Attenuation and dispersion ofSH waves due to scattering by randomly distributed cracks

The effect of randomly distributed cracks on the attenuation and dispersion ofSH waves is theoretically studied. If earthquake ruptures are caused by sudden coalescence of preexisting cracks, it will be crucial for earthquake prediction to monitor the temporal variation of the crack distribution. Our aim is to investigate how the property of crack distribution is reflected in the attenuation and dispersion of elastic waves.We introduce the stochastic property, in the mathematical analysis, for the distributions of crack location, crack size and crack orientation. The crack size distribution is assumed to be described by a power law probability density (p(a) a ^– fora _minaa _max according to recent seismological and experimental knowledge, wherea is a half crack length and the range 13 is assumed. The distribution of crack location is assumed to be homogeneous for the sake of mathematical simplicity, and a low crack density is assumed. The stochastic property of each crack is assumed to be independent of that of the other cracks. We assume two models, that is, the aligned crack model and the randomly oriented crack model, for the distribution of crack orientation. All cracks are assumed to be aligned in the former model. The orientation of each crack is assumed to be random in the latter model, and the homogeneous distribution is assumed for the crack orientation. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.We observe the following features common to both the aligned crack model and the randomly oriented crack model. The attenuation coefficientQ ^–1 decays in proportion tok ^–1 in the high frequency range and its growth is proportional tok ² in the low frequency range, wherek is the intrinsic wave number. This asymptotic behavior is parameter-independent, too. The attenuation coefficientQ ^–1 has a broader peak as increases and/ora _min/a _max decreases. The nondimensional peak wave numberk _p a _max at whichQ ^–1 takes the peak value is almost independent ofa _min/a _max for =1 and 2 while it considerably depends ona _min/a _max for =3. The phase velocity is almost independent ofk in the rangeka _max<1 and increases monotonically ask increases in the rangeka _max>1. While the magnitude ofQ ^–1 and the phase velocity considerably depend on the orientation of the crack in the aligned crack model, the above feature does not depend on the crack orientation.The accumulation of seismological measurements suggests thatQ ^–1 ofS waves has a peak at around 0.5 Hz. If this observation is combined with our theoretical results onk _p a _max, the probable range ofa _max of the crack distribution in the earth can be estimated for =1 or 2. If we assume 4 km/sec as theS wave velocity of the matrix medium,a _max is estimated to range from 2 to 5 km. We cannot estimatea _max in a narrow range for =3.     

A model for attenuation and scattering in the Earth's crust

The mechanisms contributing to the attenuation of earthquake ground motion in the distance range of 10 to 200 km are studied with the aid of laboratory data, coda wavesRg attenuation, strong motion attenuation measurements in the northeast United States and Canada, and theoretical models. The frequency range 1–10 Hz has been studied. The relative contributions to attenuation of anelasticity of crustal rocks (constantQ), fluid flow and scattering are evaluated. Scattering is found to be strong with an albedoB ₀=0.8–0.9 and a scattering extinction length of 17–32 km. The albedo is defined as the ratio of the total extinction length to the scattering extinction length. TheRg results indicate thatQ increases with depth in the upper kilometer or two of the crust, at least in New England. CodaQ appears to be equivalent to intrinsic (anelastic)Q and indicates that thisQ increases with frequency asQ=Q _o f ⁿ , wheren is in the range of 0.2–0.9. The intrinsic attenuation in the crust can be explained by a high constantQ (500Q _o2000) and a frequency dependent mechanism most likely due to fluid effects in rocks and cracks. A fluid-flow attenuation model gives a frequency dependence (QQ _o f ^0.5) similar to those determined from the analysis of coda waves of regional seismograms.Q is low near the surface and high in the body of the crust.     

