Showing papers in "Geophysical Journal International in 1972"

Active Tectonics of the Mediterranean Region

Abstract: Summary Examination of more than 100 fault plane solutions for earthquakes within the Alpide belt between the Mid-Atlantic ridge and Eastern Iran shows that the deformation at present occurring is the result of small continental plates moving away from Eastern Turkey and Western Iran. This pattern of movement avoids thickening the continental crust over much of Turkey by consuming the Eastern Mediterranean sea floor instead. The rates of relative motion of two of the small plates involved, the Aegean and the Turkish plates, are estimated, but are only within perhaps 50 per cent of the true values. These estimates are then used to reconstruct the geometry of the Mediterranean 10 million years ago. The principal difference from the present geometry is the smooth curved coast which then formed the southern coast of Yugoslavia, Greece and Turkey. This coast has since been distorted by the motion of the two small plates. Similar complications have probably been common in older mountain belts, and therefore local geological features may not have been formed by the motion between major plates. A curious feature of several of the large shocks for which fault plane solutions could be obtained for the main shock and one major aftershock was that the two often had different mechanisms.

Interpretation of Inaccurate, Insufficient and Inconsistent Data

Abstract: Sumntary Many problems in physical science involve the estimation of a number of unknown parameters which bear a linear or quasi-linear relationship to a set of experimental data. The data may be contaminated by random errors, insufficient to determine the unknowns, redundant, or all of the above. This paper presents a method of optimizing the conclusions from such a data set. The problem is formulated as an ill-posed matrix equation, and general criteria are established for constructing an ‘ inverse ’ matrix. The ‘ solution ’ to the problem is defined in terms of a set of generalized eigenvectors of the matrix, and may be chosen to optimize the resolution provided by the data, the expected error in the solution, the fit to the data, the proximity of the solution to an arbitrary function, or any combination of the above. The classical ‘ least-squares ’ solution is discussed as a special case.

On the Thermal Balance of a Mid‐Ocean Ridge

Abstract: Summary The northernmost expressions of the East Pacific Rise spreading centre, the Juan de Fuca Ridge and Explorer Trough, have unusual heat-flow distributions Crestal values are only moderately high, but flank areas that are models of undisturbed sedimentation have mean heat flows near 7 HFU (290 mW m−2) The values in these areas retain considerable scatter, but the detailed distribution is close to the opposite of that expected from conductive heat-flow refraction The high mean values confirm that sea-floor spreading occurs by the upwelling of hot (magma temperature) material The low crestal measurements and the non-refractive scatter in the flank areas strongly suggest that hydrothermal circulation is the dominant heat transfer process in fresh crestal material Much of the heat loss from the new lithospheric material must occur through open circulation near the ridge crest and is never reflected in measurements of surface conduction

Melting on Fault Planes During Large Earthquakes

Abstract: Summary For simple models of the movement on a fault during an earthquake the temperature on the fault plane is shown to reach the melting temperature for short periods if the slip is sufficiently large. The displacement required to produce melting depends on the magnitude of the regional stress and also on the friction stress. If both stresses are one kilobar melting can occur for displacements as small as one millimetre. If, however, both stresses are ten bars melting is impossible for any observed displacement. It is estimated that the width of the melted zone could be between 2 mm and lcm. Melting on fault planes during earthquakes is not in disagreement with geological and geophysical observations, and suggests a new explanation for some mylonites. Melting may be important because the molten film rock formed on the fault may act as a lubricant and in the case of large earthquakes allow the release of almost all the elastic strain in the region of the shock. This would provide an important constraint in estimating the state of stress along a fault.

Seismic Rays and Ray Intensities in Inhomogeneous Anisotropic Media

Abstract: Summary A ray series expansion for seismic body waves propagating in inhomogeneous anisotropic media is studied. Methods for calculation of rays and amplitude coefficients of the ray series are suggested. A seismic ray is described by a system of ordinary differential equations of first order which can be solved by standard numerical techniques. Another system of ordinary differential equations can be used to compute amplitude coefficients. The method may be applied to general anisotropic media in which the elastic parameters are arbitrary continuous functions of all three co-ordinates.

