Showing papers in "Journal of Geophysical Research in 1969"

Collisional model of asteroids and their debris

Abstract: A model for colliding objects in the asteroidal belt is formulated. An integro-differential equation describing the evolution of a system of particles undergoing inelastic collisions and fragmentation is derived and solved for steady-state conditions. It is found that the number density of particles per unit volume in the mass range m to m + dm is Am−a dm, where A and α are constants (provided that certain conditions are satisfied). The population index α can then be derived theoretically; for asteroids and their debris, α = 1.837, in agreement with an empirical fit to the observed distribution. Various statistical properties of the distribution can be derived from the model. It is found that, for asteroidal objects, catastrophic collisions constitute the most important physical process determining particle lifetimes and the form of the particle distribution for particles sufficiently large that radiation effects are unimportant. The lifetime of the largest asteroids is found to be of the same order of magnitude as the probable lifetime of the solar system; therefore, some of the largest asteroids may have survived since the time of creation, whereas most smaller ones have not and are collisional fragments, according to the present model.

Analysis of the seismic coda of local earthquakes as scattered waves

Abstract: A method was devised to extract useful information about the earthquake source from the coda of local small earthquakes. The method is based on the assumption that the power spectrum of coda waves of a local earthquake is only a function of time measured from the earthquake origin time and independent of distance and details of wave path to the station. Evidence supporting this assumption is presented, using the data on aftershocks of the Parkfield earthquakes of June 28, 1966. A simple statistical model of the wave medium that accounts for the observations on the coda is proposed. By applying the method to many Parkfield aftershocks, the relation between the seismic moment M0 and local magnitude ML is determined as log M0 (dyne cm) = 15.8 + 1.5ML. The size of a microearthquake with magnitude zero is estimated as 10×10 meters.

Elastic moduli, pressure derivatives, and temperature derivatives of single‐crystal olivine and single‐crystal forsterite

Abstract: Ultrasonic wave velocities in single-crystal forsterite (F) and single-crystal olivine (O) have been measured as a function of pressure and of temperature near ambient conditions. Shear and longitudinal velocities were measured in eighteen independent modes, so that each of the nine elastic constants could be calculated by at least two independent equations. The adiabatic stiffness constants cij (in Mb), their temperature derivatives dcij/dT (10−4 Mb/deg), and their pressure derivatives dCij/dP, are ij 11 22 33 44 55 66 23 31 12Cij (F) 3.284 1.998 2.353 0.6515 0.8120 0.8088 0.738 0.688 0.639 (O) 3.237 1.976 2.351 0.6462 0.7805 0.7904 0.756 0.716 0.664dcij/dT (F) 3.31 2.81 2.83 1.30 1.32 1.51 0.46 0.82 1.04 (O) 3.40 2.85 2.86 1.28 1.30 1.57 0.51 0.94 1.05dcij/dP (F) 8.47 6.56 6.57 2.12 1.66 2.37 4.11 4.84 4.67 (O) 7.98 6.37 6.38 2.17 1.64 2.31 3.76 4.48 4.74The density ρo and other isotropic properties including the adiabatic bulk modulus Ks, the shear modulus μ, the Poisson ratio σs, and their pressure and temperature derivatives (using the same dimensions as above) computed by the VRH (Voigt-Reuss-Hill) method are ρ Ks μ σs dKs/dT dμ/dT dσs/dT, 10−5 °C−1 dKs/dP dμ/dP dσs/dP(F) 3.224 1.286 0.811 0.240 −1.50 −1.30 0.93 5.37 1.80 0.42(O) 3.311 1.294 0.791 0.246 −1.56 −1.30 0.92 5.13 1.79 0.36

Standing Alfvén waves in the magnetosphere

Abstract: Transverse LF oscillations in geomagnetic field observed during January 1967, noting possibility of being second harmonic of magnetospheric standing Alfven waves

Two- quartic tropospheric refractivity profile for correcting satellite data

Abstract: This paper presents a new model for the height profile of tropospheric refractivity N and expressions derived from it for computing corrections for satellite Doppler or range data. (N ≡ 106 (n - 1), where n is the index of refraction.) The model is theoretically based on an atmosphere with constant lapse rate of temperature, as will be shown. It treats the ‘dry’ and ‘wet’ components of N separately and represents each as a fourth-degree function of height above the geoid; each component profile starts with its locally observed surface value and decreases to zero at an effective height that is different for the two components. The height parameters were obtained by a least-squares fit to observed data. A latitude dependence has been found for the ‘dry’ height. The model has been found capable of closely matching any local average N profile observed in a world-wide sample of locations throughout the height range of meteorological balloon data (up to 24 km); samples are shown. The corrections based on it are readily evaluated and are finite and usable at all elevation angles. Their effectiveness is evidenced by figures showing two different kinds of observed data: first, Doppler residuals for several satellite passes without and with the use of the correction; and the ‘navigation’ error in station-to-orbit slant range from Doppler data, again without and with the correction. The use of the correction removed obvious systematic errors. The fact that satellite Doppler data display identifiable tropospheric effects is of interest with regard to future study of the troposphere.