Scattering attenuation and intrinsic absorption using uniform and depth dependent model – Application to full seismogram envelope recorded in Northern Chile

Two seismic wave attenuation factors, scatteringattenuation Q _s ^-1 and intrinsicabsorption Q _i ^-1 are measured using theMultiple Lapse Time Window (MLTW) analysis method forthree different frequency bands, 1–2, 2–4, and 4–8 Hz.Data from 54 temporally deployed seismic stationslocated in northern Chile are used. This methodcompares time integrated seismic wave energies withsynthetic coda wave envelopes for a multiple isotropicscattering model. In the present analysis, the waveenergy is assumed to decay with distance in proportionto1/GSF·exp(- (Q _s ^-1+Q _i ^-1)· r/v), where r, and v are the propagationdistance, angular frequency and S wave velocity,respectively, and GSF is the geometricalspreading factor. When spatial uniformity of Q _s ^-1, Q _i ^-1 and v isassumed, i.e. GSF = 4r ², theestimates of the reciprocal of the extinction length,L _e ^-1 (= (Q _s ^-1+Q _i ^-1)·/v), are 0.017,0.012 and 0.010 km^-1, and those of the seismicalbedo, B ₀ (= Q _s ^-1/ (Q _s ^-1+Q _i ^-1)), are 0.48, 0.40and 0.34 for 1–2, 2–4 and 4–8 Hz, respectively, whichindicates that scattering attenuation is comparable toor smaller than intrinsic absorption. When we assumea depth dependent velocity structure, we also findthat scattering attenuation is comparable to orsmaller than intrinsic absorption. However, since thequantitative estimates of scattering attenuationdepend on the assumed velocity structure (strength ofvelocity discontinuity and/or Moho depth), it isimportant to consider differences in velocitystructure models when comparing attenuation estimates.     

Determination of characteristics of steam reservoirs by Radon-222 measurements in geothermal fluids

The authors conducted a Rn²²² survey in wells of the Larderello geothermal field (Italy) and observed considerable variations in concentrations. Simple models show that flow-rate plays an important part in the Rn²²² content of each well, as it directly affects the fluid transit time in the reservoirs. Rn²²² has been sampled from two wells of the Serrazzano area during flow-rate drawdown tests. The apparent volume of the steam reservoir of each of these two wells has been estimated from the Rn²²² concentration versus flow-rate curves.List of symbols Q Flow-rate (kg h^–1) - Decay constant of Rn²²² (=7.553×10^–3 h^–1) - Porosity of the reservoir (volume of fluid/volume of rock) - ₁ Density of the fluid in the reservoir (kg m^–3) - ₂ Density of the rock in the reservoir (kg m^–3) - M Stationary mass of fluid filling the reservoir (kg). - E Emanating power of the rock in the reservoir (nCi kg _rock ^–1 h^–1). - P Production rate of Rn²²² in the reservoir: number of atoms of Rn²²² (divided by 1.764×10⁷) transferred by the rock to the mass unit of fluid per unit time (nCi kg _fluid ^–1 h^–1). - N Specific concentration of Rn²²² in the fluid (nCi kg^–1) - Characteristic time of the steam reservoir at maximum flow-rate (=M/Q)     

Computation of the scattering functions of the haze from skylight measurements,considering the multiple scattering

Summary The primary scattering of atmospheric haze is computed by modification of an approximative method evolved byde Bary, basing on skylight measurements carried out on the Musalla, a mountain of 3000 m height in Bulgaria, at various altitudes of the sun and in different horizontal circles at a wavelength of 450 nm. This measured total radiation is reduced by the radiation induced by the scattering at molecules as well as by secondary or multiple scattering at turbidity aerosol. The single scattering of the atmospheric haze thus computed is discussed for various assumed Linke turbidity factors.The concluding deductions relate to a comparison of haze scattering functions with theoretical scattering functions, the results attained agreeing closely with superimposed logarithmic Gaussian distributions and only partly with the scattering functions computed byBullrich. These deductions prove optically the increase of larger particles (r ₀0.64 m) during forenoon. The analysis of the scattering functions conductes to a shortage of particles withr ₀=0.2 m in agreement with other investigations.

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Zusammenfassung In Abwandlung einer vonde Bary angegebenen Approximationsmethode wird die Primärstreuung des atmosphärischen Dunstes berechnet. Zugrundegelegt werden Himmelsllichtmessungen, die auf dem etwa 3000 m hohen Mus Alla in Bulgarien bei verschiedenen Sonnenhöhen und in verschiedenen Horizontalkreisen bei einer Wellenlänge von 450 nm durchgeführt wurden. Von dieser gemessenen Gesamtstrahlung werden die Anteile substrahiert, die durch Streuung an Molekülen sowie durch zwei-oder mehrfache Streuung an Trübungsaerosol hervorgerufen werden. Die so berechnete Einfachstreuung des atmosphärischen Dunstes wird für verschiednee angenommene Linke'sche Trübungsfaktoren diskutiert.Abschließend werden die Dunststreufunktionen mit theoretischen Streufunktionen verglichen, wobei eine gute Übereinstimmung mit überlagerten logarithmischen Gauß-Verteilungen und nur teilweise mit vonBullrich berechneten Streufunktionen erzielt wurde. Es kann dabei optisch die Zunahme großer Teilchen (r ₀0,64 m) im Laufe des Vormittags gezeigt werden. Die Analyse der Streufunktionen führt zu einem Fehlen von Teilchen mitr ₀=0,2 m in Übereinstimmung mit anderen Untersuchungen.

