Crossover Distances Research Articles

The sensitivity of seismic refraction velocity models to survey geometry errors, assessed using Monte Carlo analysis

Seismic refraction models should routinely be reported with their associated uncertainty. Tomographic solutions are widespread, but estimating uncertainties in these via Monte Carlo simulation places great demands on computer resource, hence this task is often omitted. By considering the Plus-Minus method of seismic refraction interpretation, we use Monte Carlo simulations to evaluate the uncertainty in seismic refraction results and determine the sources of uncertainty that are most impactful on the reliability of the output model. Our analysis considers the impact of survey mislocation (i.e., geophones misplaced from a planned position) and interpretational problems (i.e., misidentification of first-break picks and uncertainty in identifying crossover distances) on the overall uncertainty in inferred unit thicknesses and seismic velocities. These are considered for synthetic data with varying subsurface velocity structure, and for field data collected at a shallow (< 50 m) bedrock site in north Wales (UK). Analysis of synthetic data shows that the impact of the aforementioned errors on thickness estimates is ∼1000 times that on velocity estimates. Of all permutations tested, the most significant impact on thickness uncertainty was the accuracy of first-break picks, with the variance in target thickness estimates increasing roughly exponentially with first-break pick uncertainty. It is therefore prudent to minimise such uncertainty through appropriate survey practice (e.g., maximising source energy, taking multiple shots for stacking) and to properly define the resultant uncertainty in unit thickness and velocity estimates. The simplicity of the Plus-Minus method makes it an effective tool for highlighting the errors that would impact more sophisticated interpretation approaches, such as tomography or Full Waveform Inversion. The results from such analysis can be directly applied in straightforward environmental or engineering investigations and can be used to inform more advanced refraction methods. As such, the practice we highlight should be considered for any refraction interpretation.

When to Crossover From Earth to Space for Lower Latency Data Communications?

For data communications over long distances, optical wireless satellite networks (OWSNs) can offer lower latency than optical fiber terrestrial networks (OFTNs). However, when is it beneficial to switch or crossover from an OFTN to an OWSN for lower latency data communications? In this article, we introduce a crossover function that enables to find the crossover distance, i.e., a distance between two points on the surface of the Earth beyond which switching or crossing over from an OFTN to an OWSN for data communications between these points is useful in terms of latency. Numerical results reveal that a higher refractive index of optical fiber (or $i$) in an OFTN and a lower altitude of satellites (or $h$) in an OWSN result in a shorter crossover distance. To account for the variation in the end-to-end propagation distance that occurs over the OWSN, we examine the crossover function in four different scenarios. Numerical results indicate that the crossover distance varies with the end-to-end propagation distance over an OWSN and is different for different scenarios. We calculate the average crossover distance over all scenarios for different $h$ and $i$ and use it to evaluate the simulation results. Furthermore, for a comparative analysis of OFTNs and OWSNs in terms of latency, we study three different OFTNs having different refractive indexes and three different OWSNs having different satellite altitudes in three different scenarios for long-distance intercontinental data communications, including connections between New York and Dublin, Sao Paulo and London, and Toronto and Sydney. All three OWSNs offer better latency than OFTN2 (with $i_{2}$ = 1.3) and OFTN3 (with $i_{3}$ = 1.4675) in all scenarios. For example, for Toronto–Sydney connection, OWSN1 (with $h_{1}$ = 300 km), OWSN2 (with $h_{2}$ = 550 km), and OWSN3 (with $h_{3}$ = 1100 km) perform better than OFTN2 by 18.11%, 16.08%, and 10.30%, respectively, while they provide an improvement in latency of 27.46%, 25.67%, and 20.54%, respectively, compared to OFTN3. OWSN1 performs better than OFTN1 (with $i_{1}$ = 1.1) for Sao Paulo–London and Toronto–Sydney connections by 2.23% and 3.22%, respectively, while OWSN2 outperforms OFTN1 for Toronto–Sydney connection by 0.82%. For New York–Dublin connection, all OWSNs while for Sao Paulo–London connection, OWSN2 and OWSN3 exhibit higher latency than OFTN1 as the corresponding average crossover distances are greater than the shortest terrestrial distances between cities in these scenarios. Multiple satellites (or laser intersatellite links) on its shortest paths drive up the propagation distance to the extent that OWSN3 ends up with a higher latency than OFTN1 for the Toronto–Sydney intercontinental connection scenario although the related average crossover distance is less than the shortest terrestrial distance between Toronto and Sydney. The challenges related to OWSNs and OFTNs that may arise from this work in future are also highlighted.

