Shear Wave Travel Time Research Articles

Shear velocity and density of an attenuating earth

The dispersion that must accompany absorption is taken into account in many recent body-wave investigations but has been largely ignored in surface-wave and free-oscillation studies. In order to compare body-wave and free-oscillation data a correction must be made to travel times or periods to account for absorption-related physical dispersion. The correction depends on the frequency and Q of the data and can be as high as 1% which is much larger than the uncertainty of the raw data. Corrected toroidal mode data is inverted to obtain shear velocity and density versus depth. The average shear velocity in the upper 600 km is ∼2% greater than obtained from the uncorrected data. The resulting shear-wave travel times oscillate about the Jeffreys-Bullen values with an average baseline of only +0.5 second. Thus, the discrepancy between body-wave and free-oscillation studies is eliminated.

Mechanical Properties of Friable Sands From Conventional Log Data (includes associated papers 6426 and 6427 )

A new log interpretation method is presented for determining mechanical properties of friable sands. Factors considered in the method include overburden weight, fluid pressure, and additional earth loads caused by local geological conditions. Log data needed for the interpretation include conventional sonic, density, induction, and open-hole gamma ray. Introduction Certain in-situ mechanical properties of friable sands must be measured to determine if such formations will remain stable under different wellbore conditions. Stability problems that can then be resolved include estimating (1) how fast oil or gas may be produced without casing a sand problem,1,2 (2) if there is sufficient cementation between adjoining sand grains to avoid a possible sand problem when water production occurs,1,3 and (3) the formation fracture pressure gradient.4 Specific mechanical properties that enable such estimates are sand strength, strength of cementation between grains, bulk compressibility, and Poisson's ratio. This paper presents techniques for calculating these properties. The means for determining the in-situ mechanical properties of friable sands is through the use of well-log data. The accuracy of these properties determined from log data should be better than the properties determined from log data should be better than the properties determined by direct strength tests with core samples. Weakly cemented materials probably would disaggregate during the core recovery operation, and no strength of cementation would be detected in direct strength measurements. Relief of overburden load results in core expansion and subsequent breaking of weak bonds. Logs used include conventional sonic, density, induction, and open-hole gamma ray. The conventional sonic log is used in preference to a full-wave sonic log for calculating the mechanical properties of friable sands. The full-wave log can provide both compression and shear-wave travel times if the formation grains do not slip by each other as the acoustic signals pass through. Many of the rock properties could then be calculated directly5,6 from such measurements. Grain slippage apparently occurs readily in many friable sands; the shear-wave signal is dampened severely, and it is difficult to record reliable data. Techniques are developed in this paper that make it possible to substitute conventional sonic-log data for full-wave log data for calculating the mechanical properties of friable sands. Other methods have been reported1,4,7 for using log data to measure the mechanical properties incorporated all the following factors that can affect the mechanical properties:overburden weight gradients at different depths,other earth loads caused by local geological conditions,cementation,fluid saturation,fluid pressure,different bulk compressibilities, andthe change in elastic modulus values 1 of friable sands at different load conditions. These factors are considered in the calculation technique reported here.

Shear velocity in the lower mantle from explosion data

A new technique utilizing theoretical wave forms has been developed to determine precise shear wave travel times. This technique was applied to long-period World-Wide Standard Seismograph Network and Canadian network seismograms of five large nuclear explosions to obtain a surface focus shear wave data set containing about 100 travel times for distances greater than 30°. Very little scatter is present in the data from Novaya Zemlya and the Nevada test site, and so a reliable inversion to a lower mantle velocity structure is permitted. This velocity model, based on the 59 travel times from Novaya Zemlya, has significantly more structure than earlier models. The model, Sl, has proved to be appropriate for free oscillations as well as for travel times. This model should be useful in studying both lateral inhomogeneities and the mineralogical composition of the earth's mantle.

Lateral heterogeneity of the upper mantle determined from the travel times ofScS

Nearly 200 travel times of the phase ScS have been measured at World Wide Standardized Seismographic stations for 10 globally distributed deep-focus earthquakes. By comparing these times we have obtained estimates of the differences in one-way vertical shear wave travel times beneath various tectonic provinces of the earth. In particular, vertical shear wave travel times beneath normal ocean basins average about 5 s greater than times beneath continents, confirming the hypothesis advanced by Jordan and Anderson (1974) to explain the discrepancy between travel time base lines derived from free oscillation studies and those derived from body wave studies. The observed difference in vertical travel times, together with pure path surface wave dispersion data, implies that the differences between oceanic and continental structure extend to depths exceeding 400 km. ScS times for a station on the Galapagos Islands are smaller than those observed for normal ocean basins, suggesting that the velocities beneath the are higher than those beneath typical ocean basins. This observation is inconsistent with the existence of a simple thermal plume beneath the Galapagos.

Structure of the Shear-Wave Low-Velocity Channel in the Western United States

Shear-wave travel-time residuals observed at seismograph stations in the western United States indicate that there are lateral variations in the mantle low-velocity channel (LVC). Velocity models to fit the delay times are generated from the model of Ibrahim & Nuttli. Assuming that the velocity in the LVC is constant and that the depth to its bottom is fixed at 200 km, the channel velocity is found to be 3.85 km s−1. The maximum channel thickness, 160 km, occurs beneath southern Utah and central Arizona. Partial melting in the LVC of approximately 15 per cent by volume could result in S-wave delay times comparable to those found in this study, assuming that the sources of the delay times are wholly within the outer 200 km of the Earth. If they occur over a greater depth interval, a lesser amount of partial melting would be required to satisfy the observed travel-time data.

