A uniformly valid asymptotic representation of normal mode multiplet spectra on a laterally heterogeneous Earth

Summary. A new asymptotic formula is obtained for the spectrum of an isolated normal mode multiplet _nS_l or _nT_l , with n ≪ l , on a laterally heterogeneous Earth. The principal feature of this formula is that it is uniformly valid on the Earth's surface, including near the epicentre and its antipode. The formal conditions for its validity are that | δm / m ₀|≪ 1 and s _max≪ l ≪ s _min| δm / m ₀|^–1, where | δm / m ₀| is the relative magnitude of the lateral heterogeneity, and s _min and s _max are the minimum and maximum significant degrees in its spherical harmonic expansion. As well as providing a basis for the geographical interpretation of near-epicentral or near-antipodal long-period recordings, the new formula also unifies the asymptotic theory and adds insight into the phenomena which govern the details of multiplet spectra in general.     

Focal mechanisms of recent earthquakes in the Southern Korean Peninsula

We evaluate the stress field in and around the southern Korean Peninsula with focal mechanism solutions, using the data collected from 71 earthquakes ( M_L = 1.9–5.2) between 1999 and 2004. For this, the hypocentres were relocated and well-constrained fault plane solutions were obtained from the data set of 1270 clear P -wave polarities and 46 SH / P amplitude ratios. The focal mechanism solutions indicate that the prevailing faulting types in South Korea are strike-slip-dominant-oblique-slip faultings with minor reverse-slip component. The maximum principal stresses (σ₁) estimated from fault-slip inversion analysis of the focal mechanism solutions show a similar orientation with E–W trend (269°–275°) and low-angle plunge (10°–25°) for all tectonic provinces in South Korea, consistent with the E–W trending maximum horizontal stress (σ_Hmax) of the Amurian microplate reported from in situ stress measurements and earthquake focal mechanisms. The directions of the intermediate (σ₂) and minimum (σ₃) principal stresses of the Gyeongsang Basin are, however, about 90 deg off from those of the other tectonic provinces on a common σ₂–σ₃ plane, suggesting a permutation of σ₂ and σ₃. Our results incorporated with those from the kinematic studies of the Quaternary faults imply that NNW- to NE-striking faults (dextral strike-slip or oblique-slip with a reverse-slip component) are highly likely to generate earthquakes in South Korea.     

Palaeomagnetism of the Fongen-Hyllingen gabbro complex, southern Scandinavian Caledonides; plate rotation or polar shift?

Summary. Palaeomagnetic results are presented from the c . 160 km² Caledonian synorogenic layered Fongen-Hyllingen gabbro complex (of probable late Silurian age) located about 75 km SE of Trondheim, Norway, in the allochthonous Seve-Kdli Nappe Complex. A total of 80 oriented samples from eight sites in the northern part of the gabbro were investigated. After detailed af demagnetization two stable high coercivity components emerge: one with a well defined NW direction with D =325°, I =−21° (α₉₅=8°, N =8), and another, less well defined, probably younger, SW direction with D = 237°, I = 6° (α₉₅= 9°, N = 8). Correction for dip of these two directions gives D = 329°, I =−7° (α₉₅= 10°) and D = 238°, I =−11° (α₉₅= 12°), respectively. The corresponding pole positions are P ₁ : 19° N, 225° E and P ₂: 19° S, 308° E, respectively. The reversed pole -P ₂ of the SW direction lies close to other NW European palaeomagnetic poles of Caledonian, Upper Silurian-Lower Devonian age. However, the dominant pole PI is far away from these, and could be due to a late Caledonian geomagnetic excursion of considerable duration; or it could record a c . 90° rotation around a vertical axis of a crustal block within the Scandinavian Caledonides. Block rotation could have been related to nappe translation, although geological observations do not at present appear to support the occurrence of such an event.     