The Effects of Solid Earth Deformation on Global Ocean Tides

Abstract: Summary Laplace's Tidal Equations (LTE) are modified to allow for the yielding of the solid Earth to tide generating forces and to the weight of the oceanic tidal column as well as for oceanic gravitational self-attraction A realistic cotidal-corange chart for the global M2 tide is used to show that the first effect is the order of the astronomical potential itself while the second and third are roughly one order of magnitude smaller However, the later potential perturbations produce order one effects in the computed tide because they are much richer in high spherical harmonics than is the astronomical potential The existence of an appreciable solid Earth tide significantly modifies the usual expressions for stored tidal energy, for tidal energy flux and for the rate of working on the oceans by tide generating bodies An unexpectedly high value of Q(∼ 34) is found for the global M2 tide

Magnetic Mineralogy of Unheated and Heated Red Sediments by Coercivity Spectrum Analysis

Abstract: Summary A method of deriving the remanent coercivity spectrum from the isothermal remanence vs. applied field characteristic is described and applied to a series of Triassic sandstones and late Cretaceous–early Tertiary clays and limestones from France. Low- (0-1 kOe), intermediate- (1-3 kOe), and high- (3-18 kOe) coercivity remanence fractions are identified with magnetite, specularite, and haematite pigment respectively. In the limestones, specularite is the only important magnetic phase; the sandstones contain in addition considerable pigment; and the clays contain all three phases. The relative pigment content indicated magnetically agrees with the colour of each rock type. When the sandstones are heated in air, enough magnetite is produced below 675°C to account for 20-25 per cent of the saturation remanence. Secondary magnetite production may therefore be serious when red beds are thermally demagnetized, even though the heating is done in air. The source of this secondary magnetite seems to be a non-magnetic mineral, rather than haematite. Secondary haematite production is insignificant below 675°C, but the pigment coercivity spectrum becomes harder with annealing, as observed previously with synthetic fine-particle haematites. Either annealing-out of defect ferromagnetism or impurities entering the haematite lattice could explain the results. Either coercivity spectra or rotational hysteresis curves can be used to estimate pigment/specularite ratios in red beds and to monitor mineralogical changes resulting from heating, but the coercivity spectrum method is much simpler to use.

The N Plate Problem of Plate Tectonics

Abstract: Summary Plate tectonics theory is used to develop a least squares method for finding all the relative motions of any n interacting plates simultaneously. The method ensures internal consistency of results and allows full use to be made of data on relative movement of plates. The least squares fitting criteria are chosen to avoid ambiguity. Relative motions of eight major plates of the world are calculated in preliminary form, and regional and global rates of creation and destruction of lithosphere are derived from these motions.

Scaling Law of Earthquake Source Time-Function

Abstract: Summary Further evidences support the scaling law of far-field seismic spectrum based upon the ω-square model (Aki) for earthquakes with MS > 6 and for periods T > 10s. Recent observations, however, unequivocally require the modification of the above law for periods T < 10s. Unfortunately, the presently available data are not sufficient for a unique revision of the scaling law. We propose two alternatives and discuss their implications and consequences. In either case, we have to conclude that a large earthquake and a small one are substantially different. One interesting feature of the ω-square model appears to be unaffected by the required revision; that is, the spectral density of the fault-slip time-function for periods T < 5s takes the same absolute value, independent of magnitude, for earthquakes greater than Ms= 65. This result has important consequences in earthquake engineering because the seismic motion in the vicinity of an earthquake fault will scale as the fault-slip motion.

Explosive Volcanic Eruptions-II The Atmospheric Trajectories of Pyroclasts

Abstract: Summary The formulation and solution of the general equations of motion of pyroclasts in the Earth's atmosphere are described. Ranges of particles ejected from a vent, and times of fall of particles released from an eruption column or ash cloud, are computed for those values of particle radius (0.01 to 100 cm), density (0.5 to 3.5 g ~m-~), launch velocity (10 to 1000 m s-'), elevation (45, 66 and 87 degrees) and release height (0 to 50km) of practical importance. The values so obtained are presented in tabular and graphical form, and their use in determining the physical parameters of an explosive eruption is described.

