Travel Time Ratio Research Articles

Changes in Vp/Vs with depth: Implications for appropriate velocity models, improved earthquake locations, and material properties of the upper crust

Properties associated with the arrival times of shallow microearthquakes are determined for three tectonically different sites: Soviet Central Asia; the Central United States; and southern California. Simple graphical presentations of the earthquake data, including Wadati and Riznichenko diagrams, are used to resolve the trade-off in origin time and focal depth. Estimates of the average half-space velocities for P and S waves, and of the travel-time ratio ( ts/tp ) are also obtained that are relatively free of any model constraints used to initially locate the earthquake. In all cases, P and S arrivals exhibit a systematic decrease in ts/tp with depth in the upper few kilometers. This decrease is significant and matches similar variations observed in situ for the velocity ratio ( Vp/Vs ). Based on laboratory and theoretical studies, such observations are consistent with the closing of saturated microcracks with increasing confining pressure. Independent determinations of velocity structure and rock properties from both refraction studies and borehole experiments show analogous results. By specifying separate velocity models for both P and S waves that reflect this variation, rather than assuming a constant value of Vp/Vs , we find improved stability in hypocenter determination and increased resolution of shallow seismicity patterns.

The attraction of countryside sites

The distribution of car trips to countryside sites, though primarily dependent upon accessibility, is also a function of the site attraction. This paper describes an attempt to assess attraction in numerical terms drawing upon techniques used by the geographer and the transportation planner. It is based on a behavioural model in which excursion rates and travel times of visitors to countryside sites were obtained by questionnaire surveys in the West Midlands region. A method is established for determining sequentially the relative attraction of pairs of sites through plotting excursion rate ratios and the respective travel time ratios for common visitor origins; therefrom, for a travel time ratio of unity, the relative excursion rates can be found. Further investigation suggested that site extensiveness contributes to attraction in proportion to the square root of the area. Relative intrinsic attractiveness—essentially land form and mantle—can be determined using a points scoring system. These two compone...

Crustal studies, velocity inversions, and fault tectonics: Results from a microearthquake survey in the New Madrid Seismic Zone

A dense network of portable seismographs was operated in the Ridgely area of western Tennessee in May of 1978. During 32 days of operation, 122 earthquakes were detected, of which 90 were located. The high quality P and S arrivals recorded exhibit travel time ratios (ts/tp) that decrease significantly with depth. This decrease is most rapid in the upper few kilometers and necessarily reflects similar changes in the velocity ratio (Vp/Vs). Based on laboratory and theoretical studies, such observations are consistent with a decrease in crack density with increasing confining pressure. A special study of Vp, Vs, and Vp/Vs revealed strong variations with depth that also correlate with rock type. Inversion of the data for both P and S velocity structures confirms the presence of a low‐velocity zone in the depth range 2 to 5 km; a high‐velocity lid, with high Vp/Vs and thus, high crack density; and a boundary at the near surface for S to P conversion, associated with the unconsolidated saturated sediments of the Mississippi embayment. Relocated hypocenters using independent velocity structures for P and S are systematically deeper and define a seismogenic layer between 4 and 13 km depth. The earthquakes near Ridgely show that most of the activity is occurring on a northwest striking reverse fault that dips to the southwest. Minor off‐fault activity within the hanging wall was also observed representing motion on a series of small normal faults dipping to the northeast. Other composite focal mechanisms were determined for nearby regions. These solutions are all in general agreement with a horizontal compressive stress field striking northeast to east, favoring right‐lateral strike‐slip motion on left‐stepping northeast trending faults, or reverse motion on faults trending northwest and north. These results are consistent with the stress field found in a large area interior to the United States, and imply a rotation of the regional stress field since the late Cretaceous when extensional faulting occurred in the area.

