Observation of Coriolis coupled modes below 1 mHz

We present observations of spectral energy at toroidal mode frequencies in vertical seismic recordings of the 1998 Balleny Islands earthquake. Since toroidal modes on a spherically symmetric, nonrotating Earth have horizontally polarized particle motion these observations call for an explanation. We first rule out local and instrumental effects as being responsible for the verticalcomponent signal of the toroidal modes ₀ T ₃ (0.59 mHz) and ₀ T ₄ (0.77 mHz). The global effects that we consider are general heterogeneous mantle structure, ellipticity of figure and rotation. We find that rotation through Coriolis coupling of loworder spheroidal and toroidal oscillations is the dominant mechanism.     

Determination of earthquake early warning parameters, τc and Pd, for southern California

We explore a practical approach to earthquake early warning in southern California by determining a ground-motion period parameter  τ _c   and a high-pass filtered displacement amplitude parameter Pd from the initial 3 s of the P waveforms recorded at the Southern California Seismic Network stations for earthquakes with M > 4.0. At a given site, we estimate the magnitude of an event from  τ _c   and the peak ground-motion velocity ( PGV ) from Pd . The incoming three-component signals are recursively converted to ground acceleration, velocity and displacement. The displacements are recursively filtered with a one-way Butterworth high-pass filter with a cut-off frequency of 0.075 Hz, and a P -wave trigger is constantly monitored. When a trigger occurs,  τ _c   and Pd are computed. We found the relationship between  τ _c   and magnitude ( M ) for southern California, and between Pd and PGV for both southern California and Taiwan. These two relationships can be used to detect the occurrence of a major earthquake and provide onsite warning in the area around the station where onset of strong ground motion is expected within seconds after the arrival of the P wave. When the station density is high, the methods can be applied to multistation data to increase the robustness of onsite early warning and to add the regional warning approach. In an ideal situation, such warnings would be available within 10 s of the origin time of a large earthquake whose subsequent ground motion may last for tens of seconds.     

Relocation of M ≥ 2 events of the 1989 Dôbi seismic sequence in Afar: evidence for earthquake migration

The Ethiopian side of central Afar was struck in August 1989 by the largest seismic sequence (three 6.1 ≤ M _s ≤ 6.3 events, 15 with M _s or m _b ≥ 5.0) since that of Serdo in 1969. Using the Djibouti seismological network, we relocated 297 of the events of that sequence. As most of the large events took place outside the network, we assessed the accuracy and stability of earthquake relocations by using three different velocity models and two relocation codes to try to relate individual shocks to distinct faults and surface breaks. A majority of the events apparently occurred underneath the floor of the Dôbi graben, an area about 45  km long and 15  km wide, rupturing boundary and inner floor faults, in agreement with the surface cracks and scarps that we mapped in the area. The relocation shows that the principal events propagated about 50  km northwestwards along the graben in the first 40  hr. A day and a half after the beginning of the sequence, smaller events ( M ≤ 4) started to propagate more than 55  km eastwards, towards Asal Lake. Using two three-component stations installed near the Ethiopian border, we could determine reliable depths for 21 events. The depths are compatible with a seismogenic crust about 14  km thick in the Dôbi and Hanle graben area. Although the Dôbi sequence ruptured about 50  km of the fault array extending from Serdo to Asal, where the regional stress was released by earthquakes in 1969 and 1978, respectively, a seismic gap about 50  km long still subsists along the northern part of the Gaggade region (Der'êla half-graben).     

