A scattering model for seismic attenuation and its global applications

The attenuation characteristics of Indian lithosphere and its comparison with different tectonic settings in the world are determined from the observations of the Q for L_g(Q_Lg)-, and S(Q_S)-waves in the 1-30 Hz frequency range. The scattering is approximated with a Gaussian distribution of spherical scatterers. To approximate single scattering, we use Dainty's [Geophy. Res. Lett. 8 (11) (1981) 1126] model that attenuation is given by 1/Q(ω) = 1/Q_i + g(ω)v/ω, where Q_i is intrinsic Q due to anelastic attenuation, v is shear wave velocity, ω is angular frequency, g = ∫n(a)σ da is the total scattering coefficient for S-to-S scattering, n(a) da is the number of scattering spheres of radius a per unit volume, and σ is the scattering cross-section for the sphere. We find that if n(a) is described by a simple two parameter (a₀ and c) Gaussian of amplitude c and standard deviation and mean a₀, the attenuation data for different regions of the world are well approximated over the frequency band of seismic observations. Our major findings are: (1) the maximum effect of scattering on attenuation occurs at 0.84 Hz or a wavelength of 4.16 km; (2) the values of g are frequency dependent. Values of g are of the order of 10⁻³ km⁻¹ at 1-30 Hz, varying from 0.0031 to 0.01 and 0.001 to 0.0083 km⁻¹ for tectonically active and stable regions, respectively; (3) regions of active tectonics and seismicity generally have lower Q_i values (1000) than that in stable regions (2000); and (4) regions of high Q_i value exhibit low intensity of scattering.     

Estimation of the Intrinsic Absorption and Scattering Attenuation in Northeastern Venezuela (Southeastern Caribbean) Using Coda Waves

—Northeastern Venezuela has been studied in terms of coda wave attenuation using seismograms from local earthquakes recorded by a temporary short-period seismic network. The studied area has been separated into two subregions in order to investigate lateral variations in the attenuation parameters. Coda-Q ^?1 (Q _c ^?1) has been obtained using the single-scattering theory. The contribution of the intrinsic absorption (Q _i ^?1) and scattering (Q _s ^?1) to total attenuation (Q _t ^?1) has been estimated by means of a multiple lapse time window method, based on the hypothesis of multiple isotropic scattering with uniform distribution of scatterers. Results show significant spatial variations of attenuation the estimates for intermediate depth events and for shallow events present major differences. This fact may be related to different tectonic characteristics that may be due to the presence of the Lesser Antilles subduction zone, because the intermediate depth seismic zone may be coincident with the southern continuation of the subducting slab under the arc.     

On conditions for the unique inversion of seismic travel-time curves

It is shown that when the travel-time curve of a refracted wave from a surface source is known and at least one of the following conditions is satisfied, i.e. when

1. the travel-time curve of a wave reflected from a horizontal interface lying below the deepest low velocity layer is known, or
2. the travel-time curve of a wave from a deep source situated below the deepest low velocity layer is known, or
3. the measureH(u)=mes {z∶z≥0,v ^?1 (z)≥u} is analytical in some segment [c, d], where \(0< c< d< \infty , c< a_n , H(a_n ) = \bar z_n ,\bar z_n\) is the depth of the lower end of the deepest low velocity layer and in the interval [c, ∞) an analytical functionH(u)) exists which providesH(u)≡H(u)) ifu∈[c, d], then (1) velocityv(z) outside the low velocity layers and (2) the measureH _k (u)=mes {z∶z∈L _k,v ^?1 (z)≥u} for each low velocity layerL _k,k=1, 2, ..., n, are defined unambiguously.