Attenuation of short‐period P, PcP, ScP, and pP waves in the Earth's mantle

The parameter t* (ratio of body wave travel time to the average quality factor Q) was estimated under various assumptions of the nature of the earthquake sources for short‐period P, PcP, and ScP phases originating from earthquakes in the Fiji‐Tonga region and recorded at the Warramunga Seismic Array at Tennant Creek (Northern Territory, Australia). Spectral ratios were calculated for the amplitudes of PcP to P and of pP to P. The data reveal a laterally varying Q structure in the Fiji‐Tonga region. The high‐Q lithosphere descending beneath the Tonga Island arc is overlain above 350 km depth by a wedgelike zone of high attenuation with an average Qα between 120 and 200 at short periods. The upper mantle farther to the west of the Tonga island arc is less attenuating, with Qα between 370 and 560. Qα is about 500 in the upper mantle on the oceanic side of the subduction zone. The t* estimates of this study are much smaller than estimates from the free oscillation model SL8. This can be partly explained by regional variations of Q in the upper mantle. If no lateral Q variations occur in the lower mantle, a frequency‐dependent Q can make the PcP and SeP observations consistent with model SL8. Adopting the absorption band model to describe the frequency dependence of Q, the parameter τ2, the cut‐off period at the high‐frequency end of the absorption band, was determined. For different source models with finite corner frequencies, the average τ2 for the mantle is between 0.01 and 0.10 s (corresponding to frequencies between 16 and 1.6 Hz) as derived from the PcP data, and between 0.06 and 0.12 s (2.7 and 1.3 Hz), as derived from the ScP data.

Temporal variations of tS /tP ratios before and after Koyna earthquake of 10 December 1967 and calculation of its magnitude

An analysis of the body wave travel time ratios (tS /tP) has been made for four seismographic stations Koyna Nagar, Satara, Mahabaleswar and Pune-from 24 October to 15 December 1967. The arrival times of body waves in different stations have been taken from published reports on Koyna Earthquakes. Origin times of the fore-shocks and aftershocks of the main Koyna earthquake of 10 December 1967 (M =6.2) have been calculated from the plots of S-P intervals and P arrival times at different stations. A plot of tS / tP ratios against time shows the anomalous variation of the ratio with a fall of about 10 to 14 % from the mean values for the period under consideration in Koyna Nagar, Satara and Mahabaleswar. No such tS/tP variations have been observed in Pune, which shows more or less steady values. The time interval, which we call anomalous period, from the date of fall of tS/tP from the mean value upto the time of occurrence of the main shock on 10 December 1967 is 32 days in each station. this anomalous period seems to coincide with the reported sharp and simultaneous changes indicated by some strain gauge placed in Koyna Dam, for about a month prior to the occurrence or the main Koyna earthquake. On using empirical relations based on dilatancy-fluid diffusion model, this amount of anomalous period is equivalent to that of a smaller shock of magnitude between 4 and S. Consideration of aftershock area coupled with other empirical relations also indicates similar magnitude.
 These facts tend to suggest either (1) the empirical relations used here do not hold good for Koyna earthquake or, (2) a smaller shock of magnitude between 4 and 5, occurring just ahead of the main shock, gave rise to tS /tP anomalies.

Cost, convenience and quality in child care demand

This paper presents an economic analysis of child care use by employed women with children under six years of age. Observations of actual child care choices are used to estimate the relative importance assigned by parents to cost, convenience and quality in child care. On the basis of these estimates, the chances that each type of child care arrangement will be used are predicted. Projections of child care use are presented for a range of potential costs, travel times, child-staff ratios, and family circumstances. This study is unique in employing information not only on child care arrangements already used, but also on the alternative arrangements available to individual families. The child care data were collected in a 1977 survey of New York City employees. Overall, the model correctly predicted 78% of the observed child care choices. The results of the analysis show strong effects of cost in child care choice. The demand for day care centers is especially sensitive to user cost; if centers were available free of charge, for example, there is a 65% chance that the average single working mother in the sample would use one. Travel time and child-staff ratios have small but statistically significant effects on the choice of child care arrangements. Weekend work schedules and presence of infants are also important choice factors. Once costs are accounted for, family income has no significant effect on the type of child care chosen.

LISPB -- V. Studies of crustal shear waves

Summary. Many shots in the LISPB profiles produced shear waves with large amplitudes which were recorded by three-component stations. However, S waves seem to be strongly attenuated when they propagate through complex velocity structures. Upper crustal refractions (mainly land shots) and wideangle reflections (mainly sea shots) were picked with the help of particle motion plots. S to P travel-time ratios (ts/tp) were used to calculate the distribution of Poisson’s ratios in a crustal model. The results were generally close to u = 0.25 except in the upper crust south of the Southern Uplands Fault (u = 0.231) and in the middle crust under the Midland Valley (a = 0.224).

