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On the similarity of theories of anelastic and scattering attenuation

We point out basic parallels between theories of anelastic and scattering attenuation. We consider approximations to scattering effects presented by O'Doherty and Anstey (1971), Sato (1982), and Wu (1982). We use the linear theory of anelasticity. We note that the frequency dependence of Q can be related to a distribution of scales of physical properties of the medium. The frequency dependence of anelastic Q is related to the distribution of relaxation times in exactly the same manner as the frequency dependence of scattering Q is related to the distribution of scatterer sizes. Thus, the well-known difficulty of separating scattering from intrinsic attenuation is seen from this point of view as a consequence of the fact that certain observables can be interpreted by identical equations resulting from either of two credible physical theories describing fundamentally different processes.

Bulletin of the Seismological Society of America

Source inversion of the 1988 Upland, California, earthquake: Determination of a fault plane for a small event

We examined short-period P waves to investigate if waveform data could be used to determine which of two nodal planes was the actual fault plane for a small (ML 4.6) earthquake near Upland, California. We removed path and site complications by choosing a small aftershock (ML 2.7) as an empirical Green function. The main shock P waves were deconvolved by using the empirical Green function to produce simple far-field displacement pulses. We used a least-squares method to invert these pulses for the slip distribution on a finite fault. Both nodal planes (strike 125°, dip 85° and strike 221°, dip 40°) of the first-motion focal mechanism were tested at various rupture velocities. The southwest trending fault plane consistently gave better fitting solutions than the southeast-trending plane. We determined a moment of 4.2 × 1022 dyne-cm. The rupture velocity, and thus the source area could not be well resolved, but if we assume a reasonable rupture velocity of 0.87 times the shear wave velocity, we obtain a source area of 0.97 km2 and a stress drop of 38 bars. Choice of a southwest-trending fault plane is consistent with the trend of the nearby portion of the Transverse Ranges frontal fault zone and indicates left-lateral motion. This method provides a way to determine the fault plane for small earthquakes that have no surface rupture and no obvious trend in aftershock locations.

California

Near-surface velocities and attenuation at two boreholes near Anza, California, from logging data

To investigate near-surface site effects in granite rock, we drilled 300-m-deep boreholes at two sites which are collocated with stations from the digital array at Anza, California. The first borehole was sited at station KNW (Keenwild fire station), which is located along a ridge line about 8.7 km east of the San Jacinto Fault zone. Station PFO (Piñon Flat Observatory), chosen for the second site, is another 6 km further to the east of station KNW and is located on a gently sloping hillside. We logged each borehole for P- and S-wave velocities, as well as for crack density and orientation.

California

Calculation of zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an elastic half-space

Impulse responses including near-field terms have been obtained in closed form for the zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an anelastic half-space. The method is based on the correspondence principle. Through transformation of variables, the Fourier transform of the elastic impulse response is put in a form such that the Fourier transform of the corresponding anelastic impulse response can be expressed as elementary functions and their definite integrals involving distance, angular frequency, phase velocities, and attenuation factors. These results are used for accurate calculation of shear-wave arrival rise times of synthetic seismograms needed for data interpretation of anelastic-attenuation measurements in near-surface sediment.

Bulletin of the Seismological Society of America

Source parameters and effects of bandwidth and local geology on high- frequency ground motions observed for aftershocks of the northeastern Ohio earthquake of 31 January 1986