     

The electric field produced in the mantle by the dynamo in the core

A rigorous singular perturbation theory is developed to estimate the electric field E produced in the mantle M by the core dynamo when the electrical conductivity σ in M depends only on radius r, and when |r?_rln σ| ? 1 in most of M. It is assumed that σ has only one local minimum in M, either (a) at the Earth's surface ?V, or (b) at a radius b inside the mantle, or (c) at the core-mantle boundary ?K. In all three cases, the region where σ is no more than e times its minimum value constitutes a thin critical layer; in case (a), the radial electric field E_r ≈ 0 there, while in cases (b) and (c), E_r is very large there. Outside the critical layer, E_r ≈ 0 in all three cases. In no case is the tangential electric field E_S small, nearly toroidal, or nearly calculable from the magnetic vector potential A as ??_tA_S. The defects in Muth's (1979) argument which led him to contrary conclusions are identified. Benton (1979) cited Muth's work to argue that the core-fluid velocity u just below ?K can be estimated from measurements on ?V of the magnetic field B and its time derivative $\text{?}{}_{\mathrm{t}}\text{B}$. A simple model for westward drift is discussed which shows that Benton's conclusion is also wrong.In case (a), it is shown that knowledge of σ in M is unnecessary for estimating E_S on ?K with a relative error |r?_r 1nσ|^?1from measurements of E_S on ?V and knowledge of ?_tB in M (calculable from ?_tB on ?V if σ is small). Then, in case (a), u just below ?K can be estimated as $\text{?}\text{r}\text{×}\text{E}{}_{\mathrm{S}}\text{/B}{}_{\mathrm{r}}$. The method is impractical unless the contribution to E_S on ?V from ocean currents can be removed.The perturbation theory appropriate when σ in M is small is considered briefly; smallness of σ and of |r?_r ln σ|^?1 a independent questions. It is found that as σ → 0, B approaches the vacuum field in M but E does not; the explanation lies in the hydromagnetic approximation, which is certainly valid in M but fails as σ → 0. It is also found that the singular perturbation theory for |r?_r ln σ|^?1 is a useful tool in the perturbation calculations for σ when both σ and |r?_r ln σ|^?1 are small.     

The temporal series of the New Guinea 29 April 1996 aftershock sequence

The aim of our search is the analysis of aftershock temporal series following a mainshock with magnitude M ≥ 7.0. Investigating aftershock behavior may find the key to explain better the mechanism of seismicity as a whole.In particular, the purpose of this work is to highlight some methodological aspects related to the observation of possible anomalies in the temporal decay. The data concerning the temporal series, checked according to completeness criteria, come from the NEIC-USGS data bank. Here we carefully analyze the New Guinea 29 April 1996 seismic sequence.The observed temporal series of the shocks per day can be considered as a sum of a deterministic contribution (the aftershock decay power law, n(t) = K·(t + c)^−p + K₁) and of a stochastic contribution (the random fluctuations around a mean value represented by the above mentioned power law). If the decay can be modeled as a non-stationary Poissonian process where the intensity function is equal to n(t) = K·(t + c)^−p + K₁, the number of aftershocks in a small time interval Δt is the mean value n(t)·Δt, with a standard deviation .     

Seismic Wave Attenuation in the Greater Cairo Region, Egypt

In the present study, a digital waveform dataset of 216 local earthquakes recorded by the Egyptian National Seismic Network (ENSN) was used to estimate the attenuation of seismic wave energy in the greater Cairo region. The quality factor and the frequency dependence for Coda waves and S-waves were estimated and clarified. The Coda waves (Q _c) and S-waves (Q _d) quality factor were estimated by applying the single scattering model and Coda Normalization method, respectively, to bandpass-filtered seismograms of frequency bands centering at 1.5, 3, 6, 12, 18 and 24?Hz. Lapse time dependence was also studied for the area, with the Coda waves analyzed through four lapse time windows (10, 20, 30 and 40?s). The average quality factor as function of frequency is found to be Q _c?=?35?±?9f ^0.9±0.02 and Q _d?=?10?±?2f ^0.9±0.02 for Coda and S-waves, respectively. This behavior is usually correlated with the degree of tectonic complexity and the presence of heterogeneities at several scales. The variation of Q _c with frequency and lapse time shows that the lithosphere becomes more homogeneous with depth. In fact, by using the Coda Normalization method we obtained low Q _d values as expected for a heterogeneous and active zone. The intrinsic quality factor (Q _i ^?1 ) was separated from the scattering quality factor (Q _s ^?1 ) by applying the Multiple Lapse Time Domain Window Analysis (MLTWA) method under the assumption of multiple isotropic scattering with uniform distribution of scatters. The obtained results suggest that the contribution of the intrinsic attenuation (Q _i ^?1 ) prevails on the scattering attenuation (Q _s ^?1 ) at frequencies higher than 3?Hz.     

