Bounce Point Research Articles

Global upper mantle structure from long‐period differential travel times

We have made over ten thousand measurements of PP‐P and SS ‐ S differential travel times from long‐period Global Digital Seismograph Network recordings of all events with mb ≥ 5.5 which occurred during the years 1976 to 1986. We have obtained reasonable global coverage, with very good sampling of several regions of the world. The residuals range from −5 to 5 s for PP‐P and −12 to 12 s for SS‐S and reveal a large‐scale pattern of heterogeneity when plotted at the reflected phase's bounce point. Our experiments indicate that lower‐mantle structure and source‐receiver structure can each contribute approximately ±0.5 s to our measured PP – P residuals so there is considerable signal to be explained. The pattern observed in the PP – P measurements is similar to the pattern observed in the SS‐S measurements, with the SS‐S residuals 2 to 4 times larger in magnitude. Comparisons of our measured residuals to those predicted by the upper‐mantle models of Woodhouse and Dziewonski show that the overall patterns are quite similar but the amplitude of the model residuals is roughly a factor of 2 too small. Comparisons with the predictions of a whole‐mantle model of Tanimoto again shows that the predicted pattern of residuals is reasonably consistent with the observations but now the predicted residuals are too large by about a factor of 2. This variation in predicted amplitudes is probably mainly due to differences in the near‐surface structure of the models. We have also binned our measurements according to the tectonic regionalization GTR1 of Jordan and find a qualitative correlation of average residual with tectonic region. In particular, Precambrian shields show a strong anomaly, and there is a correlation of residual size with the age of oceanic crust at the bounce point. For all tectonic regions the ratio of SS ‐ S to PP ‐ P residuals is approximately 2. This ratio is consistent with a thermal origin for the observed signal. Finally, our measurements show no compelling evidence for azimuthal anisotropy which might be related to fossil spreading direction or the direction of absolute plate motion. Such a signal is probably overwhelmed by the large signal from three‐dimensional structure.

Evidence of a laterally variable lower mantle structure fromP- andS-waves

Examples of Gräfenberg-array data showing anomalous P-waves which typically arrive 3–5 s after the direct P-wave and which have a slowness 0.7–0.8 s deg-1 smaller than direct P are presented. This additional phase is most frequently observed for events located in the NE portion of the southern Kurile Island subduction zone 73°-80° from Gräfenberg, but systematically disappears for events in the SW portion of this zone. Because of the magnitude of the slowness difference, these observations cannot be attributed to a complex source rupture process nor to multipathing through the descending slab. Likewise, they may not be accounted for by near-receiver structure because these phases are not seen for all Kurile events. If present they appear at all stations of the array but they follow direct P too closely to be a multiple from the Mono. Therefore, we conclude they are very likely caused by lower mantle velocity structure. The most likely explanation is the presence of a P velocity jump of about 3 per cent approximately 290 km above the core-mantle boundary, since such a reflector in the lowermost mantle not only gives a good fit of traveltimes and slowness but is also able to model the waveform and the amplitudes of this additional P phase. The distribution of bounce points on this reflector for the Kurile events indicates a lateral extension of this velocity anomaly under northern Siberia of about 150 km by at least 200 km. The best fitting S-wave model has a reflector in the same depth, but the velocity contrast seems to be only about 2 per cent suggesting a different behaviour of the P and S velocity in D″. Few events from other regions in this distance range are suitable for a definitive analysis of this kind. From among this group some observations indicate a lower mantle anomaly under the Lomonosow Ridge and under northern Greenland; but since the lower mantle under western Siberia, northern Novaya Zemlya, the Azores Islands region and the USSR-Afghanistan border region does not produce an additional phase in the Gräfenberg recordings it is very unlikely that such a velocity anomaly in the lowermost mantle is a global feature.