A 10-station array (GEOS) yielded recordings of exceptional bandwidth (400 sps) and resolution (up to 96 dB) for the aftershocks of the moderate ( m b ≈ 4.9) earthquake that occurred on 31 January 1986 near Painesville, Ohio. Nine aftershocks were recorded with seismic moments ranging between 9 × 10 16 and 3 × 10 19 dyne-cm ( M w : 0.6 to 2.3). The two largest aftershocks (depth 5.3, 5.6 km; oblique right slip, rake ≈30°, strike ≈N25°E) yielded seismic signals above background noise at frequencies as high as 130 Hz at epicentral distances up to 17 km. The aftershock recordings at a site underlain by ≈8 m of lakeshore sediments show significant levels of high-frequency soil amplification of vertical motion at frequencies near 8, 20, and 70 Hz. Viscoelastic models for P and SV waves incident at the base of the sediments yield estimates of vertical P -wave response consistent with the observed high-frequency site resonances, but suggest additional detailed shear-wave logs are needed to account for observed S -wave response. Peak acceleration values obtained from the broadband recordings are about two and four times as large as those that would be recorded on strong-motion recorders or short-period networks with upper bandwidth limits of 30 and 15 Hz, respectively. Attenuation-corrected acceleration spectra are used to reduce the influence of high-frequency (up to 100 Hz) local site effects on corner frequency estimates. The moment versus source radius trend inferred for events with moments as small as 9 × 10 16 dyne-cm, based on the Brune source model, extends previous relations inferred for the central United States, shows little evidence for a minimum source radius, and suggests that stress drops for the smaller events ( M 0 < 10 19 dyne-cm) decrease with decreasing moment.

Ohio

Coda duration magnitudes in central California: An empirical approach

A new empirical coda magnitude M D is presented for the central California seismic network (CALNET), in which station corrections are introduced to reduce the influence of hypocenter and station distributions. The new magnitude scale is obtained by relating the lapse-time τ^ to local magnitudes M L using data from 55 earthquakes with 1.1 ≦ M L ≤ 5.6 from June 1977 through 1981. Magnitude estimates are significantly improved by introducing corrections for the seismograph instrument attenuation setting α ij and a site correction δ j . The magnitude of the i th event 〈 M D 〉, is the median value of individual M D ij = -1.03 + 2.10log 10 τˆ ij + 0.00268 τˆ ij + α ij + δ j , where τ^ ij is the lapse-time measured at the j th station. Local site effects influence the duration of the coda and cause stations to either overestimate or underestimate 〈 M D 〉, typically up to 0.5 magnitude units. The distribution of the site corrections is spatially correlated, changing coherently across major tectonic and geologic features such as the San Andreas fault. It appears that the site corrections are influenced by the physical attenuation properties near the station, seemingly contradicting the concept that the coda is related to back-scattering and attenuation in a volume with dimensions on the order of the hypocenter to receiver distance.

California

Seismic site effects and the spatial interpolation of earthquake seismograms: Results using aftershocks of the 1986 North Palm Springs, California, earthquake

We address the following two questions. Can a microearthquake's ground motions be modeled by incident P and S waves that excite a site transfer-function that is a smooth function of incidence angle? Given recorded ground motions from a set of earthquakes having known locations and mechanisms, can we derive such a site transfer-function and use it to obtain the ground motions that would result from an earthquake source occurring somewhere in the same volume but having a location and mechanism that are different from the recorded events? Although many factors will cause two distinct microearthquake sources to have different seismograms at a common station, in this paper we concentrate only upon the differences caused by source mechanisms, P- and S-wave travel-time variations and by variations in the site transfer-function. We specifically exclude the effects of waves scattered from heterogeneities in the geologic structure away from the seismic site. We express the site transfer-function as a sum of several terms having simple dependences upon incidence angle and azimuth. Each term is an independent function of time. Given a set of seismograms observed at the site, we solve a linear system of equations for the time dependences of each term. These time series may be used to calculate the seismograms that would have resulted from an earthquake having arbitrary mechanism and location. This step is an interpolation. We have applied this technique to seismograms after aftershocks of the 1986 North Palm Springs earthquake. Our interpolation technique works fairly well within the volume occupied by the recorded events, but the method is not very successful at providing accurate seismograms for sources located outside the aftershock volume. The primary causes of the inaccuracy are the inadequacy of our chosen angular functions to model the site response fully and the likely scattering of seismic waves by geological heterogeneities (in this case, the Banning and Mission Creek faults) near the seismic stations. Our methods could be used to determine the effects of single scattering from lateral heterogeneities in geologic structure.