On the boundary integral equations in the theory of elastic vibrations

Forward seismic problems are solved for elastic media by rigorous methods (i.e., methods with controllable accuracy). Analysis of the current state of research on this subject suggests that the most promising methods are based on integral and integro-differential equations, notwithstanding the rather modest results of their application to solving forward problems in the theory of elastic vibrations. The second Green integral theorem for seismic waves, formulated and proven in the paper, yields a system of two boundary (surface) integral equations for the displacement vector u(M ₀) and the normal (to the boundary surface) vector component of the stress tensor t_n(M ₀). The integrands of the surface integrals in terms of which the function t_n(M ₀) is expressed on both sides of the interface between the medium and the heterogeneity contain the second derivatives of the Green’s tensor functions ? ^e (M ₀, M) and ? ⁱ (M ₀, M), respectively, which are responsible for a cubic singularity (third-order singularity) if the integration point M coincides with the observation point M ₀. An original method of eliminating the cubic singularity proposed in the paper involves special tensor normalization of the integrals on the outer and inner sides of the interface and subsequent subtraction of one integral from another in order to construct the second integral equation.     

Transient and steady-state creep of pure forsterite at low stress

Thirty-one single crystals of synthetic forsterite, Fo₁₀₀, were deformed in 69 compressional creep tests in a 0.1-MPa confining atmosphere of H₂ + Ar. Temperature ranged from 1753 to 2023 K and stress σ (= σ₁ - σ₃) from 1.5 to 37.8 MPa. Steady-state creep under these conditions follows an empirical law of the form: strain rate $\text{?}\text{?}\text{= A}{}_{\mathrm{zigma;}}{}^{\mathrm{n}}\text{exp}\text{(}\text{?Q}\text{RT}\text{)}$ where A, n, and Q are constants. General characteristics of Fo₁₀₀ creep — uniformity of strain, shape change as a function of orientation of σ, relative deformation resistance of different orientations — match those of natural olivine single crystals of composition Fo₉₂. Specific constants in the flow law, however, are distinctly new: for σ oriented along [111]_c (equidistant from the three principal crystallographic axes), values for Fo₁₀₀ are n = 2.9 ± 0.2 and Q = 0.67 ± 0.03 MJ/mol (160 ± 7 kcal/mol). A single law covers the range 3 < σ < 30 MPa and 1753 < T < 1953 K. Steady-state deformation is preceded by a transient period of strain softening. High strain rates at σ ? 10 MPa render the transient barely resolvable; it apparently displaces the steady-state flow law by approximately ?0.5% in strain. At σ ? 7.8 MPa, the amount of strain imparted to a sample of the [101]_c orientation is typically <0.1% after one hour.     

Intrinsic absorption and scattering attenuation in the southern part of the Netherlands

