38. Trifunac, M.D. (1995a). ‘Pseudo relative velocity spectra of earthquake ground motion at long periods,’ Soil Dynam. and Earthquake Eng., 14(5), 331-346.
39. Trifunac, M.D. (1995b). Pseudo Relative Velocity Spectra of Earthquake Ground Motion at High Frequencies, Earthquake Eng. and Structural Dynamics, 24(8), 1113-1130.
40. Trifunac, M.D. (1997). ‘Differential earthquake motion of building foundations,’ J Structural Eng., ASCE, 123(4), 414-422.
41. Trifunac, M.D. (1998). ‘Stresses and intermediate frequencies of strong motion acceleration,’ Geofizika, 14, 1-27.
42. Trifunac, M.D. and V.W. Lee (1973). ‘Routine computer processing of strong motion accelerograms,’ Earthquake Eng. Res. Lab. Report, California Inst. of Tech., Pasadena, California.
43. Trifunac, M.D. and V.W. Lee (1990). ‘Frequency dependent attenuation of strong ground motion,’ Soil Dynam. and Earthquake Eng., 9(1), 3-15.
44. Trifunac, M.D. and E.I. Novikova (1995). ‘Duration of earthquake fault motion in California,’ Earthquake Eng. and Struct. Dynam., 24(6), 781-799.
45. Trifunac, M.D. and M.I. Todorovska (1996). ‘Nonlinear soil response–1994 Northridge, California, earthquake,’ J. of Geotech. Eng., ASCE, 122(9), 725-735.
46. Trifunac, M.D. and M.I. Todorovska (1997a). ‘Northridge, Claifornia, earthquake of January 17, 1994: density of red-tagged buildings versus peak horizontal velocity and site intensity of strong motion,’ Soil Dynam. and Earthquake Eng., 16(3), 209-222.
47. Trifunac, M.D. and M.I. Todorovska (1997b). ‘Northridge, California, earthquake of January 17, 1994: density of pipe breaks and surface strains,’ Soil Dynam. and Earthquake Eng., 16(3), 193-207.
48. Trifunac, M.D. and M.I. Todorovska (1997c). ‘Response spectra and differential motion of columns,’ Earthquake Eng. and Struct. Dynam., 26(2), 251-268.
49. Trifunac, M.D. and M.I. Todorovska (1998a). ‘Nonlinear soil response as a natural passive isolation mechanism–the 1994 Northridge, California, earthquake,’ Soil Dynam. and Earthquake Eng., 17(1), 41-51.
50. Trifunac, M.D. and M.I. Todorovska (1998b). ‘Amplification of strong ground motion and damage patterns during the 1994 Northridge, California, earthquake,’ Proc. ASCE Specialty Conf. on Geotechnical Earthquake Eng. and Soil Dynamics, Seattle Washington, Vol. 1, pp. 714-725.
51. Trifunac, M.D.,M.I. Todorovska and S.S. Ivanovic (1996). ‘Peak velocities and peak surface strains during Northridge, California, earthquake of 17 January, 1994,’ Soil Dynam. and Earthquake Eng., 15(5), 301-310.
52. Trifunac, M.D., S.S.Ivanovic, and M.I. Todorovska (1998). ‘Experimental evidence for flexibility of a foundation supported by concrete piles,’ (submitted for publication).
53. Udwadia, F.E. and M.D. Trifunac (1973). ‘Comparison of earthquake and microtremor ground motions in El Centro, California,’ Bull. Seism. Soc. Amer., 63(4), 1227-1253.
54. Udwadia, F.E. and M.D. Trifunac (1974). ‘Time and amplitude dependent response of structures,’ Earthquake Eng. and Struct. Dynam., 2, 359-378.
55. Vovk, V.V., G.I. Chernii, A.G. Smirnov, and V.G. Kravets (1968). ‘Principles of soil dynamics,’ Naukova Dumka, Kiev, Ukraine.

Contact: mtodorov@usc.edu