Stress-induced velocity anisotropy in rock: An experimental study

Abstract: Application of uniaxial stress to a sample of granite causes elastic wave velocity anisotropy. Compressional waves travel fastest in the direction of the applied stress. Two shear waves travel with generally different speeds in any direction, exhibiting acoustic double refraction which increases with increasing stress.

Thermal radiation from the atmosphere

Abstract: A theoretical analysis of atmospheric thermal radiation reveals that previous formulas relating this parameter to screen-level air temperature have lacked universal applicability. New considerations indicate that the effective emittance of the atmosphere is a minimum at 273°K and that it increases symmetrically to approach unity exponentially at higher and lower temperatures. A formula is developed that meets these standards and fits experimental data from Alaska, Arizona, Australia, and the Indian Ocean with a correlation coefficient of 0.992. The atmospheric radiation R integrated over all wavelengths, is specified solely in terms of the screen-level air temperature T as R = σT4{1 - c exp [−d (273 - T)2]}, where c and d are constants having values of 0.261 and 7.77×10−4, respectively. It appears that the formula may be valid at all latitudes and seasons.

Solar modulation of galactic cosmic rays, 2

Abstract: A brief description is provided of the basic principles of and the techniques which are used for describing the behavior of galactic cosmic rays in the solar wind. Several numerical examples which illustrate features of the cosmic-ray behavior are presented.

Anisotropy of the Pacific upper mantle

Abstract: : Seismic refraction measurements of the compressional wave velocity of the upper mantle, obtained in the northeast Pacific Ocean between California and Hawaii, have shown a dependence on direction indicating anisotropy of velocity with a maximum of 8.6 km/sec in a roughly easterly direction and a minimum of 8.9 km/sec. In order to test whether or not these observations represent true anisotropy, rather than geographical variation of velocity, special anisotropy experiments were conducted at two locations centered roughly at 31 degrees N, 121 degrees W and 35 degrees N, 126 degrees W respectively. At each of these locations significant anisotropy was observed, agreeing in direction with the apparent anisotropy indicated for the entire region. The magnitude of the velocity difference, 0.3 km/sec, is half of the overall variation of 0.6 km/sec. These observations do not prove the hypothesis of anisotropy throughout the entire region from California to Hawaii. However, they are consistent with this hypothesis, and give encouragement to similar observations elsewhere. (Author)

Magnetic field of lightning return stroke

Abstract: The magnetic flux density due to first and to subsequent lightning return strokes is calculated for distances from the strokes of 0.5 to 200 km. The basis of the calculations is various assumed forms for the channel current as a function of time and of channel height. Two new channel-current models are introduced for first strokes and one new model for subsequent strokes, in addition to the use of the models of Bruce and Golde and of Dennis and Pierce. The new models provide a better approximation to the real lightning channel current than do the previous models, but all models considered yield radiation fields far from the channel that are consistent with experiment. It is shown that, contrary to the claims of Norinder and co-workers, the magnetic-field rise time for a stroke within a distance of about 20 km is essentially unrelated to the current rise time in the stroke channel base. For subsequent strokes, field rise times of many tens of microseconds can be due to current rise times shorter than a microsecond. On the other hand, field rise times for subsequent strokes may be strongly influenced by current fall times. The analysis of Norinder and co-workers which relates peak channelbase current to peak magnetic field yields values of current that can be considered accurate to about a factor of 2.