Approaches to Modelling the Surface Albedo of a High Arctic Glacier

Broadband surface albedo measurements, made during the summer melt season at three weather stations on John Evans Glacier (79°40 ' N, 74°00 ' W), varied strongly with the solar zenith angle ( θ _z ). Tests were carried out to assess the impact of diurnal variations in surface albedo on seasonal net shortwave radiation ( K ^* ) totals. Removing the diurnal signal from albedo measurements by daily averaging of hourly measurements, or by applying midday measurements to all hours of the day, changed K ^* by up to 16%. Ignoring measurements made at θ _z & 75°, to account for measurement (cosine) error at high θ _z , decreased K ^* by between 5 and 18%. Given the sensitivity of K ^* to diurnal patterns in surface albedo, experiments were carried out with two albedo models. One model accounted for albedo variations with θ _z and one did not. The model driven by θ _z , when implemented within a surface energy balance model for John Evans Glacier, produced better melt estimates. This suggests that diurnal variations in surface albedo should be accounted for in energy balance models of glacier melt.     

Rapid computation of magnetic anomalies with demagnetization included, for arbitrarily shaped magnetic bodies

Summary. The potential function ø for a magnetic body of susceptibility μ in a medium of susceptibility μ* satisfies the integral equation
Here Φ* is the potential function for the region without the heterogeneity and R is the distance from the point of observation to the point on the surface, s , of the body. δΦ /δn is the normal derivative, in the direction of the outward normal. The equation allows for the effects of demagnetization. For numerical purposes the surfaces can be divided into N facets over which δΦ/δ n is a constant. The unknown quantities δΦ/δn_j can be found from the system of equations defined by:
The prime on the summation sign denotes that the summation does not include the i th element. The magnetic field in the direction of the unit vector P( P ₁, P ₂, P₃ ) is given by:      

Regional variations of heat flow differences with depth in Alberta, Canada

Summary. Differences between estimated average heat flow values for the Mesozoic and Cenozoic formations ( Q ₁) and estimated average heat flow values for the Palaeozoic formations below the erosional unconformity ( Q ₂) are calculated for the Alberta part of the western Canadian sedimentary basin. Significant heat flow differences exist for these two intervals and the map of Δ Q = Q ₁– Q ₂ shows that Q ₂ is generally greater than Q ₁ in the western and south-western part of Alberta, while in the northern part of the province Q ₂ is generally less than Q ₁. The regional variations of Δ Q are large, with standard deviation of 26 mW m⁻² and average value –13.5 mW m⁻². A regional trend of Δ Q correlates with topographic relief and the hydraulic head variations in the basin. It is shown that there is a heat flow increase with depth in water recharge areas and a decrease in heat flow with depth in the low topographic elevation water discharge areas when comparing the average heat flow in Mesozoic + Cenozoic and Palaeozoic formations.     

Fault slip in the 1997 Manyi, Tibet earthquake from linear elastic modelling of InSAR displacements

The M _w 7.6 1997 Manyi earthquake occurred in an area of central northern Tibet where sparse vegetation coverage and a lack of human habitation provide excellent conditions for Interferometric Synthetic Aperture Radar (InSAR) studies. We use coseismic pairs of radar images acquired by the ESA ERS-2 satellite to construct interferograms of the surface displacement field due to the earthquake. The location and extent of the coseismic fault rupture are mapped using a combination of optical satellite imagery, high-resolution digital topography, interferometric correlation and azimuth offset measurements; in so doing, we are able to relate prominent geomorphic features in the fault zone to bends in the fault.
Using elastic dislocation models consistent with this mapped fault trace, we then test a range of fault geometries and slip conditions to find the combination which best explains the InSAR displacements. Our favoured model contains a reversal in fault dip, approximately halfway along its length, occurring at the location of a restraining bend. Slip on this model fault is heterogeneous, with two areas of peak slip of 7 m or greater, and components of dip-slip displacement which vary significantly along-strike. The success of this model in fitting the data implies that an observed asymmetry in the coseismic interferograms can be explained in terms of the local fault geometry, rather than by using non-linear elastic rheologies as suggested by earlier authors.     