Path Attenuation and Source Characteristics during the 2019 Sichuan Changning Earthquake Sequence in China

To give an insight into the path attenuation and source characteristics of the 2019 Sichuan Changning earthquake sequence, 99 strong‐motion recordings at 33 stations were studied. The S‐wave Fourier amplitude spectra were used to determine the path‐attenuation function and key parameters of the seismic source characteristics of this sequence. The results show the following: (1) The geometric spreading effect presents hinged‐trilinear characteristics, and the corresponding geometric spreading rates were −0.97, 0.29, and −0.73 with the crossover distances 90 km and 183 km. (2) The quality factor Q is correlated with frequency and expressed as 217 × f0.82 for the range from 0.1 to 10.0 Hz. (3) The seismic moment was inversely proportional to the cube of the corner frequency, and their product was 2.37 × 1016 N. m/s3. (4) The stress drop varied from 1.18 to 12.44 MPa. Both the attenuation effect and source parameters of this sequence are significantly different from those of the Lushan and the Wenchuan aftershock sequences in the Sichuan region of China.

ASY1 acts as a dosage-dependent antagonist of telomere-led recombination and mediates crossover interference in Arabidopsis

During meiosis, interhomolog recombination produces crossovers and noncrossovers to create genetic diversity. Meiotic recombination frequency varies at multiple scales, with high subtelomeric recombination and suppressed centromeric recombination typical in many eukaryotes. During recombination, sister chromatids are tethered as loops to a polymerized chromosome axis, which, in plants, includes the ASY1 HORMA domain protein and REC8-cohesin complexes. Using chromatin immunoprecipitation, we show an ascending telomere-to-centromere gradient of ASY1 enrichment, which correlates strongly with REC8-cohesin ChIP-seq data. We mapped crossovers genome-wide in the absence of ASY1 and observe that telomere-led recombination becomes dominant. Surprisingly, asy1/+ heterozygotes also remodel crossovers toward subtelomeric regions at the expense of the pericentromeres. Telomeric recombination increases in asy1/+ occur in distal regions where ASY1 and REC8 ChIP enrichment are lowest in wild type. In wild type, the majority of crossovers show interference, meaning that they are more widely spaced along the chromosomes than expected by chance. To measure interference, we analyzed double crossover distances, MLH1 foci, and fluorescent pollen tetrads. Interestingly, while crossover interference is normal in asy1/+, it is undetectable in asy1 mutants, indicating that ASY1 is required to mediate crossover interference. Together, this is consistent with ASY1 antagonizing telomere-led recombination and promoting spaced crossover formation along the chromosomes via interference. These findings provide insight into the role of the meiotic axis in patterning recombination frequency within plant genomes.

Functionalized Mesoporous Silicas Direct Structural Polymorphism of Amyloid-β Fibrils.