     

Q measurements for PhaseX overtones

Linear stacking procedures are used to retrieve the attenuation of 91 modes belonging to the 3rd, 4th and 5th Rayleigh overtones branches in the 80–160 s period range, and contributing to the so-called PhaseX wave group. Our data show in general slightly less attenuation than expected from available models. Data space inversion shows that, when combined with previously measured fundamental modeQ's, this new dataset improves resolution significantly in the 1000–2000 km depth range. Based on this remark, we carry out a number of parameter space inversions. Our results suggest a narrow (80–200 km) zone of high attenuation (Q =75–90), low attenuation in the intermediate mantle (670–1500 km); (Q 350), and lower values in the deeper mantle (Q 200).     

La risoluzione dell'equazione di Laplace nel campo esterno a uno sferoide

Riassunto L'Autore dimostra che, nel sistema di coordinate polari , , , si possono determinare un numeros di funzioni della sola variabile :Q ₁,Q ₃, ....Q _2s–1 tali che la sommatoria delleQ _2i–1/^2i–1 rappresenti il potenzialeV di un geoide di rotazione. La condizione di armonicità determina ciascunaQ (che si riduce a un polinomio nelle potenze di sen ) a meno di una costante arbitraria; si dispone pertanto dis costanti che servono per soddisfare la natura dellaV sulla superficie del geoide. Come esempio l'Autore ha determinato la gravità sul geoide sferico, confermando i risultati delSomigliana, e su uno sferoide generico dove ha ritrovato la relazione diClairaut.

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Summary The Author proofs that, in the system of polar coordinates , , , it is possible to determine a numbers of functions only of the variable :Q ₁,Q ₃ ....Q _2s–1 in such a way as to make the summatory of theQ _2i–1/^2i–1 represent the potential function of a rotational geoid. The condition of harmonicity determines, saving an arbitrary constant, each of theQ which is reduced to a polynom developed by the sin powers; therefore one disposes of a number of constants to make use for satisfing theV on the geoid. To illustrate his theory the Author determines the gravity on the spherical geoid, thus confirmingSomigliana's formulas and on a spheroidal on which he pointed outClairaut's relations.

     

Source characteristics of the 1992 Nicaragua tsunami earthquake inferred from teleseismic body waves

We analyzed the broadband body waves of the 1992 Nicaragua earthquake to determine the nature of rupture. The rupture propagation was represented by the distribution of point sources with moment-rate functions at 9 grid points with uniform spacing of 20 km along the fault strike. The moment-rate functions were then parameterized, and the parameters were determined with the least squares method with some constraints. The centroid times of the individual moment-rate functions indicate slow and smooth rupture propagation at a velocity of 1.5 km/s toward NW and 1.0 km/s toward SE. Including a small initial break which precedes the main rupture by about 10 s, we obtained a total source duration of 110 s. The total seismic moment isM _o =3.4×10²⁰ Nm, which is consistent with the value determined from long-period surface waves,M _o =3.7×10²⁰ Nm. The average rise time of dislocation is determined to be 10 s. The major moment release occurred along a fault length of 160 km. With the assumption of a fault widthW=50 km, we obtained the dislocationD=1.3 m. From andD the dislocation velocity isD=D/0.1 m/s, significantly smaller than the typical value for ordinary earthquakes. The stress drop =1.1 MPa is also less than the typical value for subduction zone earthquakes by a factor of 2–3. On the other hand, the apparent stress defined by 2E _s /M _o , where andE _s are respectively the rigidity and the seismic wave energy, is 0.037 MPa, more than an order of magnitude smaller than . The Nicaragua tsunami earthquake is characterized by the following three properties: 1) slow rupture propagation; 2) smooth rupture; 3) slow dislocation motion.     