Study of the seismic velocity ratio for several regions of the South Island, New Zealand: evaluation of regional ts/tp and near source Vp/Vs values

The regional variations in space and time of the travel-time ratio ts/tp over a 600-km long section of the Alpine fault zone in the South Island, New Zealand, are discussed. The analyses are based on readings from micro-earthquakes. A significant difference in this ratio with depth between shallow and intermediate focus earthquakes in Fiordland was found, the former having a value of 1.72 and the latter 1.68. A 7 per cent decrease in ts/tp preceded a magnitude 3.5 earthquake in the Arthur's Pass region by about 10 day. The entire region studied was found to be characterized by regional ts/tp values of 1.74–1.70 except a 75-km long region near Arthur's Pass at the junction of the Alpine and Hope faults which had a value of about 1.63. This low value was observed in both 1972 and 1973. Near-source Vp/Vs ratios of about 1.55 were estimated for two earthquake zones (sub-regions) within the Arthur's Pass region. Computed estimates of the acoustic velocities Vp and Vs for the Arthur's Pass region yielded values of about 5.48 and 3.40 km/s, respectively. When compared to ts/tp values from other parts of the world and with ultrasonic data on rock types similar to those present in the South Island, the regional ts/tp study indicates that the Arthur's Pass region possesses a significantly low value of ts/tp. This low ratio for the Arthur's Pass region may be interpreted in two different ways. Since the ts/tp values are higher in the regions to the north and south of the Arthur's Pass region, with all three regions having the same lithologic unit exposed on the surface, it may reflect the depth to the crystalline basement. In particular, it may be suggestive of a greater thickness of sediments existing within the Arthur's Pass region. Alternatively, this low ratio may be indicative of a temporal effect precursory to a future earthquake. On this assumption, a quantitative estimate of the size, location and time of occurrence of a possible future earthquake is deduced. Such an event would have a minimum magnitude of 6.5 and would occur in the next few years. Whatever the explanation, which from this analysis cannot be definitely decided, this study, by attempting to define lateral heterogeneities in the crust, warns that in earthquake prediction studies involving the interpretation of ts/tp anomalies, considerable lateral variations in this parameter may result from local variations in geology.

The relationship between anelastic attenuation and regional amplitude anomalies of short-period P waves in North America

P-wave attenuation (expressed in terms of t* = T/Q, the ratio of travel time to the P-wave quality factor Q/sub a/) was measured for a large number of teleseismic paths using spectral ratios for nuclear explosions in the short-period band 0.5 to 4 Hz. If these new t* values along with other data in the literature are subdivided into two groups, one involving wave paths which descend and emerge entirely under shields or stable platforms and the other involving paths with either end of the wave path under the Western United States (WUS), a definite difference can be found between the average t* values of the two groups. The difference in attenuation, which gives a t* difference greater than 0.2, is sufficient to explain the fact that teleseismic events appear to be, on the average, about 0.26 units lower in magnitude when measured at WUS stations as compared to Eastern United States (EUS) stations, assuming that the observed dominant frequency of teleseismic P waves is about 1 Hz. A similar difference exists in the spectra of teleseismic short-period S waves observed in WUS relative to those seen in EUS. The observations indicate that Q/sub ..cap alpha../ is high (Q/sub ..capmore » alpha../ greater than 1500) throughout the upper mantle under shield areas while the WUS (with the possible exception of the Colorado Plateau) is underlain by a low-Q layer. If this layer coincides in vertical extent with the upper-mantle low-velocity layer, the Q/sub ..cap alpha../ there should be about one-half that of the value given by Archambeau et al. (1969). The t* values for short-period P waves are considerably lower than those derived by the other authors from body waves in the long-period band, indicating that Q/sub ..cap alpha../ is frequency dependent and increases with frequency.« less

Distribution of regional vehicle miles of travel to large zones for sketch planning

The basic feature of a sketch planning model is the relatively fast processing of a minimal amount of data to provide better than order of magnitude information about a proposed transportation plan. The goal is not a finely detailed analysis of an alternative, but rather an idea of its relative worth as compared to other alternatives on the basis of a range of impacts. Effects are desired, not only at the regional level, but also subregionally, with the level of disaggregation being such that it provides a general, but useful, degree of localization. An approach is developed for distributing travel about a region subdivided into zones with an average size of about 10–15 square miles and ranging in size from 6 to 30 square miles. Distance is used as the travel impedance parameter and time ratio is the determining factor for diversion to freeways. An exponential distance distribution formulation is used which has been empirically shown to hold in several regions and which enables the development of an approach requiring almost no calibration. Test results of the approach in two metropolitan areas of distinctly different character indicate that the analysis does represent a reasonable solution to the problem of distributing travel, by facility type, in a region composed of rather large zones.