Discrimination Between Earthquakes and Underground Explosions Employing an Improved Ms Scale

Abstract: Summary The M, Rayleigh wave magnitude formula is revised for purposes of eliminating the heretofore variable effects of near distances and propagation paths on the values computed from standard long-period seismograms. The improved formulation employs a revised distance correction function and a period-dependent path correction that normalizes M, to large teleseismic distance 20-s values. For purposes of earthquake-explosion discrimination, an empirical focal depth correction is derived on the basis of Rayleigh wave frequency content as a function of focal depth, which normalizes M, values to the surface focus equivalent, i.e. aids discrimination when it can be applied by increasing earthquake M, values and moving them away from the equivalent explosion population on M, : m, plots. The revised M, improves on previously achieved discrimination of North American events, and provides reliable discrimination between suites of Eurasian earthquakes and explosions. Having removed the dominant propagation path effects on M,, the residual differences in M, : mb among events are generally attributed to source environment and regional effects on m,,. The 42 Eurasian WWSSN stations employed are shown to have a discrimination threshold at the M,3.2 level. With the improved M, scale now equivalent to first order for North American and Eurasian continental propagation, available Nevada Test Site explosion yields are extrapolated to the Eurasian sites to illustrate that this M,3.2 discrimination threshold is equivalent to an Eurasian explosion of about 20 kt in hard rock. Given improved long-period instrumentation to reduce the Rayleigh wave detection threshold, the principal restriction on further studies of discrimination to lower levels of magnitude and yield will be the availability of earthquake occurrence information at the low magnitudes.

Observations of Normal Modes from 84 Recordings of the Alaskan Earthquake of 1964 March 28

Abstract: Summary We have taken 84 World Wide Standard Seismograph Network recordings of the Alaskan earthquake of 1964 March 28, one of the largest earthquakes in history, and have made an intensive search for the Earth's eigenperiods in their spectra. We have found 61 spheroidal overtones and nine toroidal overtones as well as all but two fundamental modes with angular order less than 46. We have used such theoretical discriminants as polarization, dissipation, group velocity, multiplet width and continuity as a function of total angular order to separate interfering multiplets. Preliminary interpretation of the overtone eigenfrequencies leads us to models of the Earth's core where either the density decreases with depth in the inner core, leaving modes 2S2 and 5S2 with unacceptably large residuals, or there is finite rigidity with a shear velocity of about 3.5 kms−1, and all residuals are acceptably small. We favour the latter interpretation as being the more satisfactory. The average eigenperiod for each multiplet has a relative precision (standard error of the mean divided by the mean) ranging from 1.4 × 10−5 for 6S1, a high Q multiplet, to about 10−3 for the higher frequency toroidal modes, 0T1. The high precision obtained for many high Q overtones, together with their dual ray interpretation as PKIKP, PKJKP, SKIKS, SKJKS. etc. lends support to the interpretation that the inner core is solid.

Elastic Dislocation Theory for a Self‐Gravitating Elastic Configuration with an Initial Static Stress Field

Abstract: Summary The linearized equations of motion and linearized boundary and continuity conditions governing small elastic-gravitational disturbances away from equilibrium of an arbitrary, uniformly rotating, self-gravitating, perfectly elastic Earth model with an arbitrary initial static stress field are derived. The appropriate form of Rayleigh's variational principle and of the Betti reciprocal theorem and the Volterra dislocation relation for such a configuration are given. The latter is then used to derive an explicit expression for the equivalent body forces to be applied in the absence of a seismic dislocation in order to produce a dynamical response of the Earth model equivalent to that produced by the dislocation. It is found that if the initial static stress in the vicinity of the dislocation is purely hydrostatic, then a point tangential displacement dislocation has as an exactly equivalent body force the familiar double couple of moment 0, A0s0. If however the hypocentral static stress field has a deviatoric part, then additional equivalent body forces must be used properly to model a seismic dislocation. The necessary additional equivalent forces are explicitly exhibited; theoretically their existence provides a method of estimating hypocentral stresses, but the application of any such method is probably premature.