Palaeomagnetism of Dhar traps and drift of the subcontinent during the Deccan volcanism

Summary. Palaeomagnetic investigations were carried out on nine lava flows around the Dhar region, which constitute the northern part of the Deccan traps. The stability of remanent magnetism of these specimens was analysed by an alternating magnetic field, thermal demagnetization and memory tests. Six flows exhibited characteristic components of magnetization, with a mean direction of D =143°, I =+46° ( K = 107.1, α₉₅=5.5°). This gives a VGP located at 29° N, 67° W (δ_p=4.5°, δ_m= 7.0°). The lower site with normal magnetization and the upper five sites with reverse magnetization indicate a geomagnetic field reversal during the initial phases of Deccan volcanism in the Early Tertiary period. A rapid northward migration of about 18° in latitude and a simultaneous anticlockwise rotation of 37° is calculated for the subcontinent.     

Temporal and spatial variations of post-seismic deformation following the 1999 Chi-Chi, Taiwan earthquake

We use GPS displacements collected in the 15 months after the 1999 Chi-Chi, Taiwan earthquake  ( M _w 7.6)  to evaluate whether post-seismic deformation is better explained by afterslip or viscoelastic relaxation of the lower crust and upper mantle. We find that all viscoelastic models tested fail to fit the general features in the post-seismic GPS displacements, in contrast to the satisfactory fit obtained with afterslip models. We conclude that afterslip is the dominant mechanism in the 15-month period, and invert for the space–time distribution of afterslip, using the Extended Network Inversion Filter. Our results show high slip rates surrounding the region of greatest coseismic slip. The slip-rate distribution remains roughly stationary over the 15-month period. In contrast to the limited coseismic slip on the décollement, afterslip is prominent there. Maximum afterslip of 0.57 m occurs downdip and to the east of the hypocentral region. Afterslip at hypocentral depths is limited to the southern part of the main shock rupture, with little or no slip on the northern section where coseismic slip was greatest. Whether this results from along strike variations in frictional properties or dynamic conditions that locally favour stable sliding is not clear. In general, afterslip surrounds the area of greatest coseismic slip, consistent with post-seismic slip driven by the main shock stress change. The total accumulated geodetic afterslip moment is  3.8 × 10¹⁹ N m  , significantly more than the seismic moment released by aftershocks,  6.6 × 10¹⁸ N m  . Afterslip and aftershocks appear to have different temporal evolutions and some spatial correlations, suggesting that aftershock rates may not be completely controlled by the rate of afterslip.     

Palaeomagnetism of the continental sector of the Cameroon Volcanic Line, West Africa

Measurement of samples from 154 sites in the continental sector of the Cameroon Volcanic Line yielded six palaeomagnetic poles, at 243.6°E, 84.6°N, α ₉₅ = 6.8°; 224.3°E, 81.2°N, α ₉₅ = 8.4°; 176.1°E, 82.0°N, α ₉₅ = 8.5°; 164.3°E, 86.4°N, α ₉₅ = 3.4°; 169.4°E, 82.6°N, α ₉₅ = 4.6° and 174.7°E, 72.8°N, α ₉₅ = 9.5°, belonging to rocks which have been dated by the K–Ar method at 0.4–0.9  Ma, 2.6  Ma, 6.5–11  Ma, 12–17  Ma, 20–24  Ma and 28–31  Ma, respectively. The results are in general agreement with other palaeomagnetic poles from Oligocene to Recent formations in Africa.
  The first three poles for rocks formed between 0.4 and 11  Ma are not significantly different from the present geographical pole. Together with other African poles for the same period, this suggests that the African continent has moved very little relative to the pole since 11  Ma. The other three poles for rocks dated between 12 and 31  Ma are significantly different from the present geographical pole, showing a 5° polar deviation from the present pole in the Miocene and 13° in the Middle Oligocene.     