California

The effect of S-wave arrival times on the accuracy of hypocenter estimation

Well-constrained hypocenters (latitude, longitude, depth, and origin time) are required for nearly all studies that use earthquake data. We have examined the theoretical basis behind some of the widely accepted “rules of thumb” for obtaining accurate hypocenter estimates that pertain to the use of S phases and illustrate, in a variety of ways, why and when these “rules” are applicable. Results of experiments done for this study show that epicentral estimates (latitude and longitude) are typically far more robust with respect to data inadequacies; therefore, only examples illustrating the relationship between S phase arrival time data and focal depth and origin time estimates are presented. Most methods used to determine earthquake hypocenters are based on iterative, linearized, least-squares algorithms. Standard errors associated with hypocenter parameters are calculated assuming the data errors may be correctly described by a Gaussian distribution. We examine the influence of S-phase arrival time data on such algorithms by using the program HYPOINVERSE with synthetic datasets. Least-squares hypocenter determination algorithms have several shortcomings: solutions may be highly dependent on starting hypocenters, linearization and the assumption that data errors follow a Gaussian distribution may not be appropriate, and depth/origin time trade-offs are not readily apparent. These shortcomings can lead to biased hypocenter estimates and standard errors that do not always represent the true error. To illustrate the constraint provided by S-phase data on hypocenters determined without some of these potential problems, we also show examples of hypocenter estimates derived using a probabilistic approach that does not require linearization. We conclude that a correctly timed S phase recorded within about 1.4 focal depth's distance from the epicenter can be a powerful constraint on focal depth. Furthermore, we demonstrate that even a single incorrectly timed S phase can result in depth estimates and associated measures of uncertainty that are significantly incorrect.

Bulletin of the Seismological Society of America

Application of an iterative least-squares waveform inversion of strong-motion and teleseismic records to the 1978 Tabas, Iran, earthquake

An iterative least-squares technique is used to simultaneously invert the strong-motion records and teleseismic P waveforms for the 1978 Tabas, Iran, earthquake to deduce the rupture history. The effects of using different data sets and different parametrizations of the problem (linear versus nonlinear) are considered. A consensus of all the inversion runs indicates a complex, multiple source for the Tabas earthquake, with four main source regions over a fault length of 90 km and an average rupture velocity of 2.5 km/sec.

Bulletin of the Seismological Society of America

Estimates of velocity structure and source depth using multiple P waves from aftershocks of the 1987 Elmore Ranch and Superstition Hills, California, earthquakes

Event record sections, which are constructed by plotting seismograms from many closely spaced earthquakes recorded on a few stations, show multiple free-surface reflections (PP, PPP, PPPP) of the P wave in the Imperial Valley, California. The relative timing of these arrivals is used to estimate the strength of the P-wave velocity gradient within the upper 5 km of the sediment layer. Consistent with previous studies, a velocity model with a value of 1.8 km/sec at the surface increasing linearly to 5.8 km/sec at a depth of 5.5 km fits the data well. The relative amplitudes of the P and PP arrivals are used to estimate the source depth for the aftershock distributions of the Elmore Ranch and Superstition Hills main shocks. Although the depth determination has large uncertainties, both the Elmore Ranch and Superstition Hills aftershock sequences appear to have similar depth distribution in the range of 4 to 10 km.

California

Criticism of some forecasts of the National Earthquake Prediction Evaluation Council

The Working Group on California Earthquake Probabilities has assigned probabilities for rupture in the interval from 1988 to 2018 to various segments of the San Andreas fault on the basis of the lognormal distribution of recurrence times of characteristic earthquakes postulated by Nishenko and Buland (1987). I question the validity of those probabilities on the basis of three separate arguments: (1) The distributions of recurrence times of the four, best-observed, characteristic-earthquake sequences are each only marginally consistent with the Nishenko - Buland Iognormal distribution. (2) The range of possible 30-year conditional probabilities for many of the fault segments is so great due to uncertainty in the average recurrence time for that segment that the assigned probability is virtually meaningless. (3) The 1988 forecasts not subject to the foregoing objection are those in which there is a low probability of an earthquake in the near future (e.g., only a 5 per cent chance of rupture of the North Coast segment before the year 2049 and of the Carrizo segment before the year 2018). The same reasoning would assign only a 5 per cent chance of rupture before mid-1993 to the southern Santa Cruz Mountains segment, the segment that failed in October 1989. Finally, the forecast of the next Parkfield earthquake (95 per cent probability before 1993.0) by Bakun and Lindh (1985) depends upon an ad hoc explanation of the out-of-sequence 1934 earthquake. A less-contrived forecast would have assigned a conditional probability of about 60 ± 20 per cent to the 1985.0 to 1993.0 interval and 30 ± 15 per cent to the 1990.0 to 1993.0 interval.

