Vladimir Graizer

Tilts in Strong Ground Motion

Most instruments used in seismological practice to record ground mo- tion are pendulum seismographs, velocigraphs, or accelerographs. In most cases it is assumed that seismic instruments are only sensitive to the translational motion of the instruments base. In this study the full equation of pendulum motion, including the inputs of rotations and tilts, is considered. It is shown that tilting the accelerographs base can severely impact its response to the ground motion. The method of tilt evaluation using uncorrected strong-motion accelerograms was first suggested by Graizer (1989), and later tested in several laboratory experiments with different strong-motion instruments. The method is based on the difference in the tilt sensi- tivity of the horizontal and vertical pendulums. The method was applied to many of the strongest records of the Mw 6.7 Northridge earthquake of 1994. Examples are shown when relatively large tilts of up to a few degrees occurred during strong earthquake ground motion. Residual tilt extracted from the strong-motion record at the Pacoima Dam-Upper Left Abutment reached 3.1 in N45E direction, and was a result of local earthquake-induced tilting due to high-amplitude shaking. This value is in agreement with the residual tilt measured by using electronic level a few days after the earthquake. The method was applied to the building records from the North- ridge earthquake. According to the estimates, residual tilt reached 2.6 on the ground floor of the 12-story Hotel in Ventura. Processing of most of the strongest records of the Northridge earthquake shows that tilts, if happened, were within the error of the method, or less than about 0.5.

Some Key Features of the Strong-Motion Data from the M 6.0 Parkfield, California, Earthquake of 28 September 2004

The 2004 Parkfield, California, earthquake was recorded by an extensive set of strong-motion instruments well positioned to record details of the motion in the near-fault region, where there has previously been very little recorded data. The strong-motion measurements obtained are highly varied, with significant variations occurring over only a few kilometers. The peak accelerations in the near fault region range from 0.13 g to over 1.8 g (one of the highest acceleration recorded to date, exceeding the capacity of the recording instrument). The largest accelerations occurred near the northwest end of the inferred rupture zone. These motions are consistent with directivity for a fault rupturing from the hypocenter near Gold Hill toward the northwest. However, accelerations up to 0.8 g were also observed in the opposite direction, at the south end of the Cholame Valley near Highway 41, consistent with bilateral rupture, with rupture southeast of the hypocenter. Several stations near and over the rupturing fault recorded relatively weak motions, consistent with seemingly paradoxical observations of low shaking damage near strike-slip faults. This event had more ground-motion observations within 10 km of the fault than many other earthquakes combined. At moderate distances peak horizontal ground acceleration (pga) values dropped off more rapidly with distance than standard relationships. At close-in distance the wide variation of pga suggests a distance- dependent sigma may be important to consider. The near-fault ground-motion variation is greater than that assumed in ShakeMap interpolations, based on the existing set of observed data. Higher density of stations near faults may be the only means in the near future to reduce uncertainty in the interpolations. Outside of the near- fault zone the variance is closer to that assumed. This set of data provides the first case where near-fault radiation has been observed at an adequate number of stations around the fault to allow detailed study of the fault-normal and fault-parallel motion and the near-field S -wave radiation. The fault- normal motions are significant, but they are not large at the central part of the fault, away from the ends. The fault-normal and fault-parallel motions drop off quite rapidly with distance from the fault. Analysis of directivity indicates increased values of peak velocity in the rupture direction. No such dependence is observed in the peak acceleration, except for stations close to the strike of the fault near and beyond the ends of the faulting.

Downhole Receiver Function: a Case Study

Receiver function is defined as the spectral ratio of the radial component and the vertical component of the ground motion. It is used to characterize converted waves. We extend the use of the receiver function to downhole data using waves recorded in a borehole, excited by an earthquake of magnitude 4.0 near San Fran- cisco, California, on 26 June 1994. The focal depth of the event was 6.6 km and the epicenter was located at a distance of 12.6 km from the borehole array. Six three- component sensors were located at different depths in a borehole. To extract a co- herent response of the near-surface from the incoherent earthquake waves, we de- convolve the waves recorded by the sensors at different depths with the waves recorded by the sensor on the surface. Deconvolution applied to the waves in the S- time window recorded by the radial component result in an upgoing and adowngoing wave propagating with S-wave velocity. For the waves in the P-time window re- corded by the radial component, deconvolution also gives an upgoing and a down- going wave propagating with S-wave velocity. This interesting result suggests a P- to-S conversion at a depth below the deepest sensor. To diagnose this we compute the receiverfunction forthe borehole recording of the earthquakewaves.Thereceiver function shows an upgoing wave with an arrival close to time t ! 0 for the deepest sensor. The agreement of the upgoing wave in the receiver function with the travel- time curve for the P-to-S converted wave, calculated using the P- and the S-wave velocity profile, supports the hypothesis of a pronounced P-to-S conversion. We present a synthetic example to illustrate that the first arrival of the receiver function applied to borehole data gives the upward-propagating P-to-S converted wave. To corroborate the observation of the mode conversion, we apply receiver function to a different earthquake data recorded by the same borehole array in 1998. The focal depth of the event was 6.9 km and the epicenter was located at a distance of 13 km from the borehole array. The receiver function for these data also show an upgoing wave with a pulse close to time t ! 0 at the deepest sensor. The moveout of the upgoing wave agrees with the travel-time curve for the P-to-S converted wave, hence supporting our observation of the mode conversion.