The aggregation of amyloid-β (Aβ) is associated with the onset of Alzheimer's disease (AD) and involves a complex kinetic pathway as monomers self-assemble into fibrils. A central feature of amyloid fibrils is the existence of multiple structural polymorphs, which complicates the development of disease-relevant structure-function relationships. Developing these relationships requires new methods to control fibril structure. In this work, we evaluated the effect that mesoporous silicas (SBA-15) functionalized with hydrophobic (SBA-PFDTS) and hydrophilic groups (SBA-PEG) have on the aggregation kinetics and resulting structure of Aβ1-40 fibrils. The hydrophilic SBA-PEG had little effect on amyloid kinetics, while as-synthesized and hydrophobic SBA-PFDTS accelerated aggregation kinetics. Subsequently, we quantified the relative population of fibril structures formed in the presence of each material using electron microscopy. Fibrils formed from Aβ1-40 exposed to SBA-PEG were structurally similar to control fibrils. In contrast, Aβ1-40 incubated with SBA-15 or SBA-PFDTS formed fibrils with shorter crossover distances that were more structurally representative of fibrils found in AD patient derived samples. Overall, our results suggest that mesoporous silicas and other exogenous materials are promising scaffolds for the de novo production of specific fibril polymorphs of Aβ1-40 and other amyloidogenic proteins.

The effect of depletion layer on diffusion of nanoparticles in solutions of flexible and polydisperse polymers

We introduce a model of diffusion of nanoparticles in solutions of flexible, polydisperse polymers. The model takes into account the effect of depletion layer with soft boundaries. The presence of depletion layer leads to nonlinear dependence of the mean square displacement (MSD) on time. Our model may be an alternative choice for the study of those experimental systems where the crossover between subdiffusion and normal diffusion is observed. Its advantage is mathematical simplicity: it allows easy identification of the crossover times and distances, which are here associated with the depletion layer thickness. The soft boundaries of the depletion layer, generated by the flexible and polydisperse polymers, are here approximated by two shells enclosed one in another, which may be interpreted as approximations of polymer density profiles around the probe. We show a very good agreement of the model with dynamic light scattering (DLS) measurements of diffusion of nanoparticles in solutions of polyethylene glycol (PEG).

Pair correlation function of soft-sphere fluids

A closed-form analytic formula for the radial distribution function (RDF) or g(r) of inverse power fluids is proposed. The RDF is expressed as a sum of separate component functions, one monotonic and a series of exponentially damped oscillatory functions. Unlike previous treatments in the literature, this formula does not rely on patching different functional forms at arbitrary crossover distances. This expression, which we refer to as g(M)(r), yields the expected asymptotic behavior at large distance and reproduces the main features of the RDF generated by molecular dynamics (MD) simulations. The g(M) is applied to the soft n = 4 inverse power fluid, and it is shown that in this case seven or fewer terms are sufficient to represent accurately the MD-generated RDF over the entire fluid domain. The relative contributions of the separate terms of the g(M) as a function of density are analyzed and discussed. The key role played by the monotonic component function and two oscillatory terms is demonstrated. The origin of the crossover from the oscillatory to the monotonic behavior is shown to be the same as that recently proposed by Evans and Henderson [R. Evans and J. R. Henderson, J. Phys.: Condens. Matter 21, 474220 (2009)] for the dispersion interactions.

Surface Electromagnetic Field Radiated by a Subwavelength Hole in a Metal Film

We present an analytical expression for the electromagnetic field at the surface radiated by a hole in a metal film. This expression is valid for any metal, from the optical range to longer wavelengths, and for distances to the hole larger than a few tens of nanometers. The field pattern presents a rich behavior, showing three regions (a complex short distance, an intermediate range dominated by surface plasmon polaritons, and a long-distance one dominated by Norton waves). The crossover distances between these regimes depend strongly on both the wavelength and the angle with respect to the incident field.