California

Off-fault ground ruptures in the Santa Cruz Mountains, California: Ridge-top spreading versus tectonic extension during the 1989 Loma Prieta earthquake

The M s 7.1 Loma Prieta earthquake of 18 October 1989 produced abundant ground ruptures in an 8 by 4 km area along Summit Road and Skyland Ridge in the Santa Cruz Mountains. Predominantly extensional fissures formed a left-stepping, crudely en echelon pattern along ridges of the hanging-wall block southwest of the San Andreas fault, about 12 km northwest of the epicenter. The fissures are subparallel to the San Andreas fault and appear to be controlled by bedding planes, faults, joints, and other weak zones in the underlying Tertiary sedimentary strata of the hanging-wall block. The pattern of extensional fissures is generally consistent with tectonic extension across the crest of the uplifted hanging-wall block. Also, many displacements in Laurel Creek canyon and along the San Andreas and Sargent faults are consistent with right-lateral reverse faulting inferred for the mainshock. Additional small tensile failures along the axis of the Laurel anticline may reflect growth of the fold during deep-seated compression. However, the larger ridge-top fissures commonly have displacements that are parallel to the north-northeast regional slope directions and appear inconsistent with east-northeast extension expected from this earthquake. Measured cumulative displacements across the ridge crests are at least 35 times larger than that predicted by the geodetically determined surface deformation. These fissures also occur in association with ubiquitous landslide complexes that were reactivated by the earthquake to produce the largest concentration of co-seismic slope failures in the epicentral region. The anomalously large displacements and the apparent slope control of the geometry and displacement of many co-seismic surface ruptures lead us to conclude that gravity is an important driving force in the formation of the ridge-top fissures. Shaking-induced gravitational spreading of ridges and downslope movement may account for 90¿ or more of the observed displacements on the linear fissures. Similar fissures occurred in the same area and elsewhere near the San Andreas fault during the predominantly right-lateral 1906 San Francisco earthquake and suggest that the Loma Prieta ground ruptures may, in large part, be independent of fault kinematics.

California

The Marina District, San Francisco, California: Geology, history, and earthquake effects

A northwest-trending valley in the bedrock surface is buried by firm Pleistocene bay clay, a dense Pleistocene sand layer, soft Holocene bay sediments, loose to dense Holocene beach and dune sands, and artificial fill that have an aggregate maximum thickness of about 90 m (300 ft). Artificial filling of a cove at the site of The Marina District proceeded gradually from the late 1860s to 1912, when major hydraulic filling was done for the Panama-Pacific International Exposition. The remains of thousands of piles driven for the Exposition very probably still exist and have had unknown effects on long-term ground settlement and earthquake-related ground displacements. Intensity maps of the 1906 earthquake, and seismic recordings and severe building damage in 1989, reported by others, indicate that ground motion was amplified on both natural and artificial ground. This suggests that the configuration of the bedrock surface and the location and thickness of various clay and sand deposits underlying the fill had an important effect on the shaking. However, most of the settlement and liquefaction and the damage to pipelines, building foundations, streets, side-walks, and curbs occurred in areas of artificial fill consisting mainly of loose sand.

California

The Loma Prieta earthquake, ground motion, and damage in Oakland, Treasure Island, and San Francisco