Ground Motion Attenuation Model for Peak Horizontal Acceleration from Shallow Crustal Earthquakes

Spatial distribution of ground motion data of recent earthquakes unveiled some features of peak ground acceleration (PGA) attenuation with respect to closest distance to the fault (R) that current predictive models may not effectively capture. As such, PGA: (1) remains constant in the near-fault area, (2) may show an increase in amplitudes at a certain distance of about 3–10 km from the fault rupture, (3) attenuates with slope of R−1 and faster at farther distances, and (4) intensifies at certain distances due to basin effect (if basin is present). A new ground motion attenuation model is developed using a comprehensive set of ground motion data compiled from shallow crustal earthquakes. A novel feature of the predictive model is its new functional form structured on the transfer function of a single-degree-of-freedom oscillator whereby frequency square term is replaced with closest distance to the fault. We are proposing to fit ground motion amplitudes to a shape of a response function of a series (cascade) of filters, stacked separately one after another, instead of fitting an attenuation curve to a prescribed empirical expression. In this mathematical model each filter represents a separate physical effect.

Prediction of Spectral Acceleration Response Ordinates Based on PGA Attenuation

Developed herein is a new peak ground acceleration (PGA)-based predictive model for 5% damped pseudospectral acceleration (SA) ordinates of free-field horizontal component of ground motion from shallow-crustal earthquakes. The predictive model of ground motion spectral shape (i.e., normalized spectrum) is generated as a continuous function of few parameters. The proposed model eliminates the classical exhausted matrix of estimator coefficients, and provides significant ease in its implementation. It is structured on the Next Generation Attenuation (NGA) database with a number of additions from recent Californian events including 2003 San Simeon and 2004 Parkfield earthquakes. A unique feature of the model is its new functional form explicitly integrating PGA as a scaling factor. The spectral shape model is parameterized within an approximation function using moment magnitude, closest distance to the fault (fault distance) and VS30 (average shear-wave velocity in the upper 30 m ) as independent variables. Mean values of its estimator coefficients were computed by fitting an approximation function to spectral shape of each record using robust nonlinear optimization. Proposed spectral shape model is independent of the PGA attenuation, allowing utilization of various PGA attenuation relations to estimate the response spectrum of earthquake recordings.

58 – Strong-Motion Data Processing

The processing of strong-motion recordings has undergone great progress from the first recording in 1933 through the modern instruments available at the end of the century. Processing went from tedious, manual calculations to almost completely computerized processing. Some problems and issues associated with sensors, offsets and tilts, and electronics remain, despite the great progress. However, these problems are relatively small. The evolution of automated strong-motion processing in the 1990s will make strong-motion data increasingly useful for emergency response and rapid post-earthquake investigation of damage as well as for long-term research.

A study of possible ground-motion amplification at the Coyote Lake Dam, California

The abutment site at the Coyote Lake Dam recorded an unusually large peak acceleration of 1.29g during the 1984 Morgan Hill earthquake. Following this earthquake another strong-motion station was installed about 700 m downstream from the abutment station. We study all events (seven) recorded on these stations, using ratios of peak accelerations, spectral ratios, and particle motion polarization (using holograms) to investigate the relative ground motion at the two sites. We find that in all but one case the motion at the abutment site is larger than the downstream site over a broad frequency band. The polarizations are similar for the two sites for a given event, but can vary from one event to another. This suggests that the dam itself is not strongly influencing the records. Although we can be sure that the relative motion is usually larger at the abutment site, we cannot conclude that there is anom- alous site amplification at the abutment site. The downstream site could have lower- than-usual near-surface amplifications. On the other hand, the geology near the abut- ment site is extremely complex and includes fault slivers, with rapid lateral changes in materials and presumably seismic velocities. For this reason alone, the abutment site should not be considered a normal free-field site.