Estimation of uncertainties in eigenspectral estimates from decaying geophysical time series

Summary. The response of many dynamical systems to an impulse is a linear combination of decaying cosines. The frequencies of the cosines have generally been estimated in geophysics by periodogram analysis and little formal indication of uncertainty has been provided. This work presents an estimation procedure by the methods of complex demodulation and nonlinear regression that specifically incorporates in the basic model the decaying aspect of the cosines (periodogram analysis does not). The use of plots of the instantaneous phase as a function of time is shown to greatly enhance resolution. Expressions for the variances of eigenfrequencies, amplitudes, phases and damping constants Q are derived by non-linear least-squares. The results are illustrated, for the problem of the free oscillations of the Earth, by computations with the record made at Trieste of the Chilean earthquake of 1960 May 22. Sample values are periods and standard errors of 737.79 ± 0.13 s, 506.25 ± 0.13 s and 429.60 ± 0.14 s for ₀ T ₈, ₀ T ₁₃ and ₀ T ₁₆ with Q values and standard errors of 200 ± 14, 230 ± 28 and 215 ± 30, respectively.     

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.     

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.     

Coupled normal-mode sensitivity to inner-core shear velocity and attenuation

We have studied the response of normal modes to perturbations in inner-core shear velocity and attenuation, using fully coupled mode synthetics. Our results indicate that (i) mode pairs   _n S _l – _{n ±1} S _l   are strongly coupled by anelasticity, (ii) this coupling causes shear velocity perturbations to strongly affect the Q values of modes through exchange of inner-core characteristics, (iii) there is no evidence for a weakly attenuating inner core in shear, and (iv) the discrepancy between attenuation models returned from normal modes and body waves is small. These results suggest that inversions for inner-core attenuation and shear velocity should be performed simultaneously and should take account of the strong cross-coupling due to attenuation.     

The attenuation mechanism of seismic waves in northwestern Himalayas

We analysed local earthquake waveforms recorded on a broad-band seismic network in northwestern Himalayas to compute the intrinsic and scattered attenuation parameters from coda waves. Similar to other tectonically active and heterogeneous regions, attenuation-frequency relation for western Himalaya is   Q ⁻¹ _c = (113 ± 7)  f ^(1.01±0.05)  where   Q_c   is the coda Q parameter. Intrinsic  ( Q ⁻¹ _i )  and scattering  ( Q ⁻¹ _s )  attenuations was separated using   Q_c   and direct S -wave Q data  ( Q_d )  . It is observed that estimated   Q ⁻¹ _c   is close to   Q ⁻¹ _i   and both of them are much larger than   Q ⁻¹ _s   suggesting that coda decay is predominantly caused by intrinsic attenuation. At higher frequencies, both the attenuation parameters   Q_c   and,   Q_d   are similar indicating that coda is predominantly composed of back-scattered S waves at these frequencies.     

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 small earthquakes in the southeastern Brazilian shield: a test of stress models of the South American plate

Focal mechanisms of small earthquakes with magnitudes of about 3 in the SE Brazilian shield are calculated using S / P amplitude ratios. Low attenuation ( Q _p from 400 to 800) in the shield upper-crustal layers allowed sharp S arrivals to be recorded up to distances of 100 km. Besides P -wave polarities, SH -wave first motions were also used to constrain the nodal-plane orientations. Normal and reverse faulting mechanisms with strike-slip components were found. The inversion of four mechanisms to estimate the stress tensor indicated a strike-slip stress regime with roughly E–W-orientated σ ₁ and N–S σ ₃. Both the orientations and the shape factor ( φ =0.7) of the inverted stress are in excellent agreement with theoretical predictions for that part of Brazil from the driving-force model of Coblentz & Richardson (1996) . Good agreement with the nature of the stress, as well as its orientation, was also found for the model of Meijer (1995) . Both of these theoretical models include spreading stresses along the continent/ocean lithospheric transition. Because the earthquakes are more than 300 km from the continental shelf they should not be affected by the local flexural forces caused by sediment load in the marginal basins. The agreement between observed and theoretical stresses then confirms the importance of continental spreading forces in modelling intraplate stresses.     

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.     