Source Time Functions and Spectra for Underground Nuclear Explosions

Abstract: Summary The model of Haskell for explosion source time functions and spectra fails to satisfy data in the short-period band recorded teleseismically from the three Amchitka Island underground nuclear tests: LONG-SHOT, MILROW, and CANNIKIN. A more recent model due to Mueller and Murphy satisfies the data quite well. The difference in the two models is basically in the fall-off at high frequencies. A simple revision of Haskell'smodel produces waveforms and spectra nearly identical to ones from Mueller and Murphy'smodel. This revision requires velocity waveforms to have a rise time of extremely short duration at the elastic boundary, a premise validated by actual near-field measurements. Waveforms are derived from the revised Haskell model and the Mueller and Murphy model and illustrated for pressure at the elastic boundary, reduced displacement potential at the elastic boundary, and far-field displacement. Corresponding spectra are derived and illustrated.

On the Estimation of Spectra by Means of Non-linear Functions of the Covariance Matrix

Abstract: Summary The estimation of spectra of random stationary processes is an important part of the statistics of random processes. There are several books on spectral analysis, e.g. Blackman & Tukey, Hannan, and Jenkins & Watts. As a rule, spectral estimators are quadratic functions of the realizations. Recently Capon suggested a new method for estimation of spectra of random fields, in which a non-quadratic function of the realization is used: he considered a homogeneous random field ζ(t,x1,x2), i.e. one which is stationary in time and space and a random function of the time and space co-ordinates t, x1, x2. For the sake of expository convenience we shall consider ordinary stationary processes of time only, ζ(t); the generalization of our results to the case of random fields is easy. Comparison of the conventional spectral estimator and the ‘high-resolution’ estimator for an artificial example showed that the latter has less smoothing effect on the true spectrum (Capon). This was later confirmed by examples using real data (Capon). However, it was not clear whether for a finite realization the high-resolution estimator distorted the true spectrum, i.e. whether it behaved for example like a conventional estimator raised to some power. In the present paper we introduce and study a new class of spectral estimators which are generally non-linear and non-quadratic functionals of the realizations. These estimators include the conventional and high-resolution ones, for which we shall give the approximate distributions. We derive under rather general conditions the limiting distribution of the new class of estimators, and illustrate them with several examples. As a matter of fact, these new estimators are weighted means of the eigenvalues of the covariance matrix, e.g. the arithmetic mean, geometric mean, and so on.

The Melting Relations of Iron, and Temperatures in the Earth's Core

Abstract: Summary Thermodynamic data on the phases of iron are assembled in the form of speculative projections on the temperature-volume plane. Following a proposal by Kraut and Kennedy, the melting curves, for each phase, are assumed to be straight lines in this representation. As the position of the triple point, gamma-epsilon-liquid, is unknown, two hypothetical locations are considered: (1) at about 4Mb, (2) at about 1 Mb. In the former case, the gamma phase is in equilibrium with the liquid at core pressures, in the latter, the epsilon phase. Nothing is known directly about the slopes of these melting curves, but the gamma melting temperatures are estimated to lie some 700" above the projection given by Higgins and Kennedy, with epsilon melting temperatures still higher. The relation of the isentropes of the liquid to these melting curves is also unknown, but ' conventional ' isentropes, originating on the melting curve, may be found which lie in the liquid field at the pressures of the outer core. Application to the Earth is complicated by the requirement for a light alloying element in the outer core; if the alloying element is silicon, a proportion of about 15 per cent by weight accounts satisfactorily for the density-velocity relation. The phase relations may be considerably modified by the presence of so much silicon: it is conjectured that the gamma phase is suppressed or confined to low pressures, that the epsilon phase will be the stable solid phase at core pressures, and that the isentrope originating at the melting temperature of the inner core-outer core boundary lies entirely in the liquid phase.