The basis of this study is the acceleration, velocity, and displacement wave-forms of the Loma Prieta earthquake (18 October 1989; M = 7.0) at two rock sites in San Francisco, a rock site on Yerba Buena Island, an artificial-fill site on Treasure Island, and three sites in Oakland underlain by thick sections of poorly consolidated Pleistocene sediments. The waveforms at the three rock sites display a strong coherence, as do the three sedimentary sites in Oakland. The duration of strong motion at the rock sites is very brief, suggestive of an unusually short source duration for an earthquake of this size, while the records in Oakland show strong amplification effects due to site geology. The S -wave group at Treasure Island is phase coherent with the Oakland records, but at somewhat diminished amplitudes, until the steps in acceleration at approximately 15 sec, apparently signaling the onset of liquefaction. All seven records clearly show shear-wave first motion opposite to that expected for the mainshock radiation pattern and peak amplitudes greater than expected for sites at these distances (95 ± 3 km) from an earthquake of this magnitude. While the association between these ground motion records and related damage patterns in nearby areas has been easily and eagerly accepted by seismological and engineering observers of them, we have had some difficulty in making such relationships quantitative or even just clear. The three Oakland records, from sites that form a nearly equilateral triangle about the Cypress Street viaduct collapse, are dominated by a long-period resonance (≃ 1 1/2-sec period) far removed from the natural frequency of the structure to transverse motion (2.5 Hz) or from high-frequency amplification bands observed in aftershock studies. A spectral ratio arbiter of this discrepancy confuses it further. The failure of the East Bay crossing of the San Francisco-Oakland Bay Bridge cannot be attributed to relative displacements of the abutments in Oakland and Yerba Buena Island, but the motions of the Bay Bridge causing failure remain unknown. The steps in acceleration at Treasure Island present unusual strong-motion accelerogram processing problems, and modeling suggests that the velocity and displacement waveforms are contaminated by a spurious response of the filtering operations to the acceleration steps. A variety of coincidences suggests that the Treasure island accelerogram is the most likely strong-motion surrogate for the filled areas of the Marina District, for which no mainshock records are available, but the relative contributions of bad ground, poor construction and truly strong ground motion to damage in the Marina District will never by known in any quantitative way. The principal lesson of all of this is that until a concerted effort is mounted to instrument ground and structures that are likely to fail during earthquakes, our understanding of the very complex relationships between strong ground motion and earthquake damage will, in general, remain rudimentary, imprecise, and vague.

California

On the characteristics of local geology and their influence on ground motions generated by the Loma Prieta earthquake in the San Francisco Bay region, California

Strong ground motions recorded at 34 sites in the San Francisco Bay region from the Loma Prieta earthquake show marked variations in characteristics dependent on crustal structure and local geological conditions. Peak horizontal acceleration and velocity inferred for sites underlain by “rock” generally occur on the transverse component of motion. They are consistently greater with lower attenuation rates than the corresponding mean value predicted by empirical curves based on previous strong-motion data. Theoretical amplitude distributions and synthetic seismograms calculated for 10-layer models suggest that “bedrock” motions were elevated due in part to the wide-angle reflection of S energy from the base of a relatively thin (25 km) continental crust in the region. Characteristics of geologic and geotechnical units as currently mapped for the San Francisco Bay region show that average ratios of peak horizontal acceleration, velocity and displacement increase with decreasing mean shear-wave velocity. Ratios of peak acceleration for sites on “soil” (alluvium, fill/Bay mud) are statistically larger than those for sites on “hard rock” (sandstone, shale, Franciscan Complex). Spectral ratios establish the existence of predominant site periods with peak amplifications near 15 for potentially damaging levels of ground motion at some sites underlain by alluvium and fill/bay mud. Average spectral amplifications inferred for vertical and the mean horizontal motion are, respectively, (1,1) for sites on the Franciscan Complex (KJf), (1.4, 1.5) for sites on Mesozoic and Tertiary rocks (TMzs), (2.1, 2.0) for sites on the Santa Clara Formation (QTs), (2.3, 2.9) for sites on alluvium (Qal), and (2.1, 4.0) for sites on fill/Bay mud (Qaf/Qhbm). These mean values are not statistically different at the 5% significance level from those inferred from previous low-strain data. Analyses suggest that soil amplification and reflected crustal shear energy were major contributors to levels of ground motion sufficient to cause damage to vulnerable structures at distances near 100 km in the cities of San Francisco and Oakland.