TriNet Strong-Motion Data from the M 7.1 Hector Mine, California, Earthquake of 16 October 1999

The M_w 7.1 Hector Mine earthquake of October 16, 1999 was recorded by more than 300 stations of TriNet, which is administered cooperatively by the California Division of Mines and Geologys California Strong Motion Instrumentation Program (CDMG/CSMIP), California Institute of Technology, and the U.S. Geological Survey (USGS). The earthquake occurred in a remote part of the Mojave Desert, approximately 190 km northeast of downtown Los Angeles, and there were no strong-motion stations close to the surface rupture. The nearest station, Hector, is about 27 km north of the epicenter; it recorded a peak horizontal ground acceleration of 0.33g. The two next closest stations, Amboy and Joshua Tree, are to the east and south, both at epicentral distances of about 50 km; each recorded peak ground accelerations of about 0.2g. The new digital instruments installed for the TriNet project recorded a large set of reliable data at epicentral distances up to 275 km. These data can significantly improve empirical peak ground motion attenuation relationships, which are usually developed for distances only up to 100 km (Boore et al., 1993, 1997) because adequate data have not been available at greater distances. Hector Mine peak ground motions demonstrate reasonable agreement with empirical attenuation relationships for acceleration. In contrast, higher than expected ground velocities and displacements were recorded at epicentral distances of about 150 to 220 km, especially in the Los Angeles sedimentary basin, where anomalously high-amplitude displacements with periods of 6 to 7 sec were recorded in Los Angeles, Long Beach, and other areas. These long-period surface- or basin-generated waves can have significant effects on large structures. The M_w 7.3 Landers earthquake of 1992 similarly produced strong, long-period waves in the basin. The peak ground motions produced by the Landers earthquake were on average 1.6 times higher than for the Hector Mine earthquake in the Los Angeles area. Ground-motion data recorded by digital instruments were uniformly processed in the frequency band 0.067 to 46 Hz (0.022–15 sec). The processed data set includes records from 213 ground-response stations. In an effort to make strong-motion data available quickly to the engineering and scientific communities, important records from this event were made available by file transfer protocol (ftp) beginning the day of the earthquake.

Comment on “Comparison of Time Series and Random‐Vibration Theory Site‐Response Methods” by Albert R. Kottke and Ellen M. Rathje

Methods of site‐response analysis require theoretical and empirical testing and validation before they can be used in seismic‐hazard assessment. Comparison of site amplification functions (SAFs) calculated using earthquake data recorded by seismic arrays with SAF obtained using analytical approaches represent the most important tests of reliability of those methods. High‐quality, low‐amplitude earthquake data recorded by the Treasure Island (TI) downhole array between 1993 and 2010 were used for comparisons with the two versions of the equivalent linear (EQL) site‐response methods implemented in the computer program STRATA (Kottke and Rathje, 2008; Rathje and Kottke, 2013): Use of the TS approach in STRATA matches well the empirically determined SAF between the bedrock and the surface. The STRATA version of the RVT approach can produce a significantly different SAF from the empirically determined and the TS approach. Further testing of different realizations of the RVT method is desirable to assess the method’s reliability and limitations. The paper of Kottke and Rathje (2013) raises a very important issue of comparison of the two site‐response analysis approaches: classical TS SHAKE‐type (Idriss and Seed, 1968; Idriss and Sun, 1992) and RVT (Vanmarcke, 1975; Der Kiureghian, 1980; Hanks and McGuire, 1981). These approaches represent two versions of EQL site‐response analyses. I found this discussion timely, because more and more probabilistic seismic‐hazard projects, including those for critical facilities, use the RVT approach. Kottke and Rathje (2013) properly pointed out that the fact that the RVT site‐response analysis does not require input TS makes it an attractive alternative to the TS approach. Nevertheless, the main questions are:

Global Ground Motion Prediction Equation for Shallow Crustal Regions

The Graizer-Kalkan ground-motion prediction equation (GMPE) for peak ground acceleration (PGA) constitutes a series of filters, each of which represents a certain physical phenomenon affecting the radiation of seismic waves from the source. The performance of this GMPE is examined by using about 14,000 records from 245 worldwide shallow crustal events. The recorded data and predictions show an excellent match as far as 100 km from the fault. Beyond 100 km, the data generally show faster attenuation on the order of Rrup−4 due to a relatively low Q (as in the western United States) or slower attenuation on the order of Rrup−1.5 due to a high Q (as in the central and eastern United States). An improved GMPE is developed to account for regional variations in ground motion attenuation. The The new GMPE produces a better match to recorded data up to 500 km from the fault.