Generalized Ray Theory for a Layered Sphere

Abstract: Summary Pulse propagation in a layered sphere can be investigated, in an approximate way, by what has come to be known as Cagniard's method. Classical methods are used in the analysis through the application of the Debye ray expansion. At this stage Lamb's observation, that the eikonal is linear in the frequency, is employed to bypass the usual methods for evaluation of the inverse transform integrals. The transient response for each Debye ray is obtained directly. It is estimated that the method can be applied to mantle S pulses with periods less than 75 s, and to mantle P pulses with periods less than 40 s. Preliminary results on lateral heterogeneity beneath North America are presented. Extension of generalized ray theory to spherical layers The application of generalized ray theory to stratified media has been limited by the requirements that the stratification must be represented by homogeneous layers, and that the interfaces must be plane-parallel. When these two requirements are met, one uses plane-wave reflection and transmission coefficients and time delays to build up the solution to the problem (Weyl 1919; Pekeris 1948; Spencer 1960). In the Cagniard-de Hoop method the time delay, t, ray parameter, p, velocity, v, and horizontal distance, R, are related by the classical formula

The Crustal Structure of Rockall Plateau Microcontinent

Abstract: Summary Interpretation of seismic refraction measurements and gravity profiles from the Rockall Plateau area of the North-east Atlantic proves that the Plateau is a microcontinent. The depth to the Moho beneath the Plateau varies between 22 and 31 km. P wave velocities of about 6.4 and 7.1 km s−1 were obtained for the main crustal layers; these velocities may be typical of microcontinents. The Plateau is approximately in isostatic equilibrium, as too is Rockall Trough. The Trough is underlain by a thin crust, possibly of oceanic origin.

Seismic Waves in Laterally Inhomogeneous Media

Abstract: Summary A new perturbation technique is presented for the approximate solution of problems involving slight lateral inhomogeneities, or moderate inhomogeneities of small lateral extent, in elastic media. The method, based on an integral equation formulation and Born-type expansion in the wavenumber domain, is an extension of the usual matrix methods for multilayered elastic media. It is thus particularly suitable for problems concerning inclusions in multilayered half spaces. As an example of this method calculations are made of the scattering effects produced by near-surface inclusions in simple half-space models. It is found that at low frequencies forward and backward scattering into surface waves are of comparable importance, but as the frequency of the incident waves increases the forward scattering tends to dominate.

A Reappraisal of the 40Ar/39Ar Stepwise Degassing Technique

Abstract: Summary The principal advantage of the 40Ar/39Ar dating method lies in the stepwise degassing technique. Despite the widespread use of the technique, each worker seems to adopt an individual criterion of choice, as to how the data should be treated, so as to extract the maximum amount of information from it. It was considered desirable to make a detailed analysis of the data taken during a number of stepwise degassing experiments to decide upon the most useful treatment of results. The basic principles of the technique are reviewed, and a method of data analysis is presented, which enables a detailed study of the argon liberation characteristics of the sample to be made. It also allows the age of the sample to be determined, such that no direct correction is made for atmospheric contaminant 40Ar. This avoids the fundamental assumption that all 36Ar, used to make this correction, is of atmospheric origin.

Estimation of Density Currents in the Liverpool Bay Area of the Irish Sea

Abstract: Summary Density currents in Liverpool Bay are evaluated on the basis of a simple hydrodynamical theory. The results are shown to account for some of the main features of the observed residual motions in the Bay, including the persistent landward drift at the sea bed.

Tectonic Strain Release by Underground Nuclear Explosions and its Effect on Seismic Discrimination

Abstract: Summary The analysis of surface waves from a large number of underground nuclear explosions reinforces the hypothesis of tectonic strain release. Such strain release is dependent on rock type and ambient stress levels. In harder media, such as granite, strain release is considerably greater than in soft media such as loose alluvium and salt. In the case of three events for which the tectonic component exceeded that of the explosion itself, the effect on the M,-mb discriminant due to the added surface wave energy was not noticeable. This was probably due to the averaging of magnitude over all azimuths. A decaying pulse-type source-time function is consistent with surface wave amplitude spectra and can explain the long-period/short-period spectral ratio.