California

The Parkfield prediction fallacy

The Parkfield earthquake prediction is generally stated as a 95% probability that the next moderate earthquake there should occur before January 1993. That time limit is based on a two-sided 95% confidence interval. Because at the time of the prediction (1985) it was already clear that the earthquake had not occurred prior to 1985, a one-sided 95% confidence interval would have been more appropriate. That confidence interval ended in October 1991. The Parkfield prediction was based on an extrapolation of five of the six events in the 1857 to 1966 earthquake sequence; the 1934 event was omitted because it did not fit the regularity exhibited by the other data. The fallacy in the prediction is that it did not take account of other less-contrived explanations of the Parkfield seismicity (e.g., not excluding the 1934 event). Even if the Parkfield earthquake should occur in the near future, it would be better explained by less-contrived hypotheses.

Bulletin of the Seismological Society of America

Site response estimates in Salt Lake Valley, Utah, from borehole seismic velocities

The general correlation of Salt Lake Valley sites located on soft, saturated unconsolidated silty and clayey deposits (that is, deposits with low S -wave velocity) with high seismic amplification at the ground surface motivated our investigation of the relationship between the P - and S -wave seismic velocity ( V p and V s ) of these units and their corresponding observed site response. We found that low, near surface V s −1.5 is proportional to seismic amplification measured on the surface, and suspected that we might be able to predict the site response if the near surface seismic velocity structure were known. With this idea in mind we constructed plane-layered seismic impedance models from borehole data in order to correlate impedance structure with variations in site response. Seismic travel times, measured in a borehole at 2-m intervals, were converted into compressional and shear wave seismic velocity profiles for 22 boreholes (average depth = 59 m) in Salt Lake Valley, Utah. Using this impedance model, we estimated site response on the ground surface of the borehole site to within 12% of the measured value in the 0.7 to 1.0 Hz frequency range for six of the twenty sites, and within 20% for 55% of the sites. All except two of our site response estimates are within a factor of two of the measured value. Thus, high values of seismic amplification appear to be partially explained by a near surface high-impedance contrast produced by the low S -wave velocities. Comparing the downhole data with published Salt Lake Valley ground motion data derived from Nevada nuclear tests shows that increased site response (sites of relative ground motion amplification) is associated with: (1) a lower value of V s (110 to 400 m/sec), and (2) high Poisson ratios (0.45 to 0.49) derived from borehole V p and V s values. The lowest S -wave velocities found in the Salt Lake Valley are comparable to other regions, such as the muds around San Francisco Bay and the lake sediments of Mexico City, with low S -wave velocities and a record of severe seismic wave amplification in previous earthquakes. The very-low-velocity surface layer in Salt Lake Valley is, however, about half as thick (10 to 14 m) as the low-velocity layers around San Francisco Bay and Mexico City. We also considered the influence of sedimentary basin fill on site response, because coincidentally, the sites of high seismic wave amplification correspond to the locations of thickest basin fill. The valley fill impedance structure, revealed in seismic reflection profiles we acquired, indicate that a more dynamic impedance structure characterizes sites near the center of the valley where the basin fill is thickest. The reflection data from mid-valley sites typically have more high-amplitude reflectors relative to basin edge sites. The sites with a more dynamic impedance structure suggest that the site response would also be correspondingly different. Thus, the broadband, deep basin effect on site response might account for some of the discrepancy between observed and predicted site response in this study.

Utah

Three-dimensional simulations of ground motions in the San Bernardino Valley, California, for hypothetical earthquakes on the San Andreas Fault

Three-dimensional finite difference simulations of elastic waves in the San Bernardino Valley were performed for two hypothetical earthquakes on the San Andreas fault: a point source with moment magnitude M5 and an extended rupture with M6.5. A method is presented for incorporating a source with arbitrary focal mechanism in the grid. Synthetics from the 3-D simulations are compared with those derived from 2-D (vertical cross section) and 1-D (flat-layered) models. The synthetic seismograms from the 3-D and 2-D simulations exhibit large surface waves produced by conversion of incident S waves at the edge of the basin. Seismograms from the flat-layered model do not contain these converted surface waves and underestimate the duration of shaking. Maps of maximum ground velocities occur in localized portions of the basin. The location of the largest velocities changes with the rupture propagation direction. Contours of maximum shaking are also dependent on asperity positions and radiation pattern.

California