We present the first systematic study of attenuation derived from the S-wave coda in the frequency range 1-32 Hz for the southern part of the Netherlands and its surroundings. For this we used two methods, the codaQ (Q _c) method and the Multiple Lapse Time Window (MLTW) method. In the interpretation of the results both single and multiple scattering in a half space are considered. Our aim is to validate these interpretations in our region and to try to identify theeffects of attenuation due to intrinsic absoprtion (Q _i)and scattering attenuation (Q _s). For this we analyzedmore than 100 3-component high-quality digital seismograms from 43 crustalevents and 23 different stations in the Netherlands, Germany and Belgium.Coda Q results show smaller Q _c (=Q ₀fⁿ) values for epicentral distances shorter than 25 km (Q ₀=90) compared to larger epicentral distances (Q ₀=190), but similar frequency dependence (f^-0.9). Interpretation of MLTW results provided a seismic albedo smaller then 0.5, suggesting that the intrinsic absorption dominates over scattering in this region. Both Q _i and Q _s show similar frequency dependences as Q _c. These results are comparable to those obtained in other areas, but we also show that more sophisticated models are required to remove ambiguities in the interpretation. For short lapse times and shortevent-station distances we find for the simple half space model a correspondinginterpretation of both methodologies, where Q _c correspondsto Q _t, suggesting that a model with single scattering in ahalf space is appropriate. For long lapse times and long event station distances, however, we find that the S-wave coda is, most probably, too much influenced by crust-mantel heterogenities and more sophisticated Qinversion models using larger data sets are required for more reliable attenuation estimates.     

Petrogenesis and tectonic implications of Late-Triassic high εNd(t)-εHf(t) granites in the Ailaoshan tectonic zone(SW China)

High εNd(t)-εHf(t) granites are robust evidence for crustal growth. In this paper we report results of petrologic, geochronological and geochemical investigations on the Huashiban granites from the Ailaoshan tectonic zone in western Yunnan(SW China). Zircon grains separated from the two samples(10HH-119 A and 10HH-120A) yield the weighted mean 206Pb/238 U ages of 229.9 ± 2.0 Ma and 229.3 ± 2.3 Ma, respectively, interpreted as the crystallization ages of the granites. Based on our results, in combination with the existing U-Pb geochronological data for the Ailaoshan metamorphic rocks, we propose that the Ailaoshan Group might be a rock complex composed of the Mesoproterozoic, Neoproterozoic, Hercynian, Indosinian and Himalayan components, rather than a part of the crystalline basement of the Yangtze block. The zircon grains show highly depleted Lu-Hf isotope compositions, with positive εHf(t) values ranging from 8.4 to 13.1. The Huashiban granites have high SiO2(72.66 wt%–73.70 wt%), low Mg#(0.28–0.34) with A/CNK=1.01–1.05, and can be classified as peralumious high-K calc-alkaline I-type granites. A synthesis of these data indicates that the Ailaoshan tectonic zone had evolved into a post-collisional setting by the Late-Triassic(229 Ma). Genesis of the Huashiban high εNd(t)-εHf(t) granites involved into two processes:(1) underplating of the sub-arc mantle into the lower crust, and(2) remelting of the juvenile crustal materials in response to the upwelling of the asthenospheric mantle in the post-collisional setting.     

Time-frequency analysis of seismic excitation and estimates of attenuation parameters for the Friuli (Italy) local earthquakes

Stochastic modelling is applied to the analysis of local earthquake recordings, which are usually extremely rich in random incident-wave trains that are chaotically superimposed because of scattering effects in the Earth's crust. The presence in the seismic signal of effects connected with the scale of inhomogeneity in the lithosphere cannot be deterministically described in detail. The application of a stochastic second-order autoregressive model to accelerometric records for the higher magnitude (M_L ? 6) Friuli earthquakes and to short-period seismometric records for the aftershocks of the strong earthquake of 6 May 1976 has allowed inferences to be drawn about the spectral properties of seismic signals and the propagation mechanisms of seismic waves. These inferences are based on an extremely small number of parameters of a mathematical model suitable for simultaneously describing the random sequence of scattered wave trains in the time and frequency domains. Useful physical information has been obtained about the dynamic characteristic correlation times and the predominant frequency of the seismic signals; moreover, the strength, σ²_e(t), of the innovation of the stochastic process fitting the real digital data set has been estimated. From the envelopes of σ²_e(t), the quantity heuristically used in the stochastic approach to describe seismic excitation, the·mean free-path between successive scatterings (l), or the equivalent diffusivity coefficient (d) and turbidity (g), and their dependence on seismic wave frequency have been investigated. For Friuli, using seismometric data at an epicentral distance of ～ 20 km and earthquakes with a magnitude just under 2, mean free-path estimates obtained by means of autoregressive parameters vary from ～ 5 km for the strong interaction model to ～ 30 km for the single scattering model. Furthermore, by means of accelerometric records for the strongest earthquakes in Friuli during May and September 1976, the dependence for the maximum of the seismic excitation on the epicentral distance R was estimated as (σ²_e)_max ～ R^?ν (with ν 1.94 ± 0.13), which is in good agreement with results obtained for the same region using standard methods by means of acceleration peaks versus R. Lastly, stochastic modelling provides a method of estimating change versus time for the predominant frequency and characteristic correlation time of narrow band digital recordings. These two parameters were computed by means of autoregressive parameters in different physical situations and were found to be functions of the earthquake source, the instrumentation frequency response, and the Earth's filtering effects.     

