Frequency dependence of magnetic susceptibility for populations of single-domain grains

A recent paper (Dearing et al . 1996) on the use of frequency dependence of magnetic susceptibility (Xfd) in magnetic grain-size investigations of environmental materic has proposed a fundamentally new model for the magnetic susceptibility of single-domain (SD) grains measured at different frequencies, and is divergent from the no well-established theory of SD behaviour. This new model appears to be founded on a confusion about the behaviour of SD grains, as predicted by theory, and magnetic measurements of real materials, which naturally have a distribution of magnetic grain sizes. Here I try to clear up this confusion by showing how different log-normal distributions of magnetic grain sizes affect the frequency dependence of magnetic susceptibility measurement. This analysis highlights that the limiting maximum Xfd value of ˜ 15 per cent obtained for environmental materials can be explained simply as a constraint imposed by the magnetic grain-size distribution having a finite minimum width (˜1.0 on a natural log scale). There is no reason to suppose that if the grain-size dispersion was narrower higher Xfd values could not be observed. Furthermore, the Xfd value is non-unique and so cannot be used quantitatively to determine the amount or grain-size distribution of SD grains in a sample     

Relationship between median destructive field and remanent coercive forces for dispersed natural magnetite, titanomagnetite and hematite

Summary. Remanent acquisition curves, remanent hysteresis curves and alternating field demagnetization curves were determined for a number of artificial rock specimens containing well-defined grain-size fractions between 5 and 250 μm of natural magnetite, titanomagnetite and hematite. From these curves, the remanent acquisition coercive force H '_cr, the remanent coercive force H _cr and the median destructive field of IRM H _½I were determined. Theoretically these parameters should be the same for an assembly of non-interacting, homogeneously distributed, randomly oriented single-domain grains. For a given hematite specimen H '_cr, H _cr and H _½I have about the same value in spite of the strong grain-size dependence of these parameters. For each specimen of magnetite and titanomagnetite the value of H '_cr is larger than H _cr which again is larger than H _½I. However, the ratios H '_cr/ H _cr and H _½I/ H _cr appear to have a (different) constant value. An interesting relationship which appears to hold for dispersed magnetite, titanomagnetite or hematite grains between 5 and 250 μm, independently of grain-size, quantity and packing density of the magnetic material, is:      

Effects of weathering on single-domain magnetite in Early Pliocene marine marls

Rock magnetic parameters are often used to recognize variations in the original magnetic mineralogy and for normalizing purposes in palaeointensity studies. Incipient weathering, however, is shown to have a profound but partly reversible influence on the rock magnetic properties of the marls of the Early Pliocene Trubi formation in southern Sicily (Italy). The remanence in the marls resides in single-domain (SD) magnetite grains, but the remanent coercive force (H_cr) shows a strong variation and most values observed are anomalously high ( H_cr) range 36–188 mT).
The enhanced coercivities are attributed to stress in the magnetite grains induced by surface oxidation at low temperature. Upon heating to 150 °C a reduction of coercivities occurs that can be explained by a stress reduction as a result of a reduction of Fe^2- gradient due to a higher diffusion rate at elevated temperature. After heating to 150 °C, coercivities are quite uniform throughout the outcrop and the values are characteristic of SD magnetite (H_cr range 30–38 mT). The bulk susceptibility increases by 4–24 per cent, and the isothermal remanent magnetization (IRM) decreases by 5–11 per cent. The increase in anhysteretic remanent magnetization (ARM) is large: 20–242 per cent. The magnitude of the changes is related to the degree of weathering.
Another effect of heating the marl samples to 150 °C is a substantial reduction of the coercivities of the secondary overprint in the natural remanent magnetization. After heating. separation of the secondary and primary components by alternating-field demagnetization is more efficient. The usual difficulties of thermal demagnetization above 300 °C may thus be avoided by a combination of moderate heating to 150 °C and subsequent alternating-field demagnetization.     

Time dependent IRM acquisition as a tool to quantify the abundance of ultrafine superparamagnetic magnetite in loessic soils

The time dependence of Isothermal Remanent Magnetization acquisition (tIRM) is a rapid, sensitive and inexpensive way to quantify the presence of ultrafine ferrimagnetic grains straddling the superparamagnetic–single domain grain size boundary, well suited for use in small rock magnetic laboratories. The technique is very selective to the presence of grains with a diameter of approximately 25 nm, and tIRM results correlate well with measurements of frequency dependent susceptibility without the need of correcting for the presence of paramagnetic minerals. A simple IRM acquisition model can be used to obtain quantitative abundance estimates for these ultrafine magnetic grains. Application of tIRM measurements to eleven soil profiles from the Midwestern United States shows that the abundance of ultrafine particles increases with precipitation, as long as the mean annual precipitation is below 850 mm a⁻¹. Sites that developed under more humid conditions show a decrease in tIRM and likely SP abundance, probably caused by increased iron reduction and translocation during more common periods of reducing conditions.     