Ultrasonic shear wave birefringence as a test of homogeneous elastic anisotropy

Ultrasonic shear wave birefringence is used as a positive indicator of elastic anisotropy. Polarized shear waves are generated by conversion of a compressional P wave to a shear S wave at a free surface (Jamieson and Haskins, 1963). The P-S conversion technique is preferred over the direct use of AC-cut quartz shear wave transducers because the wave amplitudes are considerably greater in the conversion technique. Even though the P/S wave amplitude ratio for the P-S conversion transducers is 1/80, the P wave has sufficient amplitude for recognition. The rotation of the sample allows identification and measurement of the travel times of two orthogonally polarized shear waves. Relative difference in the two shear wave travel times positively establishes homogeneous anisotropy, even though the sample may be nearly isotropic in the P wave mode. Thus P wave velocity and travel path distance need not be known in order to detect elastic anisotropy. Shear wave birefringence is not restricted to any particular scale, and a minimum of one propagation direction may be used to establish anisotropy. A suite of 20 rock samples of various lithologies was measured according to this technique. All samples were found to be anisotropic. These results point out that elastic anisotropy is probably the rule rather than the exception in describing the elastic behavior of rock materials of hand sample size. It is therefore of interest to determine at which scale, if any, elastic anisotropy is no longer the rule but the exception. The use of shear wave birefringence may aid in answering this question.

Shear velocities and elastic parameters of the mantle

The recent shear wave travel-time data of Ibrahim and Nuttli (1967) and Doyle and Hales (1967) is reinterpreted to yield a shear-velocity structure that is compatible with Johnson's (1967) compressional-velocity structure. The elastic parameters Φ, K/μ, and σ are calculated as a function of depth. All three parameters increase with depth in the homogeneous regions of the mantle but only Φ increases through the transition regions. Poisson's ratio is apparently less for the close-packed deeper mantle phases than it is for the normal phases of the upper mantle. The theoretical prediction that dμ/dP becomes negative before a phase change is verified by the seismic data.

On the synthesis of shear-coupled PL waves

ABSTRACT Using the shear-coupled PL wave hypothesis of Oliver as a basis, a method is developed for computing synthetic long-period seismograms between the onset of the initial S-type body phase and the beginning of surface waves. Comparison of observed and synthetic siesmograms shows that this hypothesis can explain, in considerable detail, most of the waves with periods greater than about 20 sec recorded during this interval. The synthetic seismograms are computed easily on a small digital computer; they resemble the observed seismograms much more closely than the synthetic seismograms obtained through the superposition of normal modes of the Earth that have been reported in the literature. The synthesis of shear-coupled PL waves depends on a precise knowledge of the phase-velocity curve of the PL wave and travel-time curves of shear waves. Hence, in principle, if one of these quantities is well-known the other can be determined by this method. Phase-velocity curves of the PL wave are determined for the Baltic shield, the Russian platform, the Canadian shield, the United States, and the western North-Atlantic ocean, on the assumption that J-B travel-time curves of shear waves apply to these areas. These dispersion curves show the type of variations to be expected on the basis of the current knowledge of the crustal structures in these areas. Examples are presented to show that J-B travel-times of shear waves along paths between Kenai Peninsula, Alaska and Palisades, equatorial mid-Atlantic ridge and Palisades, and Kurile Islands and Uppsala need to be revised. Shear-wave travel-time curves that are not unique for reasons explained in the study but that give synthetic seismograms in agreement with the observed seismograms were obtained. The new S curves are compared with the J-B travel-time curves for S; and they all predict S waves to arrive later than the time given by J-B tables for epicentral distances smaller than about 30°. The new S curve for the Alaska to Palisades path appears to agree with one of the branches of a multi-branched S curve proposed recently by Ibrahim and Nuttli for the ‘average United States’ insofar as travel-times are concerned, but there are some differences in the slopes of the two curves.

Earth models obtained by Monte Carlo Inversion

The problem of uniqueness of earth structures obtained by the inversion of geophysical data is still unsolved. Monte Carlo methods offer the advantage of exploring the range of possible solutions and indicate the degree of uniqueness achievable with currently available geophysical data. This procedure was applied to the earth by using the following data: 97 eigenperiods, travel times of compressional and shear waves, and mass and moment of inertia of the earth. Indirect use was made of dt/dΔ data obtained from arrays. Five million models have been examined, and six have passed all tests. Results are as follows: (1) The earth's core is inhomogeneous, consistent with Fe(15–25%)-Si for the outer core and Fe(20–50%)-Ni alloy for the inner core. (2) The radius of the core is increased by 5 to 20 kilometers. (3) Large density and velocity gradients are found in the transition region without prior assumption of an equation of state. The transition region is a compositional boundary as well as a zone in which phase changes occur. The lower mantle shows an increase of the FeO/MgO + FeO ratio by a factor of 2 compared with the upper mantle. This could inhibit mantle-wide convection. (4) Upper mantle models fit better than ‘standard’ models when they are more complex, showing large fluctuations in shear velocity and density. Such complexity might be expected if the mantle is chemically and mineralogically zoned, if there are high thermal gradients, and if partial melting takes place. However, the magnitude of the fluctuations suggests that the zoning is lateral in nature and that the mantle is variable in composition laterally ranging from pyrolite to eclogite.