Heat flow, stress, and rate of slip along the San Andreas Fault, California

Abstract: The absence of a heat flow anomaly greater than ∼0.3 µcal/cm2/sec associated with the San Andreas fault is used to estimate the upper limit for the steady state or initial shear stress. Under the assumption that the long-term rate of motion along the fault is 5 cm/yr and occurs primarily in the form of creep, this upper limit is about 100 bars. If the motion is primarily accomplished by faulting during large earthquakes and if the frictional stress is equal to the final stress as suggested by E. Orowan (1960), the upper limit is estimated to be about 200 bars. Without Orowan's assumption, the estimation of the upper limit is about 250 bars, based on earthquake energy-magnitude-moment relations. If the long-term rate of motion along the San Andreas fault is only ∼2 cm/yr, these results are increased to 250, 350, and 400 bars, respectively.

Some remarks on polar wandering

Abstract: Earth polar wanderings attributed to rotation axis angular displacements generated by density redistribution on geologic time scale

Lateral variations of attenuation in the upper mantle and discontinuities in the lithosphere

Abstract: This study demonstrates the existence and determines the pattern of lateral variations of attenuation in the uppermost mantle on a worldwide scale. The evidence comes mostly from a comparison of the gross characteristics of the seismic phase Sn for over 1500 paths, which taken together cross as many regions of the earth as possible with the current configuration of the World-Wide Standardized Seismograph Network. Sn is a seismic shear wave that propagates in the uppermost mantle and that does not penetrate the low-velocity channel. It propagates very efficiently across the stable regions of the earth, the continental shields, and deep-ocean basins, but propagation is very inefficient when paths cross the crests of the mid-ocean ridge system or the concave sides of most island arcs. These observations suggest that attenuation is more pronounced in the uppermost mantle near the ridge crests and the islands arcs than in the more stable regions. If low attenuation, or high Q, correlates with high strength, the data imply that the uppermost mantle is considerably weaker under the ridge crests and the concave sides of the island arcs than it is elsewhere. Thus, the part of the strong outer shell, or lithosphere, in the mantle is discontinuous with gaps in it at the ridges and island arcs. The low attenuation for Sn for paths crossing the transform faults that connect ridge crests suggests that any gap at the transform faults is very narrow. In addition, S waves recorded at stations in and near the Mariana, New Britain, Solomon, and South American arcs from local deep shocks were found to follow the pattern previously observed in the Tongan and Japanese arcs. As was suggested for the Tongan arc, the observations imply that one piece of lithosphere has underthrust another to great depth at these arcs. Hence, data presented in this paper are in accord with recent ideas of sea-floor spreading in which large plates of lithosphere move with respect to each other as rigid bodies, spreading apart at the ocean ridges, sliding past one another at the transform faults, and underthrusting at the island arcs.

Bow shock associated waves observed in the far upstream interplanetary medium

Abstract: Fifty orbits of Explorer 34 data have been used to study 0.01–0.05 Hz transverse waves in the interplanetary medium region between the bow shock and the spacecraft apogee of 34 RE. It is concluded that the waves are associated with the earth's bow shock since they only occur when projection of the interplanetary field observed at the spacecraft intersects the shock. The waves are observed 18.5% of the time when a total of 134 days of interplanetary data is considered, but more than 90% of the time when the field has the proper orientation with respect to the bow shock. On the basis of this result it is suggested that these waves with 20–100 second periods are a permanent feature of the solar wind-earth interaction. The transverse component of the waves is typically several gammas in amplitude in 4–8 gamma fields. The disturbance vector in the XY plane generally exhibits the same sense of rotation in a coordinate system where the field is oriented along the positive z axis. Attenuation of wave amplitudes with distance from the bow shock is estimated to be only a factor of 2 when the spacecraft is 15 RE from the bow shock. The absence of waves at particular field orientations, even though the field line intersects the shock, is interpreted as a propagation effect. This observation is the basis for calculations that yield an average velocity in the plasma frame of 2.7 ± 0.4 times the solar wind velocity. Whistler propagation and local generation by two-stream instability are discussed as alternate theoretical explanations for the presence of the waves. It is suggested that the data favor the latter mechanism.

Seismicity and tectonics of the western Pacific: Izu-Mariana-Caroline and Ryukyu-Taiwan regions