Anelasticity of the crust and upper mantle beneath north and central India from the inversion of observed Love and Rayleigh wave attenuation data

The fundamental mode Love and Rayleigh waves generated by earthquakes occurring in Kashmir, Nepal Himalaya, northeast India and Burma and recorded at Hyderabad, New Delhi and Kodaikanal seismic stations are analysed. Love and Rayleigh wave attenuation coefficients are obtained at time periods of 15–100 seconds, using the spectral amplitude of these waves for 23 different paths along northern (across Burma to New Delhi) and central (across Kashmir, Nepal Himalaya and northeast India to Hyderabad and Kodaikanal) India. Love wave attenuation coefficients are found to vary from 0.0003 to 0.0022 km^–1 for northern India and 0.00003 km^–1 to 0.00016 km^–1 for central India. Similarly, Rayleigh wave attenuation coefficients vary from 0.0002 km^–1 to 0.0016 km^–1 for northern India and 0.00001 km^–1 to 0.0009 km^–1 for central India. Backus and Gilbert inversion theory is applied to these surface wave attenuation data to obtainQ ^–1 models for the crust and uppermost mantle beneath northern and central India. Inversion of Love and Rayleigh wave attenuation data shows a highly attenuating zone centred at a depth of 20–80 km with lowQ for northern India. Similarly, inversion of Love and Rayleigh wave attenuation data shows a high attenuation zone below a depth of 100 km. The inferred lowQ value at mid-crustal depth (high attenuating zone) in the model for northern India can be by underthrusting of the Indian plate beneath the Eurasian plate which has caused a low velocity zone at this shallow depth. The gradual increase ofQ ^–1 from shallow to deeper depth shows that the lithosphere-asthenosphere boundary is not sharply defined beneath central India, but rather it represents a gradual transformation, which starts beneath the uppermost mantle. The lithospheric thickness is 100 km beneath central India and below that the asthenosphere shows higher attenuation, a factor of about two greater than that in the lithosphere. The very lowQ can be explained by changes in the chemical constitution taking place in the uppermost mantle.     

Differences between Mean Sea Levels for the Pacific,Atlantic and Indian Oceans From Topex/Poseidon Altimetry

Geopotential values W of the mean equipotential surfaces representing the mean ocean topography were computed on the basis of four years (1993 - 1996) TOPEX/POSEIDON altimeter data: W = 62 636 854.10m ² s ^–2 for the Pacific (P), W = 62 636 858.20m ² s ^–2 for the Atlantic (A), W = 62 636 856.28m ²s^–2 for the Indian (I) Oceans. The corresponding mean separations between the ocean levels were obtained as follows: A – P = – 42 cm, I– P = – 22 cm, I – A = 20 cm, the rms errors came out at about 0.3 cm. No sea surface topography model was used in the solution.     

A method of searching for radial velocity anomalies in the lower mantle using interfering signals

Radial velocity anomalies in the lower mantle that give rise to triplications in the travel-time curve for short-periodP waves will produce arrivals havingdT/d values that differe by roughly 0.2–0.5 s/deg. The first two arrivals associated with such triplications will be separated by less than one second over a distance range of 4°–10° they may not, therefore, be separable visually on single seismograms, so that their presence can only be inferred from some measurable property that depends on their mutual interference. If there are lateral variations in the regions of anomalous velocity gradients, the interfering signals will also have different azimuths of arrival. Using two synthetic wavelets we have investigated the effect of interference on bothdT/d and azimuth measurements at the Yellowknife Array. We found that if the interfering pulses have a dominant frequencyv, there is a range of time separations (0.30/v0.55/v) over which the measureddT/d and azimuth values may fluctuate by much more than the differences indT/d and azimuth between the interfering signals. We have evaluated the following empirically defined functions for three different primary signals, and for three different relative amplitudes of the interfering signals:f (t), the drift function, which expresses how the measured slownesses,p, and azimuths, , differ from the slownesses and azimuths of the primary wavelets; f(), the range function, which describes the behaviour of the upper and lower bounds ofp and as a function of the difference in arrival times of the signals, andf , studied the properties of these functions, and have outlined how these properties provide criteria based on the numerical and statistical characteristics of the arrival vectors, and on the waveform of the signal that will enable small radial velocity anomalies to be more clearly delineated.Contribution No. 863 from the Earth Physics Branch.     