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.     

Three-dimensional Rayleigh hysteresis of oriented core samples from the German Continental Deep Drilling Program: susceptibility tensor, Rayleigh tensor, three-dimensional Rayleigh law

Rayleigh hysteresis, as defined by the well-known Rayleigh relations, has been observed not only when magnetization of pyrrhotite-bearing KTB-samples is measured in parallel to a weak dc magnetic field, but also in experiments where field and measuring directions have been adjusted strictly perpendicularly to each other. Nine-tupels of independent Rayleigh hysteresis loops could thus be compiled. Their characteristic coefficients X ^ijk of initial susceptibility together with the Rayleigh loss coefficients α^jk have been proved to determine completely the samples' weak-field magnetic anisotropy. Interpreting the coefficient matrices ( X ^ijk) and (α^jk) as the tensor of initial susceptibility and the Rayleigh tensor, respectively, generalization of the isotropic Rayleigh relations in terms of corresponding tensor relationships has been suggested for the anisotropic case. Application to the KTB samples showed 3-D Rayleigh hysteresis measurements to be an excellent tool for rock magnetic analysis in terms of ore content and crystalline texture. In particular, a magnetocrystalline double texture of the basal planes of pyrrhotite precipitates and their [1120] directions of easy magnetization have been clearly detected. Surprisingly, the welt-known theorem α= const. X ²_I, formulated by Néel (1942) for the isotropic case, has been found to hold true even in tensor generalization (α_jk) = const ( X ²_jk). To reach sufficient resolution for the measurements performed, a sensitive vibrating coil magnetometer (VCM) has been developed.     

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

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

Seismic image of a CO2 reservoir beneath a seismically active volcano

Mammoth Mountain is a seismically active volcano 200 000 to 50 000 years old, situated on the southwestern rim of Long Valley caldera, California. Since 1989 it has shown evidence of unrest in the form of earthquake swarms (Hill et al. 1990), volcanic 'long-period' earthquakes (Pitt & Hill 1994), increased output of magmatic ³He (Sorey et al. 1993) and the emission of about 500 tonnes day ⁻¹ of CO₂ (Farrar et al. 1995; Hill 1996; M. Sorey, personal communication, 1997), which has killed trees and poses a threat to human safety. Local-earthquake tomography shows that in mid-1989 areas of subsequent tree-kill were underlain by extensive regions where the ratio of the compressional and shear elastic-wave speeds V_P/V_S was about 9 per cent lower than in the surrounding rocks. Theory (Mavko & Mukerji 1995), experiment (Ito, DeVilbiss & Nur 1979), and experience at other geothermal/volcanic areas (Julian et al. 1996) and at petroleum reservoirs (Harris et al. 1996) indicate that V_P/V_S is sensitive to pore-fluid compressibility, through its effect on V_P . The observed V_P/V_S anomaly is probably caused directly by CO₂, and seismic V_P/V_S tomography is thus a promising tool for monitoring gas concentration and movement in volcanoes, which may in turn be related to volcanic activity.     

Magnetic properties of metal-substituted haematite

Mineral and isothermal magnetic properties of Al-, Mn- and Ni-substituted haematites were characterized and their relationships evaluated in order to interpret better the results of magnetic analyses of soils and recent sediments. Aluminium, manganese and nickel haematites generally behaved as single-domain (SD) particles. The influence of incorporated Al on the magnetic behaviour of haematite was consistent with Al acting as a paramagnetic dilutent. Mass magnetic susceptibility ( χ ) and SIRM₈₀₀ decreased as the level of Al substitution increased. Incorporation of Mn and Ni increased χ , which could be associated with enhancement of the spin canting effect of haematite. The stability of SIRM₈₀₀ to demagnetization for Al-haematite appears to be related to a defect mechanism associated with the development of smaller crystallites arising from Al substitution. Magnetic domain rotation or flipping was probably inhibited, being blocked by structural defects during magnetization and demagnetization, and resulted in a low but stable partial SIRM (SIRM₈₀₀ ). %IRM/SIRM₈₀₀ demagnetization curves and estimated ( B _o )_CR values of ≤100  mT for Mn-haematite indicate pseudo-single-domain/multidomain-like behaviour despite Mn-haematite having particle and crystallite dimensions similar to Ni-haematite, which did not show this behaviour. Data indicate that parameters involving unsaturated, partial SIRM should be used with caution in magnetic studies of soils and sediments.     