Stacking for the frequencies and Qs of 0S0 and 1S0

Summary. Using nine IDA records for the Indonesian earthquake of 1977 August 19, we have formed an optimal linear combination of the records and have measured the frequency and Q of ₀ S ₀ and ₁ S ₀. The frequency was measured using the moment ratio method. The attenuation was measured by the minimum width method and by the time-lapse method. The frequency and attenuation were measured simultaneously by varying them to obtain a best fit to the data. A 2000-hr stack, the sum of nine individual records, for ₀ S ₀ gave a frequency of 0.814664 mHz±4 ppm. The values for the Q of ₀ S ₀ for the three different methods of measurement were 5600,5833 and 5700, respectively. The error in the estimates of Q ^-1 is about 5 per cent for the minimum power method. For ₁ S ₀ a 300-hr stack yielded a frequency of 1.63151 mHz±30 ppm. The values of Q for this mode were 1960, 1800 and 1850, respectively, with an error in Q ^-1 of about 12 per cent for the minimum power method.     

On the nature of regional seismic phases–II. On the influence of structural barriers

The blockage of the L _g wave by crustal barriers such as continental margins and graben structures has long been recognized as providing a very useful tool for mapping large-scale lateral crustal variations along the propagation path. Numerical simulation of L _g -wave propagation in complex anelastic media using the pseudospectral method provides insight into the nature of the propagation process using both snapshots of the wavefield and synthetic seismograms. A variety of 2-D structures have been investigated, including the influence of sediments, crustal thickness and attenuation.
Thick sedimentary basins covering a graben structure can have a major influence, since they remove L _g energy by generating P conversion and scattering–the principal mechanisms for strong L _g attenuation across a graben. The reduction of the L _g energy is reinforced by anelastic attenuation in the sediments as well as the influence of the gradually thinning crustal waveguide associated with an elevated Moho.
The extinction of L _g in a sequence of explosions fired across the central graben of the North Sea can be simulated by numerical calculations for the structure derived from refraction experiments.     

On the linear relation between mb and Ms for discrimination between explosions and earthquakes

Summary. The statistical capability of the m _b: M _s discriminant for the discrimination of earthquake and explosion populations is examined by application of discriminant functions to a group of 83 explosions and 72 earthquakes in Eurasia. Equations are derived for the probability that an event is an earthquake or an explosion. The positive sign of DIS in the decision index equation, DIS _i = 34.3383 – 11.9569 mb _t + 7.1161 M _si , indicates that the event i is an earthquake. Its negative sign indicates that event i is an explosion. The probability of correct classification for an event, P _i , is related to its DIS _i value, by P _i = [1-exp (DIS _i )]⁻¹, where a large, positive DIS indicates a high probability that an event is an earthquake and a large, negative DIS indicates a high probability that an event is an explosion. The discrimination line M _s = 1.680 m _b– 4.825, or m _b= 0.595 M _s+ 2.872 very successfully separates the explosion population from the earthquake population. The points on this line have an equal chance of being an earthquake or an explosion; moreover, for any event, the distance parallel to the M _s-axis from the point representing that event in the m _b: M _s plane to this line is a measure of the probability for the correct classification of that event.     

Lower-crustal rifting in the Rukwa Graben, East Africa

An M_w 5.9 earthquake occurred in the Lake Rukwa rift, Tanzania, on 1994 August 18, and was well recorded by 20 broad-band seismic stations at distances of 160 to 800 km and 21 broad-band stations at teleseismic distances. The regional and teleseismic waveforms have been used to investigate the source characteristics of the main shock, and also to locate aftershocks that occurred within three weeks of the main shock. Teleseismic body-wave modelling yields the following source parameters for the main shock: source depth of 25 ± 2 km, a normal fault orientation, with a horizontal tension axis striking NE-SW and an almost vertical pressure axis (Nodal Plane I: strike 126°–142°, dip 63°–66°, and rake 280°–290°; Nodal Plane II: strike 273°–289°, dip 28°–31°, and rake 235°–245°), a scalar moment of 4.1 times 10¹⁷ N m, and a 2 s impulsive source time function. Four of the largest aftershocks also nucleated at depths of 25 km, as deduced from regional sPmp–Pmp times. The nodal planes are broadly consistent with the orientation of both the Lupa and Ufipa faults, which bound the Rukwa rift to the northeast and southwest, respectively. The rupture radius of the main shock, assuming a circular fault, is estimated to be 4 km with a corresponding stress drop of 6.5 MPa. Published estimates of crustal thickness beneath the Rukwa rift indicate that the foci of the main shock and aftershocks lie at least 10 km above the Moho. The presence of lower-crustal seismicity beneath the Rukwa rift suggests that the pre-rift thermal structure of the rifted crust has not been strongly modified by the rifting, at least to depths of 25 km.     