The traveltime perturbations for seismic body waves in factorized anisotropic inhomogeneous media

The traveltime perturbation equations for the quasi-compressional and the two quasi-shear waves propagating in a factorized anisotropic inhomogeneous (FAI) media are derived. The concept of FAI media simplifies considerably these equations. In the FAI medium, the density normalized elastic parameters a _ijkl ( X _i ) can be described by the relation a _ijkl ( X _i) = f ²( x _i ) A _ijkl, where A _ijkl are constants, independent of coordinates x _i and f ²( x _i) is a continuous smooth function of x _i . The types of anisotropy ( A _ijkl ) and inhomogeneity [ f ( x _i)] are not restricted. The traveltime perturbations of individual seismic body waves ( q ^P , qS 1 and qS 2) propagating in the FAI medium depend, of course, both on the structural pertubations [δ f ²( x _i)] and on the anisotropy perturbations (δ A _ijkl ), but both these effects are fully separated. The perturbation equations for the time delay between the two qS -waves propagating in the FAI medium are simplified even more. If the unperturbed (background) medium is isotropic, the perturbation of the time delay does not depend on the structural perturbations (δ f ²( x _i) at all. This striking result, valid of course only in the framework of first-order perturbation theory, will simplify considerably the interpretation of the time delay between the two split qS -waves in inhomogeneous anisotropic media. Numerical examples are presented.     

Earthquake intensity attenuation pattern in the United States

Summary. Attenuation of earthquake intensities with epicentral distance was studied by analysing the intensity data for 39 earthquakes in the United States. Attenuation of MM intensity ( I ) with distance (Δ km) follows a simple relation of the type log I = log I ₀ - m Δ, where I ₀ is the intensity at the epicentre and m is a constant. Slope m is found to be inversely proportional to the square of the focal depth. Intensity attenuation pattern in the United States in general can be represented by a unified relation I/I ₀= exp [-(0.8999/ h ²+ 0.0014)Δ] where 16km ≤ h ≤ 60km. Intensities were calculated with the help of this equation and a good agreement with the observed intensities were found. A comparative study has also been made between the attenuation relations applicable to India and the United States.     

Magnetic fabric and its significance in the Florianópolis dyke swarm, southern Brazil

Magnetic fabric was determined by applying the anisotropy from the low-field magnetic susceptibility (AMS) technique in 62 mafic dykes from the Mesozoic Florianópolis (Santa Catarina Island) dyke swarm, southern Brazil. These dykes cut the crystalline basement rocks, which are mainly Proterozoic. They are vertical or subvertical in dip and trend mainly NE, although NW-trending dykes are also found. Dykes are tholeiitic in composition and are geochemically similar to those from the Ponta Grossa swarm. Thicknesses vary from 0.3 to 60 m. Polished sections show that titanomagnetites carry the AMS in these dykes. Hysteresis parameters show that the magnetic minerals fall in the PSD range. Two types of magnetic fabric are recognized. Type I is characterized by K ₁- K ₂ parallel to the dyke wall, representing magma flow within the dykes; type II, with K ₁- K ₃ parallel to the dyke wall, was found in four dykes. Type I is found in 94 per cent of the dykes, and approximately 20 per cent of these have K ₁ inclinations of less than 30°, suggesting horizontal or subhorizontal flow. About 80 per cent have K ₁ inclinations of greater than 30°, due to inclined to vertical flow. The comparison of AMS studies from both the Florianópolis and the Ponta Grossa dykes suggests a source position closer to Santa Catarina Island than the Ponta Grossa arch.     

Palaeomagnetics and igneous activity of the area adjoining the south-westem margin of the Cuddapah basin, India