Method for extending the lateral subsurface coverage in VSP surveys

In a VSP survey, the subsurface coverage of the bounce points of primary reflections is limited to one-half the offset between a borehole and a seismic-source point. The subsurface coverage may be extended by use of selected multiply-reflected wavefield arrivals.

Periodic bounce trajectories with a low number of bounce points

In this paper we study the existence of a periodic trajectory with prescribed period, which bounoes against the boundary of an open subset of ℝN, in presence of a potential field. We prove the existence of periodic solutions with at most N + 1 bounce points.

The relationship of target and response complexity in coincident timing performance.

This paper reports two experiments concerned with the interaction of response and target factors in a coincident timing situation. Coincident timing involves executing a response to intercept a moving target. The target response relationship was manipulated in the first experiment by providing some targets with no structure (linear path) and others containing 1 and 2 bounce points. In the second experiment, responses required 0, 1, or 2 reversals in direction. The results provide tentative support for the notion that structure in the target path could be linked to the key temporal response dynamics for improved performance consistency, and that subjects may alter their response structure to incorporate this linkage. This can be further extended to the advantage of simply moving while perceiving movement. This paper stresses the importance of examining the perceptual and motor requirements of the coincident timing skill in unison.

P‐coda at distances 80° – 120° and structure beneath subduction zones: Example of Chile

Strong phases are sometimes observed between P and PP for earthquakes at epicentral distances 80° – 120°. The present study analyzes as an example broadband data from a Chilean earthquake recorded in Europe by the NARS network, and by worldwide distributed GEOSCOPE stations. Clear phases are observed in the P‐coda only for the European stations.Underside reflections at upper mantle discontinuities beneath the PP bounce point at the Mid‐Atlantic Ridge are unable to explain these phases. A discontinuity in the lowermost mantle at the top of D″ is also discarded as a possible explanation.Reflections and conversions at a strong reflector about 200 km deep beneath Chile provide a satisfying explanation of the observations. The P‐coda is dominated by waves leaving the focus as S‐waves. The focal solution and the resulting radiation pattern explain the variations with azimuth and epicentral distance of the phases observed in the P‐coda.The reflector at 200 km beneath Chile may be the upper boundary of a piece of slab detached from the Nazca plate. Alternatively, it may result from the chemical differenciation of the slab during its subduction. Modelling P‐coda generated in other subduction zones may help to specify this differenciation process.

Detection of underside P reflections at mantle discontinuities by stacking broadband data

Underside P‐reflections at mantle discontinuities are difficult to observe directly on seismograms mainly because of their low amplitude. It is shown that stacking seismograms obtained at several epicentral distances but having their PP bounce points in the same region, enables the identification of such phases. This method is applied to data from Japanese and Taïwan events recorded by the NARS array and other broadband European stations; discontinuities at about 670 and 300 km are revealed beneath Northern Eurasia.

Lateral heterogeneity and azimuthal anisotropy in the North Atlantic determined from SS‐S differential travel times