Scattering and intrinsic attenuation in Cairo metropolitan area using genetic algorithm

A total number of 46 local earthquakes (2.0≤ML≤4.0) recorded in the period 2000–2011 by the Egyptian seismographic network (ENSN) were used to estimate the total (Q_t⁻¹), intrinsic (Q_i⁻¹) and scattering attenuation (Q_sc⁻¹) in Cairo metropolitan area, Egypt. The multiple lapse time window analysis (MLTWA) under the assumption of multiple isotropic scattering with uniform distribution of scatters was firstly applied to estimate the pair of L_e⁻¹, the extinction length inverse, and B₀, the seismic albedo, in the frequency range 3–24 Hz. To take into account the effect of a depth-dependent earth model, the obtained values of B₀ and L_e⁻¹ were corrected for an earth structure characterized by a transparent upper mantle and a heterogeneous crust. The estimated values of Q_t⁻¹, Q_sc⁻¹ and Q_i⁻¹ exhibited frequency dependences. The average frequency-dependent relationships of attenuation characteristics estimated for the region are found to be: Q_t⁻¹=(0.015±0.008)f ^{(−1.02±0.02)}, Q_sc⁻¹=(0.006±0.001)f ^{(−1.01±0.02)}, and Q_i⁻¹=(0.009±0.008)f ^{(−1.03±0.02)}; showing a predominance of intrinsic absorption over scattering attenuation. This finding implies that the pore-fluid contents may have great effect on the attenuation mechanism in the upper crust where the River Nile is passing through the study area. The obtained results are comparable with those obtained in other tectonic regions.     

Attenuation in Southeastern Sicily (Italy) by applying different coda methods

The attenuation in Southeastern Sicily has been investigated using 40aftershocks of the December 13 1990, earthquake. The quality factor ofcoda waves (Q_c) was estimated in the frequency range 1.5–24 Hz,applying three different methods in time and frequency domains. On thewhole, a clear dependence of Q_c on frequency was observed,according to the general law Q = Q₀(f/f₀)ⁿ . Thefrequency dependence relationships obtained from the analysis of codawaves at three lapse time windows (10, 20 and 30 seconds) show that, forall methods, Q₀ (Q_c at 1 Hz) significantly increases with lapsetime. In particular, Q₀ is approximately 20 at short lapse time (10s) and increases to about 70 at longer lapse time (30 s). This is attributedto the fact that larger lapse times involve deeper parts of the crust andupper lithosphere which may be characterized by larger quality factors.Moreover, the value of the exponent n decreases with increasing codalengths from about 1.3 to 0.9, suggesting a decrease in heterogeneity ofthe medium with depth.Finally, Q_c-values here found are of the same order as thosereported from other tectonic regions like the Anatolian Highlands orSouthern Spain, while significantly higher than in the neighboring volcanicarea of Mt. Etna.     