Palaeoclimatic record from a loess–soil profile in northeastern Bulgaria—I. Rock magnetic properties

A detailed record of mineral magnetic properties of a loess–palaeosol profile comprising seven loess horizons, six interbedded palaeosols and recent soil at the top in NE Bulgaria is analysed. A strong contrast between the soil and loess susceptibilities as well as other concentration-dependent hysteresis parameters is present, similar to the well-documented magnetic characteristics of the Chinese loess ( Hus & Han 1992 ; Maher & Thompson 1992 ; Heller & Evans 1995 ; Hunt et al. 1995 ). The magnetic enhancement of the palaeosol units is caused by very fine-grained pedogenic magnetite with superparamagnetic behaviour. Thermomagnetic analyses on bulk material suggest magnetite and maghemite as the main ferrimagnetic carriers in both soil and loess horizons. Their relative proportions are shown to reflect different palaeoclimatic conditions. Chernozem soils, which include recent soil S₀ and first and second palaeosols S₁ and S₂ developed under steppe vegetation, show a high degree of low-temperature oxidation of the pedogenic magnetite to maghemite. This material is characterized by coercive force H _c showing even higher values than those of the parent loess material. The older palaeosols (S₄ to S₆ ) were formed during more humid climatic conditions and therefore probably developed as forest types. Rock magnetic data suggest the existence here of only partly oxidized magnetite grains. The behaviour of the thermomagnetic curves, characterized by a kink at 200 °C, may be due to either a release of internal stress (built up as a result of partial low-temperature oxidation) or interactions between two phases.     

A New Magnitude-Frequency Relation for Earthquakes and a Classification of Relation Types

Summary. In this paper some aspects of the deviations of frequency distributions of earthquakes from a linear trend are considered. For recurrence curves with inflexions, the formula
is proposed as a magnitude-frequency relation, with critical magnitude M _cr. Comparison with actual data shows better agreement than other formulae. The slope of the frequency graph is considered in the most general case to be a function of M and some parameters p ₁, p ₂, …. A classification of the types of magnitude-frequency relation is given and all known types of relations N : M and N: K ( K = log E , E = seismic energy) are summarized.     

EPR evidence for maghemitization of magnetite in a tropical soil

Electron paramagnetic spectroscopy (EPR) was used in combination with standard rock magnetic methods to study magnetic minerals in a tropical soil. The susceptibility and hysteresis measurements showed magnetite grains with a Curie temperature near 850 K as the dominant magnetic remanence carriers in the soil. A minor Ti content in the magnetite was found by energy dispersive X-ray analysis. In order to get insight into the weathering status of the magnetite, different chemical treatments, including oxalate and citrate–bicarbonate–dithionite (CBD) extraction, were applied to the soil samples. The hysteretic properties exhibited no significant differences between the untreated and the CBD or oxalate treated samples. By contrast, the comparison of the EPR spectra revealed a significant broadening of the linewidth (δB) and a shift of the g -values ( g _eff) to lower fields after the CBD treatment. Furthermore, the spectral parameters g _eff and δB exhibited an angular dependence. At low temperature, the CBD treated samples showed a jump in δB between 120 and 100 K, the temperature range characteristic for the Verwey transition in magnetite. The changes in the spectral properties after the CBD treatment, which dissolves ferric oxides, were attributed to the removal of maghemite formed by the oxidation of magnetite, that is, during the maghemitization of the magnetite grains.     

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.     

Annual and daily variation in the occurrence of positive Dst index

Summary. The frequency of occurrence of the positive D_st for each UT hour has been computed using data for the years 1957–77. For all hours the seasonal variation shows a peak in June. The annual variation conforms with the Malin-Isikara mechanism. While the annual component of D_st+ exhibits a significant UT dependence which cannot be explained by the McIntosh effect, the semi-annual component has a relatively smaller significant time dependence. The diurnal component of D_st+ has a pronounced annual variation with a June maximum. The results presented here are compared and discussed in the light of an earlier analysis of D_st by Mayaud.     

Palaeoclimatic implications of the magnetic record from loess/palaeosol sequence Viatovo (NE Bulgaria)

Loess-palaeosol deposits in the lower Danube area represent the southeastern edge of the loess cover in Europe. Detailed rock magnetic investigations of the loess/palaeosol sequence in Viatovo in NE Bulgaria reveal that magnetite and maghemite of very fine superparamagnetic grain size are responsible for the magnetic enhancement of palaeosol units. A detailed palaeoclimatic record is obtained through high-resolution measurements of magnetic susceptibility, frequency dependent magnetic susceptibility and CaCO₃ content. Magnetic proxies indicate a more warm and humid climate during the development of the older palaeosol units (S₄–S₆).     