Torsional vibration of non-homogeneous isotropic hollow thick cylinder

Summary Free vibration of a thick hollow cylinder of non-homogeneous elastic material having rigidity and density varying according to the laws: (i) =₀(₀+₀ z) and Q=Q₀(Q₀+₀ z) for finite and infinite length of the cylinder and (ii) ₁/r = and Q = ₁/r for finite length only are considered in this paper. Frequency equations are deduced and respective numerical solutions are obtained.     

Radioactivity and geochemistry of granulites and some related rocks from the saxonian granulite complex

Summary The distribution of radioactive(Th, U, K), major and selected trace(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) elements of granulites from the Saxonian Granulite Complex was studied. Similarly to the South Bohemian granulites, the Saxonian granulites can be divided according to the contents of their major and trace elements into two main groups, groupA containing mostly acid and subacid granulites (K ₂ O>2.5%, SiO ₂ >68%), and groupB containing mostly intermediate and basic granulites (K ₂ O<2.5%, SiO ₂ <68%). Statistically significant differences between groupsA andB were found for all major oxides and several trace elements(Rb, V, Cr, Ni). The Saxonian granulites follow the same calc-alkaline trend as the South Bohemian, granulitesA being placed mostly in the rhyolite field and granulitesB mostly in the dacite, andesite and basalt fields of this trend. The investigated granulites are characterized by a considerable scatter ofTh andU contents accompanied by very variableTh/U ratios; theTh andU concentrations of granulitesA are substantially lower than is usual for rocks of corresponding acidity.

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¶rt;a an¶rt;u a¶rt;uamu(Th, U, K) u ua ¶rt;u(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) m aum n¶rt;a aaum na. naa, m u¶rt;aum n uu aam n aaum u ¶rt;u am aua, u u uu. aum n u uu ma a¶rt;um ¶rt; ¶rt;nn; nnA nua¶rt;ama a au¶rt; u au¶rt;aum (K ₂ O>2,5%, Si O ₂ >68%), nnB ¶rt;u u aum (K ₂ O<2,5%, SiO ₂ <68%). ¶rt; muunnau mm mamumuu m au ¶rt; a u u ¶rt; m ¶rt;u m(Rb, V, Cr, Ni). auaum n¶rt;¶rt;m um- m¶rt; a u -uaum;aumA a¶rt;ma a uum n, uaumB a a ¶rt;aum, a¶rt;um u aam n m m¶rt;a. ¶rt;aum — u unnA — aamum uu ¶rt;au da¶rt;uamu mTh uU.

     

Scattering attenuation and the fractal geometry of fracture systems

Scattering of seismic waves can be shown to have a frequency dependenceQ ^{–1 3–v} if scattering is produced by arrays of inhomogeneities with a 3D power spectrumW _3D(k) k ^–v. In the earth's crust and upper mantle the total attenuation is often dominated by scattering rather than intrinsic absorption, and is found to be frequency dependent according toQ ^–1 , where –1<–0.5. IfD ₁ is the fractal dimension of the surface of the 3D inhomogeneities measured on a 2D section, then this corresponds respectively to 1.5<D ₁1.75, since it can be shown that =2(D ₁–2). Laboratory results show that such a distribution of inhomogeneities, if due to microcracking, can be produced only at low stress intensities and slow crack velocities controlled by stress corrosion reactions. Thus it is likely that the earth's brittle crust is pervaded by tensile microcracks, at least partially filled by a chemically active fluid, and preferentially aligned parallel to the maximum principal compressive stress. The possibility of stress corrosion implies that microcracks may grow under conditions which are very sensitive to pre-existing heterogeneities in material constants, and hence it may be difficult in practice to separate the relative contribution of crack-induced heterogeneity from more permanent geological heterogeneities.By constrast, shear faults formed by dynamic rupture at critical stress intensities produceD ₁=1, consistent with a dynamic rupture criterion for a power law distribution of fault lengths with negative exponentD. The results presented here suggest empirically thatD ₁-1/2(D+1), thereby providing the basis for a possible framework to unify the interpretation of temporal variations in seismicb-value (b-D/2) and the frequency dependence of scattering attenuation ().This is PRIS contribution 046.     