Nanoscale Flexibility Parameters of Alzheimer Amyloid Fibrils Determined by Electron Cryo‐Microscopy

Nanoscale Flexibility Parameters of Alzheimer Amyloid Fibrils Determined by Electron Cryo‐Microscopy

Effect of Different Salt Ions on the Propensity of Aggregation and on the Structure of Alzheimer’s Aβ(1-40) Amyloid Fibrils

The formation of amyloid fibrils and other polypeptide aggregates depends strongly on the physico-chemical environment. One such factor affecting aggregation is the presence and concentration of salt ions. We have examined the effects of salt ions on the aggregation propensity of Alzheimer’s Aβ(1-40) peptide and on the structure of the dissolved and of the fibrillar peptide. All salts examined promote aggregation strongly. The most pronounced effect is seen within the cationic series, i.e. for MgCl2. Evaluation of different possible explanations suggests that Aβ(1-40) aggregation depends on direct interaction between ions and Aβ(1-40) peptide, and correlates with ion-induced changes of the surface tension. Salts have profound effects on the fibril structure. In the presence of salts, fibrils are associated with smaller diameters, narrower crossover distances and lower amide I maxima. Since Aβ(1-40) aggregation responds to salts in a manner unlike that for other polypeptides, such as glucagon, β2-microglobulin or α-synuclein; these data argue that there is no fully uniform way in which salts affect aggregation of different polypeptide chains. These observations are important for understanding and predicting aggregation on the basis of simple physico-chemical properties.

The northern Walker Lane refraction experiment: Pn arrivals and the northern Sierra Nevada root

In May 2002, we collected a new crustal refraction profile from Battle Mountain, Nevada across western Nevada, the Reno area, Lake Tahoe, and the northern Sierra Nevada Mountains to Auburn, CA. Mine blasts and earthquakes were recorded by 199 Texan instruments extending across this more than 450-km-long transect. The use of large mine blasts and the ultra-portable Texan recorders kept the field costs of this profile to less than US$10,000. The seismic sources at the eastern end were mining blasts at Barrick's GoldStrike mine. The GoldStrike mine produced several ripple-fired blasts using 8000–44,000 kg of ANFO each, a daily occurrence. First arrivals from the larger GoldStrike blasts are obvious to distances of 300 km in the raw records. First arrivals from a quarry blast west of the survey near Watsonville, CA, located by the Northern California Seismic Network with a magnitude of 2.2, can be picked across the recording array to distances of 600 km. The Watsonville blast provides a western source, nearly reversing the GoldStrike blasts. A small earthquake near Bridgeport, CA. also produced pickable P-wave arrivals across the transect, providing fan-shot data. Arrivals from M5 events in the Mariana and Kuril Islands also appear in the records. This refraction survey observes an unexpectedly deep crustal root under the northern Sierra Nevada range, over 50 km in thickness and possibly centered west of the topographic crest. Pn delays of 4–6 s support this interpretation. At Battle Mountain, Nevada, we observe anomalously thin crust over a limited region perhaps only 150 km wide, with a Moho depth of 19–23 km. Pn crossover distances of less than 80 km support this anomaly, which is surrounded by observations of more normal, 30-km-thick crust. A 10-km-thick and high-velocity lower-crustal “pillow” is an alternative hypothesis, but unlikely due to the lack of volcanics west of Battle Mountain. Large mine and quarry blasts prove very effective crustal refraction sources when recorded with a dense receiver array, even over distances exceeding 600 km. New elastic synthetic seismogram modeling suggests that Pn can be strong as a first arrival, easing the modeling and interpretation of crustal refraction data. Fast eikonal computations of first-arrival time can match pickable Pn arrival times.

Optimizing pinhole and parallel hole collimation for scintimammography with compact pixellated detectors

The relative resolution and sensitivity advantages of pinhole and parallel hole collimators for planar scintimammography with compact, pixellated gamma detectors were investigated using analytic models. Collimator design was studied as follows. A desired object resolution was specified for a pixellated detector with a given crystal size and intrinsic spatial resolution and for a given object-to-collimator distance. Using analytic formulas, pinhole and parallel hole collimator parameters were calculated that satisfy this object resolution with optimal geometric sensitivity. Analyses were performed for 15 cm /spl times/ 20 cm field of view detectors with crystal elements 1.0, 2.0, and 3.0 mm on a side and 140 keV incident photons. The sensitivity for a given object resolution was greater for pinhole collimation at smaller distances, as expected. The object distance at which the pinhole and parallel hole sensitivity curves cross each other is important. The crossover distances increased with larger crystal size for a constant object resolution and increased as the desired object resolution decreased for a constant crystal size. For example, for 4 mm object resolution and a pinhole collimator with focal length 13 cm, these distances were 5.5 cm, 6.5 cm, and 8 cm for the 1 mm, 2 mm, and 3 mm crystal detectors, respectively. The results suggest a strategy of parallel hole collimation for whole breast imaging and pinhole collimation for imaging focal uptake. This could be accomplished with a dual detector system with a different collimator type on each head or a single head system equipped with two collimators and a rapid switching mechanism.

