A FAST ALGORITHM FOR THE COMPUTATION OF RADON TRANSFORMS1

A fast algorithm is presented for numerical evaluation of forward and inverse Radon transforms. The algorithm does not perform exact one-to-one mapping as the discrete Fourier transform but, due to the use of band-limited basis functions, it is robust and sufficiently accurate for seismic applications. By rewriting the transform as a convolution, a computational speed is obtained similar to the speed of the 2D fast Fourier transform.     

Cr-Saturation Arrays in Concentrate Garnet Compositions from Kimberlite and their Use in Mantle Barometry

The spinel–garnet transition in Cr/Al-enriched peridotiticbulk compositions is known from experimental investigationsto occur at 20–70 kbar, within the pressure range sampledby kimberlites. We show that the Cr₂O₃–CaO compositionsof concentrate garnets from kimberlite have maximum Cr/Ca arrayscharacterized by Cr₂O₃/CaO 0·96–0·81, andinterpret the arrays as primary evidence of chromite–garnetcoexistence in Cr-rich harzburgitic or lherzolitic bulk compositionsderived from depth within the lithosphere. Under Cr-saturatedconditions on a known geotherm, each Cr/Ca array implicitlydelineates an isobar inside a garnet Cr₂O₃–CaO diagram.This simplification invites a graphical approach to calibratean empirical Cr/Ca-in-pyrope barometer. Carbonaceous chromite–garnetharzburgite xenoliths from the Roberts Victor kimberlite tightlybracket a graphite–diamond constraint (GDC) located atCr₂O₃ = 0·94CaO + 5·0 (wt %), representing a pivotalcalibration corresponding to 43 kbar on a 38 mW/m² conductivegeotherm. Additional calibration points are established at 14,17·4 and 59·1 kbar by judiciously projecting garnetcompositions from simple-system experiments onto the same geotherm.The garnet Cr/Ca barometer is then simply formulated as follows(in wt %):

if Cr₂O₃ 0·94CaO + 5, then P₃₈ (kbar) = 26·9+ 3·22Cr₂O₃ – 3·03CaO, or

if Cr₂O₃ <0·94CaO + 5, then P₃₈ (kbar) = 9·2+ 36[(Cr₂O₃+ 1·6)/(CaO + 7·02)].

A small correction to P₃₈ values, applicable for 35–48mW/m² conductive geotherms, is derived empirically by requiringconventional thermobarometry results and garnet concentratecompositions to be consistent with the presence of diamondsin the Kyle Lake kimberlite and their absence in the Zero kimberlite.We discuss application of the P₃₈ barometer to estimate (1)real pressures in the special case where chromite–garnetcoexistence is known, (2) minimum pressures in the general casewhere Cr saturation is unknown, and (3) the maximum depth ofdepleted lithospheres, particularly those underlying Archaeancratons. A comparison with the P_Cr barometer of Ryan et al.(1996, Journal of Geophysical Research 101, 5611–5625)shows agreement with P₃₈ at 55 ± 2 kbar, and 6–12%higher P_Cr values at lower P₃₈. Because the P_Cr formulationsystematically overestimates the 43 kbar value of the GDC by2–6 kbar, we conclude that the empirical Cr/Ca-in-garnetbarometer is preferred for all situations where conductive geothermsintersect the graphite–diamond equilibrium. KEY WORDS: Cr-pyrope; chromite; P₃₈ barometer; mantle petrology; lithosphere thickness     

An Archean(?) to Paleozoic Evolution for a Garnet Peridotite Lens with Sub-Baltic Shield Affinity within the Seve Nappe Complex of Jamtland, Sweden, Central Scandinavian Caledonides

Mineralogical, isotopic, geochemical and geochronological evidencedemonstrates that the Friningen body, a garnet peridotite bodycontaining garnet pyroxenite layers in the Seve Nappe Complex(SNC) of Northern Jämtland, Sweden, represents old, certainlyProterozoic and possibly Archean, lithosphere that became incorporatedinto the Caledonian tectonic edifice during crustal subductioninto the mantle at c. 450 Ma. Both garnet peridotite and pyroxenitecontain two (M₁ and M₂) generations of garnet-bearing assemblagesseparated by the formation of two-pyroxene, spinel symplectitearound the M₁ garnet and the crystallization of low-Cr spinel_1Cin the matrix. These textures suggest initial high-pressure(HP) crystallization of garnet peridotite and pyroxenite succeededby decompression into the spinel stability field, followed byrecompression into the garnet peridotite facies. Some pyroxenitelayers appear to be characterized solely by M₂ assemblages withstretched garnet as large as several centimeters. Laser ablationmicroprobe–inductively coupled plasma mass spectrometryRe–Os analyses of single sulfide grains generally definemeaningless model ages suggesting more than one episode of Reand/or Os addition and/or loss to the body. Pentlandite grainsfrom a single polished slab of one garnet peridotite, however,define a linear array on an Re–Os isochron diagram that,if interpreted as an errorchron, suggests an Archean melt extractionevent that left behind the depleted dunite and harzburgite bodiesthat characterize the SNC. Refertilization of this mantle bymelts associated with the development of the pyroxenite layersis indicated by enriched clinopyroxene Sr–Nd isotope ratios,and by parallel large ion lithophile-enriched trace elementpatterns in clinopyroxene from pyroxenite and the immediatelyadjacent peridotite. Clinopyroxene and whole-rock model Sm–Ndages (T_DM = 1·1–2·2 Ga) indicate that fertilizationtook place in Proterozoic times. Sm–Nd garnet₂–clinopyroxene₂–wholerock ± orthopyroxene₂ mineral isochrons from three pyroxenitelayers define overlapping ages of 452·1 ± 7·5and 448 ± 13 Ma and 451 ± 43 Ma (2     

Effect of compacton on chemistry of solutions expelled from montmorillonite clay saturated in sea water

The total mineralization of solutions squeezed out of montmorillonite clay saturated in sea water was determined at different overburden pressures. The subsequent fractions of expelled solutions were also analysed for various anions (Cl^?, SO^2-₄, HCO^?₃, F^?) and cations (Na⁺, K⁺, Mg²⁺, Ca²⁺, B³⁺). The results indicate that the concentrations of squeezed-out solutions during the initial stages of compaction (at pressures up to 35 kg/cm²) are slightly higher than that of interstitial solution present initially. The concentration of squeezed-out solution goes through a maximum, or at least remains constant, before starting to decrease with increasing overburden pressure.     

RESOLUTION ANALYSIS OF BAND-LIMITED AND OFFSET-LIMITED SEISMIC DATA FOR PLANE-LAYERED SUBSURFACE MODELS1

A singular-value decomposition technique is presented for quantifying the information content of band-limited and offset-limited seismic reflection data for the case of plane-layered subsurface models. With the aid of this method, vertical resolution, tuning effects and ambiguities between different types of lithological parameters can be analysed simultaneously. The method is applied in a model study for quantifying the effects of offset-limitation and the presence of different wavetypes on the ability to discriminate different types of parameters.