To explore upper mantle heterogeneity beneath the North Atlantic we have measured 70 SS‐S differential travel times using the waveform cross‐correlation method. Both the two‐way preliminary reference earth model (PREM) and J‐B (Jeffreys‐Bullen) residuals exhibit a maximum variation of 17 s, ranging from −10 to 7 and −9 to 8 s, respectively. The lack of correlation between SS‐S and S residuals, along with the strong correlation between SS‐S and SS residuals, suggests that SS‐S differential travel times eliminate source and receiver effects and sample the upper mantle anomalies near the SS bounce points without being strongly affected by lower mantle heterogeneities. We find evidence for a strong local anomaly in the North Atlantic; residuals for bounce points immediately to the north of the Azores‐Gibraltar plate boundary average about 4 s faster than for the bounce points to the south of the boundary. We infer that this velocity contrast exists in the lithosphere and continues below a depth of 200 km. A series of linear multiple‐regression experiments demonstrate that variation in velocity with increasing age of the seafloor and azimuthal anisotropy are both significant contributors to the PREM and J‐B residuals. Assuming that travel time delays are a linear function of the square root of the seafloor age, we find the coefficient for (age)½ to be about −1.0 s/(m.y.)½. This is smaller than but not significantly different from the corresponding slope for the S delays of intraplate earthquakes in the Atlantic reported by J. D. Duschenes and S. C. Solomon (1977) and favors the presence of small amounts of water (e.g., 0.1%) in the upper mantle. In modeling anisotropy we carry out an experiment using synthetic seismograms to examine the shear wave splitting phenomena in the anisotropic medium and investigate three possible forms for SH wave delay as a function of azimuth (θ): sinusoidal variations as a function of 2θ, 4θ, and a combination of 4θ (predominant) and 2θ that mimics the delay expected in olivine crystals when the α axis is aligned horizontally. Our regression models strongly prefer the predominance of a 4θ to a 2θ variation, and the last type of anisotropy explains our data best. From the preferred anisotropy model the olivine α axis, or the upper mantle shearing flow, is inferred to be oriented N‐S. The magnitude of the azimuthal variation suggests that anisotropy extends over a depth range of several hundred kilometers in the upper mantle.

The geoid, small‐scale convection, and differential travel time anomalies of shear waves in the central Indian Ocean

We have measured 37 differential travel times for the phase pairs SS‐S, sSS‐sS, ScS2‐ScS, ScS2‐S, sScS2‐sScS, and sScS2‐sS. Each pair included a surface bounce point in the central Indian Ocean between 4°N and 21°S and 69° and 85°E. Residuals were calculated relative to both the J‐B travel time tables and the PEM‐C earth model and were corrected for the elevation of the bounce points. The mean J‐B residual associated with bounce points in the Central Indian Basin is −2.8±0.7 s (fast). This contrasts with +4.2 s (slow) reported for the western Pacific by Sipkin and Jordan, and is similar to the −4.0 s found for old continental nucleii. After correcting for known differences between continental and oceanic crustal structure and for differences in measurement technique, we find that travel times in the mantle beneath the Central Indian Basin are midway in character between those beneath pre‐Cambrian shields and those beneath the western Pacific ocean basin. The fastest differential travel times occur along a line passing close to the center of the large Indian Ocean geoidal low. There is a clear increase in travel time with distance from the center of the geoid low, suggesting that the source of the geoid anomaly may also be largely responsible for the difference between the Central Indian and Pacific basins. The Chagos‐Laccadive Ridge seems to coincide with a transition from the fast differential travel times of the Central Indian Basin to slower differential travel times associated with bounce points beneath young seafloor near active spreading centers. There are also variations within the Central Indian Basin that are not related to surface geological features or to the age of the seafloor. These variations are periodic with a wavelength of about 640 km and with a NNE trend, which agrees approximately with the trend that would be expected for linear, convective rolls in the upper mantle.

Reassessment of a reported S‐delay under Trindade

We present a correction to a paper by Okal and Anderson (1975) about multiple ScS travel‐time anomalies. We have reanalyzed data for ScS2 surface bounces in the South Atlantic Ocean. From these data an ScS2‐S residual of 23.6 seconds was found by Okal and Anderson (1975). This corresponded to an ScS2 surface bounce point under Trindade island and was inferred to be due to very slow upper mantle associated with the Trindade hot spot. The analysis we present here invalidates this conclusion. The nature of the upper mantle under Trindade is an open issue.

Performance Equations for a "Stationary" Passive Satellite Relay (22,000-Mile Altitude) for Communication

Performance equations are given for the use of a single fixed satellite used as a passive bounce point for almost hemispherical coverage of the earth for communication purposes. The antenna size and transmitter power per cps of bandwidth for desired signal-to-noise ratio (SNR) at RF are given for various types of passively-reflecting satellites. Possible limitations due to terrestrial and extraterrestrial noise and future possibilities using low-noise receivers are discussed.