Intensities and travel times of seismic rays in a sphere with a linear velocity function

Abstract Equations are presented which permit the calculation of distances, travel times and intensity ratios of seismic rays propagating through a spherical body with concentric layers having velocities which vary linearly with radius. In addition, a method is described which removes the infinite singularities in amplitude generated by second-order discontinuities in the velocity profile. Numerical calculations involving a reasonable upper mantle model show that the standard deviations of the errors for distance, travel time and intensity ratio are 0.0046°, 0.057 sec, and 0.04 dB, respectively. Computation time is short.

Shear dilatancy in rock and precursory changes in seismic velocities

The observed decrease and subsequent increase of the travel time ratio of shear and compressional waves prior to the occurrence of earthquakes in the U.S.S.R. and in the U.S.A. is related to shear dilatancy of rocks around the focal area. Shear‐dilatancy is identified as an integral part of elastic and post‐elastic deformation of solid isotropic media; it is not, as is widely believed, the result of cracking, but the cause of crack initiation.

Spatial and temporal variations ints/tpand inPwave residuals at Blue Mountain Lake, New York: Application to earthquake prediction

Renewed earthquake activity at Blue Mountain Lake (BML), New York, in July 1973 provided an excellent opportunity to monitor the travel time ratio of S to P waves (ts/tp) in real time and to test the ts/tp technique as a predictive tool. From a mean value of 1.73 on July 30, 1973, ts/tp decreased to about 1.5 over the next 2–3 days. On August 1 a prediction was made that an earthquake of magnitude 2.5–3 would occur in a few days. Upper limits of the magnitude and the time of occurrence of the expected earthquake were inferred from the spatial extent of the seismic anomaly. As a result of the prediction an additional strong motion accelerograph (SMA) was installed in the source region. At 2310 UT on August 3,1973, a magnitude 2.6 earthquake occurred at BML and triggered two SMA's. In addition to the seismic activity a number of explosions were recorded from a variety of azimuths. The P wave arrivals from distant quarry blasts, refracted from a high-velocity layer at 4 km beneath BML, showed late arrivals at five stations during the premonitory low in ts/tp. The P wave delays were maximum (0.13 s) in the hypocentral region of the earthquake and decreased away from it along two profiles. These results indicate that changes in ts/tp are caused by changes in the material properties of the earthquake source region. The anomalous zone (region of low P velocity) for the August 3 earthquake (aftershock length 1 km, depth 1±0.1 km) was about 3–5 km in radius and was wholly or largely limited to the layer above the interface at 4-km depth. In contrast to the P delays observed from distant quarry blasts, P and S arrivals from local construction blasts (Δ < 10 km) show no large premonitory changes in either P or S travel times. This observation suggests that either no significant velocity anomalies occurred in the upper 0.5 km of the BML region or that the dilatant cracks were predominantly horizontal, the result being strong velocity anisotropy. This conclusion is supported by data from seismic sources; events located at shallow depths show normal (1.75) to high (1.85) ts/tp values even when values as low as 1.5 are observed from deeper sources. This finding places constraints on the use of artificial sources to monitor changes in velocity, since the effects of anisotropy may have to be taken into account in addition to ensuring that ray paths to the recording stations penetrate the zone of anomalous velocity. A maximum likelihood method was used to invert data from individual small earthquakes to determine P and S velocities in the anomalous zone. The results, which are consistent with the explosion data, indicate that the premonitory decreases in P and S velocities were much more pronounced for sources at depths of 1–2 km than for those near the surface. The inferred low values of P and S velocities were, respectively, about 22 and 12% below normal. This study also shows that ts/tp inferred from a Wadati plot is a function of the distribution of stations relative to the anomalous zone. To optimize the use of ts/tp as a predictive tool, this study suggests that not only temporal but spatial variations of velocity anomalies should be monitored. This emphasizes the need for multistation coverage for reliable earthquake prediction.