Abstract: The hypocenters of about 1000 earthquakes in the Izu-Bonin, Mariana, Palau, Caroline, and Ryukyu-Taiwan regions were relocated by computer, and earthquake mechanism solutions based on the first motions of P, pP, and S were determined for 26 earthquakes. The spatial distribution and the mechanisms were compared with major tectonic features such as volcanic zones, island arcs, and trenches. Although a nearly continuous zone of shallow earthquakes can be traced from Honshu to Palau, deep shocks were not detected south of 16°N; intermediate-depth events were not found south of the Marianas. A region of low seismicity for shallow earthquakes and a discontinuity for deeper events occurs in the Volcano Islands adjacent to a prominent gap in the trench where the Marcus-Necker ridge intersects the arc. In some profiles of this series of arcs, the deep seismic zone is nearly planar, but in other cases it is more contorted and the thickness of the zone appears to vary from place to place. Maxima and minima in seismic activity occur for deep and intermediate depths, and these features migrate in depth similar to that found in the Tonga arc. Activity as deep as about 680 km occurs in the northern Marianas where the deep focal zone is nearly vertical for depths greater than about 200 km. This nearly vertical distribution suggests that gravitational tectonics may play an important role as a motive force for global tectonics. Seismicity in the Ryukyu arc is concentrated in a thin planar zone that dips 35° to 45° northwest to a depth of about 280 km. Near the northwest coast of Taiwan all tectonic elements change strike abruptly, and the mechanisms change from thrusting of the Philippine Sea plate beneath the Ryukyu arc to strike slip near the east coast of Taiwan. South of this point, most of the events are shallower than 100 km, and the focal zone is not well defined in vertical sections. No events were detected from the Kyushu-Palau ridge, from the Central Basin fault, or from the rest of the interior of the Phillipine Sea. Thus, this region appears to be a single lithospheric plate. Normal faulting is found for some earthquakes either in the deepest parts of the trench or along the seaward wall. A zone of shallow earthquakes also can be identified on many of the profiles near the volcanic axis. Mechanism solutions for two events near this zone are also of the normal-fault type. Mechanism solutions for shallow earthquakes beneath the islandward margins of the Izu-Bonin and Mariana trenches indicate that the Pacific plate is underthrusting the Philippine Sea plate in a westerly direction. The results of the relocations and other pertinent data are given in a separate appendix, which is available on microfiche along with the entire article. Order from the American Geophysical Union, Suite 435, 2100 Pennsylvania Ave., N.W. Washington, D.C. 20037. Document J69-002; $1.00. Payment must accompany order.

New analysis of attenuation in partially melted rock

Abstract: A model of partially melted rock is analyzed in which melt occurs as thin films along grain boundaries. For analysis, the liquid phase is assumed to be a dispersion of randomly oriented ellipsoidal inclusions with minor axes much smaller than major axes. Expressions are derived for complex bulk modulus and rigidity. Rigidity and attenuation in pure shear are found to depend on the number of sites at which melting has occurred rather than to depend only on the concentration of melt, in agreement with published observations. On the other hand, response in pure dilatation depends on concentration alone, with the result that attenuation in pure dilatation is low and bulk modulus is approximately equal to that for unmelted material.

Rip currents: 1. Theoretical investigations

Abstract: The nearshore circulation of water on a plane beach produced by a wave train, normally incident on the beach, which has a longshore variation in wave height is investigated theoretically. The radiation stress arising from the excess flux of momentum due to the presence of the waves (M. S. Longuet-Higgins and R. W. Stewart, 1964) is found to provide driving terms for a steady flow pattern only inside the surf zone. A circulation pattern is thus produced by a longshore variation in the radiation stress in the surf zone. In shallow water, the radiation stress is proportional to the square of the wave height. The nearshore circulation is therefore directly related to longshore variation in breaker height, currents flowing seaward where the breaker height is low. When the inertial terms are included in the vorticity equation, an increase in the effective Reynolds number produces a narrowing, and consequently a strengthening, of the Seaward flow, which suggests an explanation for the existence of the strong, narrow currents known as rip currents.

The relationship between andesitic volcanism and seismicity in Indonesia, the Lesser Antilles, and other island arcs

Abstract: The relationship between K, the level of potash content in lavas erupted from an andesite volcano, and h, the depth to the center of the inclined seismic (Benioff) zone beneath the volcano, is extended using new data from Indonesia, the Lesser Antilles, and New Zealand. Coefficients of correlation between K and h of +0.86 (K55) and +0.80 (K60) are obtained by straight-line regression. This is compared with a coefficient between K55 and distance d of the volcano from the trench of only +0.60. The coefficients of correlation of K against hmin, which is the depth to the upper surface of the Benioff zone, are not significantly different from those between K and h.