Summary. Fifty-six orientated samples were collected from 13 sites on five dolerite dykes (between lat.14°23°N, long.77°43'E and lat.14°08'N, long. 77°49'E), which adjoin the south-western margin of the Cuddapah basin in Anantapur district, Andhra Pradesh. After af demagnetization, two dykes (five sites) striking ENE possess similar magnetic directions, (1) D = 57°, 1=-69° (K = 52, α₉₅= 7°) and (2) D = 71°, I = -72° ( K = 260, α₉₅= 5°). Again dykes (3) (three sites), and (4) (two sites) have similar strike (NE) and magnetic directions, D = 64°. I=-7 α( K = 142, α₉₅ = 8°) and D = 53°, I =-8° (K = 142, α₉₅= 6°) and dyke (5) (two sites) striking NW shows D = 320°, I = -34° ( K = 68, α₉₅= 13°). Remanent directions estimated from total field magnetic anomaly data agree well with these results. Synthesis of these data with 10 other published palaeomagnetic studies of Precambrian dolerite dykes on the Indian peninsula, suggest that these three systems of dykes adjoining the Cuddapah basin had been emplaced prior to the basin formation perhaps representing the initial thermal event responsible for the basin development and also that there have been at least three separate periods of dyke emplacement on this shield. The radiometric data, however, are very sparse and these periods cannot be dated with confidence.     

Three-dimensional VP and VP /VS models of the upper crust in the Friuli area (northeastern Italy)

3-D images of P velocity and P - to S -velocity ratio have been produced for the upper crust of the Friuli area (northeastern Italy) using local earthquake tomography. The data consist of 2565 P and 930 S arrival times of high quality. The best-fitting V _P and V _P / V _S 1-D models were computed before the 3-D inversion. V _P was measured on two rock samples representative of the investigated upper layers of the Friuli crust. The tomographic V _P model was used for modelling the gravity anomalies, by converting the velocity values into densities along three vertical cross-sections. The computed gravity anomalies were optimized with respect to the observed gravity anomalies. The crust investigated is characterized by sharp lateral and deep V _P and V _P / V _S anomalies that are associated with the complex geological structure. High V _P / V _S values are associated with highly fractured zones related to the main faulting pattern. The relocated seismicity is generally associated with sharp variations in the V _P / V _S anomalies. The V _P images show a high-velocity body below 6 km depth in the central part of the Friuli area, marked also by strong V _P / V _S heterogeneities, and this is interpreted as a tectonic wedge. Comparison with the distribution of earthquakes supports the hypothesis that the tectonic wedge controls most of the seismicity and can be considered to be the main seismogenic zone in the Friuli area.     

Experimental study of the anisotropy of longitudinal and transverse waves from local earthquake records

Summary. The paper gives the results of a study of the anisotropy of seismic wave velocities within the Ashkhabad test field in Central Asia. The anisotropy was studied by analysing variations in the values of apparent velocities of first arrivals for epicentral distances ranging from 30 to 130 km and by analysing the delays (Δ t_s1-_s2 ) between the arrival times of shear waves with different polarizations.
The velocities of P -waves vary with azimuth from 5.3 to 6.27 km s^-1 and the velocities of S -waves vary from 3.15 to 3.5 km s^-1.
The delay times Δ t_S1 - _S2 depend on the direction of the propagation. The character of the variation of the propagation velocity of the longitudinal wave, the presence of two differently polarized shear waves S 1 and S 2 propagating at different velocities, and the character of the distribution of Δ t_S1 - _S2 on the stereogram suggest that the symmetry of the anisotropic medium is close to hexagonal with a nearly horizontal symmetry axis coinciding with the direction of maximal velocity. The azimuth of the symmetry axis of the medium is 140° and coincides with the direction of geological faults.     

Linearity spectrum analysis of multi-component magnetizations and its application to some igneous rocks from south-eastern Australia

Summary. A method that enables the objective resolution of almost parallel multi-component magnetizations is described and demonstrated. A feature distinguishing this method from others is its simultaneous analysis of demagnetization data from a group of specimens, rather than the analysis of data from one specimen at a time. The only prerequisite is that the specimens are derived from a homogeneous source. Thus for a formation carrying a simple single component magnetization, all specimens from the formation may be simultaneously reduced. For a more complicated two component magnetization it is shown that only specimens from a particular site can be considered homogeneous, and for a complex three component system each sample often requires undivided attention. Thus the workload is proportionally increased to achieve analyses of comparable reliability from data of variable quality.
New pole positions from Mesozoic intrusions of the Sydney Basin, NSW are: from the Marsden Park Breccia pipe 48°S, 127°E ( A ₉₅= 6°); the St Marys Breccia pipe 46°S, 150°E ( A ₉₅= 8°); the Prospect Dolerite 60°S, 142°E ( A ₉₅= 13°) and 53°S, 180°E ( A ₉₅= 6°); and from the Dundas Breccia pipe 58°S, 162°E ( A ₉₅= 36°) and 31°S, 195°E ( A ₉₅= 16°). The last two formations possess multi-component magnetizations. These pole positions are consistent with previous results from south-eastern Australia.     