A Quantitative Evaluation of Seismic Signals at Teleseismic Distances—III Computed P and Rayleigh Wave Seismograms

Abstract: Summary Body (P) and Rayleigh wave seismograms are computed for explosions and earthquakes using the expressions developed by Hudson; many of the features of observed seismograms are noted. For the earthquake source models used average Rayleigh wave magnitudes relative to P wave magnitudes are larger than for the explosion source models. This is true even for point sources; increasing the dimensions of the earthquake source only accentuates this difference in the relative excitation of Rayleigh waves. However the relative amplitudes are strongly dependent on the orientation of the observer relative to the fault plane of the earthquake owing to the radiation pattern of the P and Rayleigh waves. Where the observer is at an anti-node of the P radiation the relative amplitudes of the Rayleigh waves are not significantly greater than for explosions. A detailed study of observed P and Rayleigh amplitudes is now needed to see if the same effects of the P radiation pattern can also explain the observed differences in the relative excitation of P and Rayleigh waves by earthquakes and explosions.

Higher Seismic Activity During Local Night on the Raw Worldwide Earthquake Catalogue

Abstract: Shimshoni (1971) has reported that a greater seismic activity during local nighttime than during local daytime is to be found in the raw worldwide earthquake catalogue 1969-1971 of the National Ocean Survey (NOS). We agree that the daynight correlation exists on the raw catalogue, but believe that this would disappear after several corrections are applied to reduce the extent of the sample catalogue to which the day-night test is applied. Statistical analysis of an earthquake catalogue should be applied to unbiased samples. We have repeated Shimshoni’s analysis applied to a catalogue sample which has been restricted in extent. The reasons for these reductions are

Crustal Low-Velocity Zones Under the Peru-Bolivia Altiplano

Abstract: Summary In 1968, the Carnegie Institution of Washington together with North and South American collaborators carried out a reconnaissance explosion seismic experiment to investigate the apparently highly anomalous crustal structure under the Peru-Bolivia altiplano. The data of this experiment have been reinterpreted by ray-tracing in a spherical Earth so as to fit as closely as possible arrival times, relative amplitudes, cusps, etc., of seismograms displayed in record section. The resultant model confirms the previous average model consisting of three major refractors: the sedimentarymetamorphic layer 49 km thick and 4.54.9 km s-' velocity; the ' granitic ' layer with 6 .O-6.1 km s-' velocity down to 26-30 km depth; and the ' gabbroic ' layer reaching depths of 68-70 km below sea level with 6.8-6.9 km s-' velocity. However, in order to account for relatively large amplitudes in the secondary arrivals with apparent velocities close to the first arrivals, two low-velocity zones are postulated within the crust under the Peru-Bolivia altiplano. In Peru, the shallow and thinner lowvelocityzone with boundaries at 9 km and 12 km depth is between materials of 6.0 km s-' and 6.1 km s-'. The deeper and thicker low-velocity zone with upper and lower bounds at about 30 km and 40 km under Bolivia, and more approximately at 36 km and 46 km under Peru, is embedded in 6.8 and 6.9 km s-' materials. The shallower low-velocity zone is conceivably related to the parent magma of volcanic and intrusive acidic rocks with the deeper low-velocity zone related to the volcanic and intrusive basic rocks in accord with petrological and geochemical findings of Pichler and Zeil in the Andes of northern Chile. The presence of velocity inversions above the 50km depth is also in harmony with the postulated existence of a high electrical conductivity zone shallower than 50 km depth under the Andes as postulated recently by Schmucker to explain magnetic ' day-time fluctuation ' anomalies.

Palaeomagnetic Evidence about the Source of the Geomagnetic Field

Abstract: Summary The availability of a large body of palaeomagnetic data from Eastern and Western Iceland has made possible several deductions about the nature of the source of the geomagnetic field. We conclude that the assumption of a centred dipole source leads to a simple and reasonable time-average dependence of absolute dipole strength on dipole orientation (dipole moment on pole position). The relationship is nearly axially symmetrical, and provides natural definitions of ‘normal’ and ‘reversed’ fields. The normal state has been more stable over the past 12 My than the reversed state. The dependence of time-average dipole strength on dipole orientation provides a considerable constraint on any postulated mechanism for field generation, although it does not necessarily give direct insight into the behaviour in the core.