Ionisations-Neutralisationsbilanz in derE-Schicht nach Angaben von der totalen Sonnenfinsternis am 15. Februar 1961

Zusammenfassung Es werden die Grundgleichungen der Ionisations-Neutralisationsbilanz in derE-Schicht präzisiert und auf die Notwendigkeit der Berücksichtigung des Einflusses der lokalen ionisierenden Strahlungsquellen auf der Sonnenscheibe, der dynamischen ionosphärischen Vorgängen und der Veränderungen des äquivalenten Rekombinationskoeffizienten hingewiesen. Ferner wird eine Methodik zur Bestimmung der charakteristischen Grössen der Ionisations-Rekombinationsbilanz (q _0m ,q _d, ) dargelegt. Zu dem Zweck werden die Messergebnisse aus der Periode der Sonnenfinsternis von zwei unweit voneinander gelegenen Ionosphärenstationen verwendet. Die Methodik wird auf die während der totalen Sonnenfinsternis am 15. Februar 1961 auf den Ionosphärenstationen in Sofia und Nesebar erhaltenen Ergebnisse angewandt. Für den Rekombinationskoeffizienten werden Werte zwischen 0,63·10^–7 cm³sec^–1 und 2,32·10^–7 cm³sec^–1 und für die Elektronenproduktion unter dem Einfluss der ionisierenden Strahlung von der homogenen Sonnenscheibeq _0m 1700 cm^–3sec^–1 erhalten.

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Summary The basic equations for the ionisation-neutralisation balance in theE layer have been shown the necessity to take in account the influence of the local ionisation sources on the disk of the sun, the dynamic ionospheric processes and the variations in the equivalent recombination coefficient. The method for determining the characteristic quantities of the ionisation-recombination balance (q _0m ,q _d, ) has been exhibited for this purpose are used measurement data from two ionospheric stations located not far from each other, in the period of the solar eclips on 15 February, 1961. The quantity of the recombination coefficient lay between 0.63×10^–7 sec^–1 cm³ and 2.32×10^–7 sec^–1 cm³; the electron production under the action of the ionising radiation of the homogen disk showsq _0m 1700 sec^–1 cm^–3.

     

Density fluctuations measured by ISEE 1–2 in the Earth’s magnetosheath and the resultant scattering of radio waves

Radio waves undergo angular scattering when they propagate through a plasma with fluctuating density. We show how the angular scattering coefficient can be calculated as a function of the frequency spectrum of the local density fluctuations. In the Earths magnetosheath, the ISEE 1–2 propagation experiment measured the spectral power of the density fluctuations for periods in the range 300 to 1 s, which produce most of the scattering. The resultant local angular scattering coefficient can then be calculated for the first time with realistic density fluctuation spectra, which are neither Gaussian nor power laws. We present results on the variation of the local angular scattering coefficient during two crossings of the dayside magnetosheath, from the quasi-perpendicular bow shock to the magnetopause. For a radio wave at twice the local electron plasma frequency, the scattering coefficient in the major part of the magnetosheath is b(2f_p) 0.5–4 × 10^–9 rad²/m. The scattering coefficient is about ten times stronger in a thin sheet (0.1 to IR_E) just downstream of the shock ramp, and close to the magnetopause.     

Chemical aspects of iron oxide coagulation in water: Laboratory studies and implications for natural systems

Initial coagulation rates of colloidal hematite (-Fe₂O₃) particles (diameter less than 0.1 µm) were measured experimentally in well-defined laboratory systems at constant temperature. The relative stability ratio,W, was obtained at various ionic strengths in NaCl medium and at pH values in the range from 3 to 12. ExperimentalW values ranged from 1 to 10⁴ in various systems. The results delineate the roles ofspecific andgeneralized coagulation mechanisms for iron oxides. Among the specifically-interacting species (G _ads ⁰ >G _coul ⁰ ) studied were phosphate, monomeric organic acids of various structures, and polymeric organic acids. The critical coagulation-restabilization concentrations of specifically-interacting anions (from 10^–7 to 10^–4 molar) can be compared with the general effects of non-specific electrolyte coagulants (10^–3 to 10^–1 molar). The laboratory results are interpreted with the help of a Surface Complex Formation/Diffuse Layer Model (SCF/DLM) which describes variations of interfacial charge and potential resulting from variations of coagulating species in solution. Comparison of these laboratory experiments with observations on iron behavior in estuarine and lake waters aids in understanding iron removal mechanisms and coagulation time scales in natural systems.     