Electrical properties of rocks and their significance for lunar radar observations

Abstract: Terrestrial solid powdered rocks HF electrical properties measurements at 450 MHz and 35 GHz for lunar radar observation

Infrared emissivities of silicates: Experimental results and a cloudy atmosphere model of Spectral emission from condensed particulate mediums

Abstract: Infrared emissivities of powered silicates are shown by experiment to contain new maximums and minimums that are representative of both composition and particle size. A cloudy atmosphere model for radiative transfer in a condensed powder is developed in which the scatter is considered to be both nonconservative and linearly anisotropic. The scattering parameters are computed as functions of frequency from the Mie diffraction theory. Detailed calculations of the spectral emissivity of quartz are presented. The model is shown to account for many features observed experimentally in the spectrums of quartz powders and sand. Changes in the spectrum with particle size can be understood in terms of changes in the albedo for single scattering and the degree of forward scatter with particle size. The principal Christiansen frequencies of silicate powder films obtained from transmission measurements are shown to be diagnostic of mineralogy and to be frequencies of maximum emissivity for powders. The relationship is discussed in detail for quartz.

Magnetic properties and oxidation of iron‐titanium oxide minerals in Alae and Makaopuhi Lava Lakes, Hawaii

Abstract: Measurements of strong-field magnetization over the temperature range −196° to 700°C have been made on forty-eight drill core samples of tholeiitic basalt from Alae and Makaopuhi lava lakes, Kilauea volcano, Hawaii. These samples were originally obtained at temperatures ranging from 50° to 1020°C. Nearly all samples contain abundant hemoilmenite with Curie temperatures in the range −100° to −160°C. Samples quenched from high temperatures (800° to 1000°C) have second Curie temperatures ranging from 150° to 290°C, due to unoxidized titanomagnetite, and samples obtained at lower temperatures (50° to between 400° and 700°C) have second Curie temperatures ranging from 500° to 580°C. This transition from medium to high Curie temperatures occurs between 850° and 300°C, varying from one drill hole to another, and is accompanied by a marked increase in the strong-field magnetization at room temperature. Oxidation of original titanomagnetite to Ti-poor titanomagnetite containing ilmenite lamellas is the cause of the increase in Curie temperature. Comparison of the compositions of the oxide minerals with the oxygen fugacity data of Sato and Wright and the equilibrium reaction data of Buddington and Lindsley shows that oxygen fugacity was controlled largely by the buffering action of the oxide minerals; hence titanomagnetite was oxidized, whereas the more abundant hemoilmenite was little changed as the lava cooled. This oxidation occurred at temperatures well below equilibrium, the difference being generally of the order of 100°C but as much as 400°C. We conclude that in some basaltic lavas the magnetic minerals may form through subsolidus reactions at temperatures well below their final Curie temperatures. In such lavas the natural remanent magnetization is a mixture of thermoremanent magnetization and high-temperature chemical remanent magnetization.

Banded chorus - A new type of VLF radiation observed in the magnetosphere by OGO 1 and OGO 3.

Abstract: Banded chorus, VLF discrete emissions in magnetosphere in single variable frequency band with frequency depending on equatorial electron gyrofrequency

Fine structure of the upper mantle

Abstract: The spectral amplitudes and travel times of seismic body waves are used to determine mantle velocity structures appropriate to distinct structural provinces within the western continental United States. In addition to basic amplitude and time data, travel-time delays and Pn velocity data from other studies are used as constraints in the systematic inversion of the data for mantle structure. The regional structures for the upper mantle determined in this manner show collectively rather sharp zones of transition (high velocity gradients) near 150, 400, 650 km and possibly near 1000 km. Comparatively, the regional structures indicate strong lateral variations in the upper mantle structure down to 150 km and possibly as deep as 200 km. The structures appropriate to the Rocky Mountain and Colorado plateau physiographic provinces show low-velocity zones capped by high-velocity lid zones, with variability in both the lid and the low-velocity zone properties from province to province and within these provinces to a much lesser degree. The mantle properties obtained for the Basin and Range contrast sharply with the plateau and mountain structures, with the lid zone being very thin or absent and abnormally low velocities extending from, or very near, the base of a thin crust to 150 km. The velocity determinations are coupled with estimates of the variation of the intrinsic dissipation function (Q) as a function of depth and frequency. These results show a pronounced low-Q zone corresponding to the average low-velocity zone depth range for the velocity models. The data suggest a frequency-dependent Q, with Q increasing with frequency. In total the results of the study strongly suggest phase transitions in the mantle, including a partially melted region corresponding to the low-velocity zone, the latter being highly variable in its properties over the region studied and strongly correlated with tectonic activity.