Magnitude and Q determinations in southern Africa using Lg wave amplitudes

b
The amplitude of vertical, short period (1 s) Lg -waves from 575 shallow earthquakes recorded within the distance range 0|Mo-30|Mo by the Rhodesian seismograph network during the period 1968–77 are analysed to separate the effects of earthquake size, epicentral distance and station structure.
When corrected for geometrical spreading and Airy phase dispersion the decay of amplitude with distance yields an estimate of anelastic attenuation of 0.160 deg^-1 which gives an average value of Q (the specific quality factor) of 603 |Mp 50 for propagation paths that lie along and across the East African Rift System. Inversion of the amplitude—distance curve gives the calibration or distance normalizing function. Thereby the amplitude of Lg can be used to provide an estimate of the size of small, local earthquakes in terms of the teleseismic body wave magnitude m_b (after Henderson). The station effects of the six seismograph stations making up the network all lie within |Mp0.1 magnitude units. Since three of the stations lie on the Rhodesian craton while the remaining three lie on Precambrian mobile belts adjacent to the craton, the Precambrian basement geology does not significantly affect the amplitude of Lg     

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.     

Lateral variation and frequency dependence of coda-Q in the southern part of Iberia

b
A method based on the coda attenuation law: Q = Q ₀( f/f ₀)^v leads to the determination of the lateral variation of coda- Q in the southern part of the Iberian Peninsula using seismograms belonging to the seismological network of the Cartuja Observatory, located in Granada. The lateral variation of Q ₀ ( Q value corresponding to a reference frequency f ₀ of 1 Hz) and its frequency dependence for the 1 to 5 Hz frequency range are, in general, in agreement with coda- Q values for frequencies less than about 1 Hz, previously determined in the region under study.
To determine the coda- Q values analytical functions have been used to fit the magnification curves of the vertical component short-period seismographs belonging to the Cartuja network. The problem is solved by using least-squares techniques and non-linear inversion. The determined coda- Q ₀ values and its frequency dependence correlate well with several known geophysical parameters in the southern part of the Iberian Peninsula.     

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.     

Run-up from impact tsunami

We report on calculations of the on-shore run-up of waves that might be generated by the impact of subkilometre asteroids into the deep ocean. The calculations were done with the COULWAVE code, which models the propagation and shore-interaction of non-linear moderate- to long-wavelength waves  ( kh < π)  using the extended Boussinesq approximation. We carried out run-up calculations for several different situations: (1) laboratory-scale monochromatic wave trains onto simple slopes; (2) 10–100 m monochromatic wave trains onto simple slopes; (3) 10–100 m monochromatic wave trains onto a compound slope representing a typical bathymetric profile of the Pacific coast of North America; (4) time-variable scaled trains generated by the collapse of an impact cavity in deep water onto simple slopes and (5) full-amplitude trains onto the Pacific coast profile. For the last case, we also investigated the effects of bottom friction on the run-up. For all cases, we compare our results with the so-called 'Irribaren scaling': The relative run-up   R / H ₀=ξ= s ( H ₀/ L ₀)^−1/2  , where the run-up is   R , H ₀  is the deep-water waveheight, L ₀ is the deep-water wavelength, s is the slope and ξ is a dimensionless quantity known as the Irribaren number. Our results suggest that Irribaren scaling breaks down for shallow slopes   s ≤ 0.01  when  ξ < 0.1 − 0.2  , below which   R / H ₀  is approximately constant. This regime corresponds to steep waves and very shallow slopes, which are the most relevant for impact tsunami, but also the most difficult to access experimentally.