A comparative study of the ARM and Isr of some natural magnetites of MD and PSD grain size

Summary. ARM and I _sr stability with respect to alternating field and low-temperature treatment were measured for a set of artificial rock specimens. Each of the specimens contained a known amount of a natural magnetic mineral of a known grain size. The following minerals were used: a homogeneous natural magnetite, a natural titanomagnetite with submicroscopic Fe-rich inclusions, and a natural titanomagnetite and a natural titano-maghemite that both show exsolution phenomena. The grain size of the fractions varied from < 5 to 250 μm. It is found that the stability of ARM and I _rs of multi-domain grains with respect to alternating fields and low-temperature treatment is similar, whereas for the smallest grains studied (< 5 μm) ARM is more stable than I _sr. Multi-domain ARM data from this study are in agreement with current multi-domain ARM theory. Low-temperature behaviour of ARM and I _sr can be explained either in terms of a model in which stable moments in the bulk of the grains are screened by the surrounding matrix or in terms of a model in which regeneration of the bulk remanence plays a role and in which stable moments are situated on the surfaces of the grains.     

Transient and impulse responses of a one-dimensional linearly attenuating medium—II. A parametric study

Summary. We investigate one-dimensional waves in a standard linear solid for geophysically relevant ranges of the parameters. The critical parameters are shown to be T*= t_u/Q_m where t _u is the travel time and Q_m the quality factor in the absorption band, and τ⁻¹ _m , the high-frequency cut-off of the relaxation spectrum. The visual onset time, rise time, peak time, and peak amplitude are studied as functions of T* and τ _m. For very small τ _m , this model is shown to be very similar to previously proposed attenuation models. As τ _m grows past a critical value which depends on T* , the character of the attenuated pulse changes. Seismological implications of this model may be inferred by comparing body wave travel times with a'one second'earth model derived from long-period observations and corrected for attenuation effects assuming a frequency independent Q over the seismic band. From such a comparison we speculate that there may be a gap in the relaxation spectrum of the Earth's mantle for relaxation times shorter than about one second. However, observational constraints from the attenuation of body waves suggest that such a gap might in fact occur at higher frequencies. Such a hypothesis would imply a frequency dependence of Q in the Earth's mantle for short-period body waves.     

Seismic anisotropy within the uppermost mantle of southern Germany

This paper presents an updated interpretation of seismic anisotropy within the uppermost mantle of southern Germany. The dense network of reversed and crossing refraction profiles in this area made it possible to observe almost 900 traveltimes of the P_n phase that could be effectively used in a time-term analysis to determine horizontal velocity distribution immediately below the Moho. For 12 crossing profiles, amplitude ratios of the P_n phase compared to the dominant crustal phase were utilized to resolve azimuthally dependent velocity gradients with depth. A P -wave anisotropy of 3–4 per cent in a horizontal plane immediately below the Moho at a depth of 30 km, increasing to 11 per cent at a depth of 40 km, was determined. For the axis of the highest velocity of about 8.03 km s⁻¹ at a depth of 30 km a direction of N31°F was obtained. The azimuthal dependence of the observed P_n amplitude is explained by an azimuth-dependent sub-Moho velocity gradient decreasing from 0.06 s⁻¹ in the fast direction to 0 s⁻¹ in the slow direction of horizontal P -wave velocity. From the seismic results in this study a petrological model suggesting a change of modal composition and percentage of oriented olivine with depth was derived.     

Observation of Tidal Tilt On Kilauea Volcano, Hawaii

Summary. We have analysed the east-west tilt components, O₁, K₁, N₂, M₂ and S₂ from a continuously recording tiltmeter located in Uwekahuna Vault on Kilauea Volcano, Hawaii, for the period 1971—79. Detailed analysis of the M₂ component gives values of 30.9 ± 2.0 (95 per cent) nrad and 116.0 ± 2.0° for the amplitude and phase, respectively, compared to values of 48.5 nrad and 139.4° for the equilibrium tide. the total theoretical tide, found by summing the equilibrium and load tides, amounts to 37.2 nrad at a phase of 121.7°. the 20 per cent discrepancy with that observed may be due to an inaccurate cotical chart, cavity effects in the vault, strain—tilt coupling or an inappropriate solid earth model. In the vicinity of Hawaii (≤ 3°) two independent cotidal charts give almost identical results for the near field ocean load. At greater distances, we use the Schwiderski (1978) cotidal chart. We estimate that local cavity and strain—tilt coupling effects are less than 12 per cent owing to the agreement between geodetically determined and instrumental tilt but we can not rule out regional effects. Assuming these are small and the cotical charts correct, we find that the M₂ results are brought into satisfactory agreement if, instead of using an average oceanic earth model in the (< 75 km) vicinity of Hawaii, we use an earth model with nearly one-half the oceanic rigidity. Such a low upper mantle and crustal rigidity is consistent with Kilauea's position above the thermal upwelling associated with the Hawaiian hotspot.     

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

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