Anelastic degradation of acoustic pulses in rock

Measurements on acoustic pulses propagating in massive rock lead to a simple empirical relationship between the pulse rise time, τ and the time of propagation of a pulse, t:

$\text{τ=τ}{}_0\text{+C}\text{∫}\text{)}\text{T}\text{Q}{}^{\mathrm{?1}}\text{d}\text{t}$

where τ₀ is the initial rise time (at t = 0), Q is the anelastic parameter which may be expressed in terms of the fractional loss of energy per cycle of a sinusoidal wave, Q = 2π(ΔE/E)^?1, and is assumed to be essentially independent of frequency, and C is a constant whose value we estimate experimentally to be 0.53 ± 0.04. Of the linear theories of seismic pulse attenuation, model 2 of Azimi et al. (1968) is favoured. Pulse shapes computed from equations of Futterman (1962) also give C = 0.5, but the pulse arrives earlier than in a non-attenuating medium with the same elasticity and density. Pulse shapes calculated using Strick's (1967, 1970, 1971) theory give values of C incompatible with our results. The observations suggest that a method of estimating the Q-structure of the earth from seismic pulse rise times may have a particular advantage over the spectral ratio method.     

Time-dependent electromagnetic core-mantle coupling

The magnetic field in the Earth's mantle is computed using a depth-dependent electrical conductivity, of form σ = σ_a(r/a)^?α, and an approximation scheme in which the electromagnetic time constant of the mantle is assumed small compared with the time scales of the secular variation, and in which the induced currents and fields are obtained iteratively. We first associate the toroidal fields in the mantle with motions at the core surface (r = a) which create the observed geomagnetic field by flux rearrangement, and compute the resulting couple, Γ, parallel to the geographical axis. Using only zonal core motions, and values σ_a = 3 × 10³ω^?1m^?1, α = 30 for the conductivity profile, we find that the toroidal induced fields create a couple, Γ_T, that over most of this century has been roughly ten times greater than the poloidal part, Γ_S, of Γ, and has the same sign. The total couple, Γ, has fluctuations of order 10¹⁸ Nm as required for the observed decade fluctuations in the length of the day. Its average is ～ ?1.5 × 10¹⁸ Nm, i.e., it is too large to remain unbalanced. We suppose that an equally important couple in the opposite sense is created by flux leakage from the core, and we estimate the necessary gradient of toroidal field in the core to be of order ?0.5 Gs km^?1 at the core surface. During the course of the data analysis needed for the present work, we found some evidence for a torsional wave in the Earth's core with a period of ～ 60 y.     

Attenuation of coda waves and Q c value beneath the Chengdu telemetered seismic network

Based on the single scattering model of coda power spectrum analysis, digital waveform data of 50 events recorded by the real-time processing system of the Chengdu telemetry network are analyzed to estimate the Q _c values of earth medium beneath the Chengdu telemetry network for several specified frequencies. It is found that the Q _c shows the frequency dependency in the form of Q _c = Q ₀ f ⁿ in the range of 1.0 to 20.0Hz. Estimated Q ₀ ranges from 60.83 to 178.05, and n is found to be 0.713 to 1.159. The average value of Q ₀ and n are 117 and 0.978 respectively. This result indicates the strong frequency dependency of the attenuation of coda waves beneath the Chengdu telemetry network. Comparing with the results obtained in other regions of the world, it is found that Q ₀ ⁻¹ value and its change with frequency are similar to those in regions with strong tectonic activity. This subject is supported by the Ministry of Personnel, China for partly sponsoring.     