Frequency dependence of crustalQ β in stable and tectonically active regions

Fundamental-mode Rayleigh wave attenuation data for stable and tectonically active regions of North America, South America, and India are inverted to obtain several frequency-independent and frequency-dependentQ models. Because of trade-offs between the effect of depth distribution and frequency-dependence ofQ on surface wave attenuation there are many diverse models which will satisfy the fundamental-mode data. Higher-mode data, such as 1-Hz Lg can, however, constrain the range of possible models, at least in the upper crust. By using synthetic Lg seismograms to compute expected Lg attenuation coefficients for various models we obtained frequency-dependentQ models for three stable and three tectonically active regions, after making assumptions concerning the nature of the variation ofQ with frequency.In stable regions, ifQ varies as , where is a constant, models in which =0.5, 0.5, and 0.75 satisfy fundamental-mode Rayleigh and 1-Hz Lg data for eastern North America, eastern South America, and the Indian Shield, respectively. IfQ is assumed to be independent of frequency (=0.0) for periods of 3 s and greater, and is allowed to increase from 0.0 at 3 s to a maximum value at 1 s, then that maximum value for is about 0.7, 0.6, and 0.9, respectively, for eastern North America, eastern South America, and the Indian Shield. TheQ models obtained under each of the above-mentioned two assumptions differ substantially from one another for each region, a result which indicates the importance of obtaining high-quality higher-mode attenuation data over a broad range of periods.Tectonically active regions require a much lower degree of frequency dependence to explain both observed fundamental-mode and observed Lg data. Optimum values of for western North America and western South America are 0.0 if is constant (Q is independent of frequency), but uncertainty in the Lg attenuation data allows to be as high as about 0.3 for western North America and 0.2 for western South America. In the Himalaya, the optimum value of is about 0.2, but it could range between 0.0 and 0.5. Frequency-independent models (=0.0) for these regions yield minimumQ values in the upper mantle of about 40, 70, and 40 for western North America, western South America, and the Himalaya, respectively.In order to be compatible with the frequency dependence ofQ observed in body-wave studies,Q in stable regions must be frequency-dependent to much greater depths than those which can be studied using the surface wave data available for this study, andQ in tectonically active regions must become frequency-dependent at upper mantle or lower crustal depths.On leave from the Department of Geophysics, Yunnan University, Kunming Yunnan, People's Republic of China     

The role of wavegroup velocity in the blocking problem

Considering the blocking problem as a baroclinic instability problem in a dispersive wave system with diabatic heating effects, it is of great interest to investigate the role of wavegroup velocityv _gr in blocking processes, becausev _gr controls the energy transfer in the wave field. Using a Newtonian Cooling —type of forcing with a phase differencek to the main field and taking the linearized version of a two-level model, the phase speedc _r, the group velocityv _gr and the growth ratekc _i have been obtained as analytical functions of the mean zonal windU, the thermal windU _T, the coefficient of diabatic heating x, the phase differencek and the wavelengthL. Now the hypothesis is introduced, that a blocking should be expected, ifv _gr has a maximum value in the vicinity ofL _o, for whichc _r vanishes and thee-folding timet=1/kc _i (kc _i>0) is smaller than 6 days (see condition (20) in the text). One finds, that for special parameter combinations (U _T, U, ), where 15 m/secU _T25m/sec,U=10m/sec, 0.8·10^–51.5·10^–5 [sec^–1], certain valuesL _o with an appropriate phase differencek exist, which satisfy the conditions mentioned above (for values see Table 2). TherebyL _o varies within the range 8500 km <L _o<11000 km corresponding to the preferred planetary blocking wavenumber 2 in middle latitudes 50°<<70° N.     

Experimental investigation of the elastic modulus of a fractal system—A model of fractured rocks

The elastic properties of a physical model representing a damaged rock matrix were studied using a square lattice deformed under tensile stress. The elastic modulusM of such a system varies in agreement with percolation theory as|x–x _c | ^f , wherex is the damage parameter andx _c the threshold value of the damage parameter,f3.6. Atxx _c the scale dependence ofM can be expressed asML ^–f/v , whereL is the size of the sample andv the correlation exponent in percolation theory.The experimental results are of interest in assessing elastic properties in earthquake focal zones and fault zones in general.