The Theory of Stress Wave Radiation from Explosions in Prestressed Media

Abstract: Stress wave radiation from underground explosions has been observed to contain an anomalous shear wave contribution which is most likely of tectonic origin. In this paper the theoretical radiation field to be expected from an explosion in a prestressed medium is given under the assumption that no secondary low symmetry faulting on a large scale occurs and that the total tectonic component of the field is due to stress relaxation around the roughly spherical fracture zone created by the explosive shock wave. Evidence for the occurrence of this simple kind of tectonic source is considered, and it is concluded that this model is appropriate in many, if not most, instances involving underground explosions. Expressions for the spectrum of the radiation field and its spatial radiation pattern are given in terms of multipole expansions for the components of the rotation potential and the dilatation potential. Several possible rupture formation models are treated. All models show that the tectonic radiation is of simple quadrupole form, as has been observed. The energy radiated due to stress relaxation is considered in detail, and it is also shown that, in terms of the energy released, a dislocation source can be used as an equivalent for the stress relaxation effects. The theoretical energy partition between compressional and shear waves for the tectonic field is in the ratio of (approximately) 1 to 10, so that tectonic stress release does not affect the direct compressional body wave particularly, but gives rise to totally anomalous SH polarized waves (e. g. Love waves) and affects Rayleigh type surface waves significantly, as is also observed. The theory can be applied to obtain estimates of source dimensions and the orientation and magnitude of the initial prestress field in the region of the explosion. In addition, application of this particular form of the general tectonic source theory to deep earthquakes and volcanic earthquakes also appears to be reasonable in view of the probable high symmetry of the failure or phase transition regions for such events.

Inverse Theory with Grossly Inadequate Data

Abstract: Summary When only a few observations are available as data for an inverse problem, it is proposed that the best way to use them is to obtain bounds on various functionals of the structure. To do this, the model is found that has the smallest (or largest) value of the functional. In this way, for example, equations are derived for finding the model value that is exceeded somewhere by all structures satisfying the data, and thus this value must be exceeded in the Earth itself. The same techniques can be used to derive conditions for the existence of a solution, when a certain data set is given; this is an important problem in non-linear inverse theory. Three examples are given, including the non-linear problem of electrical conductivity in the mantle. There, one- and two-data problems are solved and, by means of the existence theory, self-consistency criteria are defined for amplitude and phase measurements and for amplitude measurements at two different frequencies.

Magnetic Remanence Related to Slow Rotation of Ferromagnetic Material in Alternating Magnetic Fields

Abstract: Summary The experiments described in this paper show that a permanent remanence can be induced in a ferromagnetic specimen if it is rotating even very slowly, during the slow decrease of an alternating field pervading the specimen. The remanence is antiparallel to the rotation vector, when the rotation axis is perpendicular to the alternating field axis. The result therefore seems incompatible with existing electromagnetic theories for rotating conducting paramagnetic bodies, but the solution for ferromagnetic bodies might still be compatible with Maxwell's equations. Precautions were taken to ensure that the remanence was neither an anhysteretic remanence, nor other spurious remanence. From the practical point of view, the results are relevant to the design of alternating field demagnetization equipment, such as is used by palaeomagnetists to separate various components of magnetization in a single specimen. Without care in design, a spurious remanence could be induced by the ' tumbling ' of the specimen. lntroduction The experiments described in this paper show that a permanent remanence can be induced in a ferromagnetic specimen if it is rotating even very slowly, during the slow decrease of an alternating field surrounding the specimen. The remanence is not an ordinary anhysteretic remanence due to small superimposed steady fields, but is clearly related to the act of rotation in the alternating field.

Earthquake-Tide Correlation

Abstract: Summary The detection of moonquakes that occur when the Moon is at perigee has prompted a search for tidal effects on earthquake occurrences. An attempt was made to correlate earthquakes listed in the CGS-NOA epicentre determinations with the tidal phase of semidiurnal tides. This study was confined to several seismic regions representative of tectonic and non-tectonic regions. An extended form of Schuster's test was used to decide whether significant correlations existed. Though some tidal influences could be accepted at a 5 per cent significance level, the effect was not consistent or stable with time. Earthquakes, if they are affected by tides, show a slight tendency to occur at times when the tidal stress is changing most rapidly. Insufficient data was available to compare tectonic to non-tectonic areas. An analysis of the Japanese aftershock sequence which began 1969 August 11 was found to have no significant tidal correlation.