High-latitude plasma transport: The polar wind

Abstract: Plasma transport models of polar ionosphere, discussing physical processes involved and effects on electron concentration, ion composition and speeds

Heliographic Latitude Dependence of the Dominant Polarity of the Interplanetary Magnetic Field

Abstract: Interplanetary magnetic field measurements from Mariner and OGO satellites at various paths, regions and intervals, finding dominant polarity effect dependent on sun latitude

Wind stress and surface roughness at air‐sea interface

Abstract: Based on the compiled data of thirty independent oceanic observations, this article systematically presents the wind-stress coefficient, the surface roughness, and the boundary layer flow regime at the air-sea interface under various wind conditions. The air flow near the water surface is shown to be aerodynamically rough or in the transition region except at a very low wind velocity (U10 < 3 m/sec). Both the wind-stress coefficient and the surface roughness are found to increase with the wind velocity when U10 is less than 15 m/sec and to reach a saturated value for U10 greater than 15 m/sec. From the oceanic wave observations, the presence of this discontinuity at U10 = 15 m/sec is found to be due to an increase in the wind velocity (measured at the significant wave amplitude above the mean water level) beyond the average wave phase velocity. This finding provides a well-defined separation for the often quoted terms ‘light’ and ‘strong’ winds. The compiled data also show that the surface roughness is governed by the amplitude of the short gravity waves. Charnock's relationship is shown to be applicable to most of the oceanic data and Charnock's proportionality constant is determined, η/(u*2/g) = 0.0156. Finally, two approximate formulas for the windstress coefficient C10 = 0.5 × U101/2 × 10−3 for light wind and C10 = 2.6 × 10−3 for strong wind are suggested for oceanic applications.

Fission track annealing in apatite and sphene

Abstract: Study of the annealing characteristics of fission tracks in sphene and fluorapatite shows that all tracks will be annealed out in 1 hour at 350°C for fluorapatite and 625°C for sphene. Extrapolation of the experimentally determined annealing temperatures suggest that all tracks will disappear in 106 years as 170°C for fluorapatite and 420°C for sphene. The experiments were made at atmospheric pressure, but increasing the pressure to 2 kb of water had no additional effect on the annealing of apatite. Concordant sphene and apatite fission track ages were determined at Magnet Cove, Arkansas (99±10 m.y.), and Eldora, Colorado (Bryan Mountain stock 73±7 m.y.). Discordant sphene and apatite ages were determined on the Tishomingo granite of southern Oklahoma (sphene = 1330 m.y., apatite = 590 m.y.) and the Boulder Creek granite of Colorado (sphene = 1200 m.y., apatite = 75 m.y.).

On the Coulomb-Mohr failure criterion

Abstract: Coulomb's criterion for the shear fracture of a brittle material is that total shearing resistance is the sum of the cohesive shear strength (independent of direction) and the product of the effective normal stress and the coefficient of internal friction (a constant independent of normal stress). Mohr generalized this criterion by extending it to a three-dimensional state of stress, and by allowing for a variable coefficient. The coefficients of internal and external (sliding) friction are not the same in general. Both tend to decrease with increasing normal stress, and their relative magnitudes may determine if failure occurs by new shear fracturing or by slip on pre-existing cohesionless surfaces like joints in rocks.

Rip currents: 2. Laboratory and field observations

Abstract: The nearshore circulation of water on a plane beach exposed to a uniform wave train, normally incident on the beach, was investigated experimentally in the laboratory. The incident waves generated standing edge waves on the beach of the same frequency as the incoming waves. The interaction between these edge waves and the incident waves gave rise to steady flow patterns (nearshore circulation cells) consisting of an onshore flow toward the breakers, a longshore current in the surf zone, and an offshore flow in relatively strong, narrow rip currents. The rip currents were found to occur at alternate antinodes of the edge waves, and the spacing of the rip current was therefore equal to the longshore wavelength of the edge waves. Although the incoming wave may interact with all the possible edge wave modes of the same frequency, it was found that the interaction with one particular mode is often dominant. A useful estimate of the relative importance of the modes is given by the parameter w2xb/(g tan β), where ω is the radian frequency of the edge waves, tan β is the beach slope, and xb is the width of the surf zone. Field observations made in the Gulf of California strongly suggest that this mechanism is important on real beaches.

Elastic constants of single‐crystal forsterite as a function of temperature and pressure

Abstract: Adiabatic elastic stiffness constants of single crystal forsterite measured as function of hydrostatic pressure and temperature, using pulse superposition technique