A stability analysis of a conduit flow model for lava dome eruptions

Periodic variations in magma discharge rate and ground deformation have been commonly observed during lava dome eruptions. We performed a stability analysis of a conduit flow model by Barmin et al. [Barmin, A., Melnik, O., Sparks, R.S.J., 2002. Periodic behavior in lava dome eruptions. Earth and Planetary Science Letters 199 (1-2), 173–184], in which the periodic variations in magma flow rate and chamber pressure are reproduced as a result of the temporal and spatial changes of the magma viscosity controlled by the kinetics of crystallization. The model is reduced to a dynamical system where the time derivatives of the magma flow rate (dQ/dt) and the chamber pressure (dP/dt) are functions of Q and P evaluated at a shifted time t − t_?. Here, the time delay t_? represents the time for the viscosity of fluid particle to increase in a conduit. The dynamical system with time delay is approximated by a simple two-dimensional dynamical system of Q and P where t_? is given as a parameter. The results of our linear stability analyses for these dynamical systems indicate that the transition from steady to periodic flow depends on nonlinearities in the steady state relation between Q and P. The steady state relation shows a sigmoidal curve in Q − P phase plane; its slope has negative values at intermediate flow rates. The steady state solutions become unstable, and hence P and Q oscillate periodically, when the negative slope of the steady state relation ([dP/dQ]_S) exceeds a critical value; that is [dP/dQ]_S < − t_?γ/(2V_ch), where V_ch is the chamber volume and γ is an elastic constant which is related to the rigidity of chamber wall. We also found that the period and the pattern of oscillation of the conduit flow primarily depend on a quantity defined by LV_ch/r⁴, where L is the conduit length and r is the conduit radius.     

Attenuation characteristics of coda waves and estimation ofQc values in eastern China

For short-period near-earthquake records in eastern China, from the empirical attenuation formula of coda ground motion amplitudeA with timeτ: lgA=G?2. 235 lgτ, using the single scattering theory modified with epicentral distance, we obtain the curve family of corrected coda amplitudeA _c(r,t), andω/2Q _c values for each time interval of coda. From this,Q _c(f,h) values, which correspond to each observational average frequency and sampling depth, are calculated. The results substantially agree with those observationalQ _c values in Yunnan, Beijing and central Asia.     

Oxysulfates of copper, sodium, and potassium in the lava flows of the 2012–2013 Tolbachik Fissure Eruption

Samples from the surface of lava flows discharged by the 2012–2013 Tolbachik Fissure Eruption were found to contain oxysulfates of copper, sodium, and potassium: K₂Cu₃O(SO₄)₂ (fedotovite), NaKCu₂O(SO₄)₂, and Na₃K₅Cu₈O₄(SO₄)₈. The last two phases have no naturally occurring or synthetic analogues that we are aware of. They form flattened crystals of prismatic to long-prismatic habits. The crystals of Na₃K₅Cu₈O₄(SO₄)₈ have a chemical composition corresponding to the empirical formula Na_2.22K_5.47Cu_8.02S_8.05O₃₆. An X-ray analysis of this compound showed that it has a monoclinic symmetry, P2/c, a = 13.909(4), b = 4.977(1), c = 23.525(6) Å, β = 90.021(5)°, V = 1628.3(7) ų. The crystal structure was determined by direct techniques and refined to yield R ₁ for 3955 reflexes//web// with F ² > 4σF. The compound NaKCu₂O(SO₄)₂ also belongs to the monoclinic system, P2/c, a = 14.111(4), b = 4.946(1), c = 23.673(6) Å, β = 92.052(6)°, V = 1651.1(8) ų. The structure was determined by direct techniques to yield a tentative structural model that has been refined up to R ₁ = 0.135 for 4088 reflexes with F ² > 4σF. The crystal structure of Na₃K₅Cu₈O₄(SO₄)₈ is based on chains of [O₂Cu₄]⁴⁺ consisting of rib-coupled oxy-centered tetrahedrons of (OCu₄)⁶⁺. The chains are surrounded by sulfate radicals, resulting in columns of {[O₂Cu₄](SO₄)₄}^4? aligned along the b axis. The interchain space contains completely ordered positions of Na⁺ and K⁺ cations. The principle underlying the connection of NaKCu₂O(SO₄)₂ columns in the crystal structure of {[O₂Cu₄](SO₄)₄}^4? is different, in view of the relation Na:K = 1 as contrasted with 3:5 for the compound Na₃K₅Cu₈O₄(SO₄)₈. The presence of oxy-centered tetrahedrons in the structure of these new compounds furnishes an indirect hint at the importance of polynuclear copper-oxygen radicals with centering oxygen atoms as forms of transport of copper by volcanic gases.