Upper mantle velocities determined from local observations of deep earthquakes

abstract A method for determining upper mantle velocities is presented. Observations of deep earthquakes at small epicentral distances enable standard travel-time tables to be modified for regional studies. This is done by calculating the ratio of the actual travel time to that given in the tables, for a range of focal depths. Local velocity models may then be determined. The Jeffreys-Bullen travel times have been modified to suit the New Zealand region. Strong evidence is presented for velocities higher than the Jeffreys-Bullen values at depths less than about 160 km, and below that a low-velocity zone extending to a depth of at least 300 km.

Dilatancy and premonitory variations of P, S travel times

abstract Nur's (1972) explanation of the observed premonitory decrease in the travel-time ratio of shear and compressional waves, ξ, in terms of dilatancy is modified by considering the anisotropic characteristics of dilatant rock in the focal region. The expected change in ξ is influenced by the orientation and type of geologic fault as well as the geometry of source and observation points. The shear wave will in general split into two components traveling with somewhat different velocities.

Dilatancy, pore fluids, and premonitory variations of ts/tp travel times

Abstract Nerseov et al. (1969) found that the travel-time ratio of shear and compressional waves, ξ = ts/tp varies prior to the occurrence of earthquakes in the Garm region, USSR. Laboratory results indicate that the decrease of ξ can result from dilatancy of rocks around the focal zone. The subsequent increase of ξ, which terminates with an earthquake, can be caused by the flow of ground water into the dilated zone. The increasing pore pressure weakens the rock and leads to the observed failure.

Laboratory Identification Of The Quality Factor Q: Comparative Presentation And Evaluation Of Spectral Ratio And Rise Time Methods

Two different methods for evaluating attenuation through the quality factor Q are presented, tested and compared. Both methods are based on laboratory experiments of ultrasonic P waves propagation at ad-hoc rock samples. The advantages of each experimental method are discussed. The spectral method is a rather laboratory oriented methodology providing attenuation information over a range of frequencies and seems to be well adapted for intermediate attenuative media of propagation. Its outcome is strongly influenced by parasitic signal reflections, coupling functions and scattering effects. On the other hand, the rise time method, less influenced by scattering phenomena, is dependent on the coupling functions (role of interfaces) and the experimental set-up. For a given experimental set-up a linear relation can be determined between the rise time and the ratio of travel time over the quality factor (T/Q) when a known source signal is simulated by a realistic linear viscoelastic model of propagation.

Transit Trip Estimation - San Francisco Bay Area

By 1975, transit patronage and operating speed will increase by 26% and 36% respectively in the San Francisco Bay Area. The traffic estimates embrace coordination of three local systems—BARTD, Muni, and AC Transit—and are based upon estimating models developed for 1965 and projected to 1975. The data processed quantifies and correlates the socioeconomic factors which generate transit use-transit systems, characteristics of riders, and spatial organization of land use. Initially, independent and correlated data on travel characteristics of riders in 474 zones, travel time ratios, and transit routes, were coded to develop the amount of riding on each link of 128 routes. Comparative analyses with auto and highway data provided insight into relative attractiveness of transportation modes. Correlation of relevant variables by simple and multiple regression determined reliable measures of trip production and attraction by zones (gravity model) and of trip distribution between zones (transit trip end model). Comparable models for 1975 transit use produce informed estimates incorporating projected network and demographic data.

Possible Subjective Significance of the Ratio of Height to Width of Concert Halls

For positions along the center aisle of a rectangular hall, the ratio of travel times of early reflections from the ceiling and walls is approximately equal to 2H/W, where H is the height and W is the width of the hall. This ratio was determined for 38 concert halls and opera houses and the results were compared with the subjective categories compiled in Beranek's extensive investigation [L. L. Beranek, Music, Acoustics and Architecture (John Wiley &amp; Sons, Inc., New York, 1962)]. The correlation coefficient for 2H/W and a numerical scale of the subjective categories is 0.71. Thus it appears that this ratio, which determines the relative arrival times of early lateral and vertical reflections, accounts for a major portion of the subjective ratings. The importance of lateral versus vertical reflections has been substantiated by laboratory experiments conducted in an anechoic chamber, using delayed speech and music signals played through loudspeakers.