Odd zonal harmonics in the geopotential, from analysis of 28 satellite orbits

Summary. The geopotential is usually expressed as an infinite series of spherical harmonics, and the odd zonal harmonics are the terms independent of longitude and antisymmetric about the equator: they define the 'pear-shape' effect. The coefficients J ₃, J ₅, J ₇, … of these harmonics have been evaluated by analysing the variations in eccentricity of 28 satellite orbits from near-equatorial to polar. Most of the orbits from our previous determination in 1974 are used again, but three new orbits are added, including two at inclinations between 62° and 63°, which have been specially observed for more than five years by the Hewitt cameras. With the help of the new orbits and revised theory, we have obtained sets of J -coefficients with standard deviations about 40 per cent lower than before. A 9-coefficient set is chosen as representative, and is as follows (all × 10⁹): J ₃=– 2530 ± 4, J ₅=–245 ± 5, J ₇=–336 ± 6, J ₉=–90 ± 7, J ₁₁= 159 ± 9, J ₁₃=–158 ± 15, J ₁₅=– 20 ± 15, J ₁₇=– 236 ± 14, J ₁₉=– 27 ± 19. With this set of values, the pear-shape asymmetry of the geoid (north polar minus south polar radius) amounts to 45.1 m instead of the previous 44.7 m. The accuracy of the longitude-averaged geoid profile is estimated as 50 cm, except at latitudes above 86°. The geoid profile and predicted amplitude of the oscillation in eccentricity are compared with those from other sources.     

Core–mantle boundary deformations and J2 variations resulting from the 2004 Sumatra earthquake

The deformation at the core–mantle boundary produced by the 2004 Sumatra earthquake is investigated by means of a semi-analytic theoretical model of global coseismic and postseismic deformation, predicting a millimetric coseismic perturbation over a large portion of the core–mantle boundary. Spectral features of such deformations are analysed and discussed. The time-dependent postseismic evolution of the elliptical part of the gravity field ( J ₂) is also computed for different asthenosphere viscosity models. Our results show that, for asthenospheric viscosities smaller than 10¹⁸ Pa s, the postseismic J ₂ variation in the next years is expected to leave a detectable signal in geodetic observations.     

Coseismic slip model of the 2007 August Pisco earthquake (Peru) as constrained by Wide Swath radar observations

The Pisco earthquake ( M _w 8.0; 2007 August 15) occurred offshore of Peru's southern coast at the subduction interface between the Nazca and South American plates. It ruptured a previously identified seismic gap along the Peruvian margin. We use Wide Swath InSAR observations acquired by the Envisat satellite in descending and ascending orbits to constrain coseismic slip distribution of this subduction earthquake. The data show movement of the coastal regions by as much as 85 cm in the line-of-sight of the satellite. Distributed-slip model indicates that the coseismic slip reaches values of about 5.5 m at a depth of ∼18–20 km. The slip is confined to less than 40 km depth, with most of the moment release located on the shallow parts of the interface above 30 km depth. The region with maximum coseismic slip in the InSAR model is located offshore, close to the seismic moment centroid location. The geodetic estimate of seismic moment is 1.23 × 10²¹ Nm ( M _w 8.06), consistent with seismic estimates. The slip model inferred from the InSAR observations suggests that the Pisco earthquake ruptured only a portion of the seismic gap zone in Peru between 13.5° S and 14.5° S, hence there is still a significant seismic gap to the south of the 2007 event that has not experienced a large earthquake since at least 1687.