Self-affine random surfaces

We consider general d-dimensional random surfaces that are characterized by power-law power spectra defined in both infinite and finite spectral regions. The first type of surfaces belongs to the class of ideal fractals, whereas the second possess both the smallest and the largest scales and physically is more realistic. For both types we calculate the structure functions (SF) exactly; in addition for the second type we obtain the SF's asymptotic expansions. On this basis we show that the surfaces are (in statistical sense) self-affine and approximately self-affine, respectively. Depending on the value of the spectral exponent, we find imbalance between the finite size effects which results in systematic discrepancy in the scaling properties between the two types of surfaces. Explicit expressions for the topothesy, and in the case of second type of surfaces for the large correlation length and cross-over distances are also derived.

Interactions and structure of the nuclear pore complex revealed by cryo-electron microscopy.

Nuclear pore complexes (NPCs) play a central role in mediating nucleocytoplasmic transport and exchange processes in eukaryotic cells. The arrangement and interactions of NPCs within amphibian nuclear envelopes have been studied using cryo-electron microscopy of unfixed and frozen hydrated specimens. The nuclear lamina in Necturus forms an orthogonal network with crossover distances which vary between 1,600 and 4,000 A and which may be related to the basic filament repeat of lamins. Furthermore, the NPCs are attached randomly within the confines of the lamin network, presumably by their nucleoplasmic rings. Image analysis of edge-on and en face projections of detergent-extracted NPCs has been combined with data on the coaxial thin rings to provide a quantitative evaluation of the triple ring model of NPC architecture proposed previously (Unwin, P. N. T., and R. Milligan. 1982. J. Cell Biol. 93:63-75). Additional details of the complex have been visualized including an intimate association of the inner spoke domains as an inner spoke ring, extensive domains within the spokes and coaxial thin rings, and interestingly, a central channel-like feature. Membrane-associated NPCs and detergent-extracted NPCs both possess peripherally located radial arms resulting in an effective diameter of approximately 1,450-1,500 A. In projection, the radial arms possess approximate mirror symmetry suggesting that they originate from both sides of the assembly. Moreover, membrane-associated NPCs are asymmetric at most radii and right-handed as viewed from the cytoplasm; detergent-extracted NPCs appear to be symmetric and have approximately 822 symmetry. Taken together, the data suggests that the framework of membrane-associated NPCs is perturbed from a symmetrical configuration, either during isolation of nuclei or by interactions with the lamina and the nuclear envelope in vivo. However, detergent extraction of nuclei appears to result in a more symmetrical alignment of components in apposing halves of the assembly.

Flexural isostasy and uplift of the Sierra Nevada of California

The Sierra Nevada of California has experienced several kilometers of uplift in the last 10 m.y., but its present elevation is isostatically compensated by a crustal root that has probably existed since Late Cretaceous. Flexural isostasy can reconcile these observations: Basin and Range faulting and extension starting 10 m.y. ago allowed rapid uplift of an eroded and regionally compensated magmatic arc underlain by an excess crustal root. A quantitative model of an unbroken elastic plate buoyed up by the excess root provides an explanation for the estimated 10‐m.y. paleotopography of the range. The same model fits the present topography when broken (shear and fiber stresses not transmitted) at the location of the Owens Valley fault zone. The broken‐plate model predicts the appropriate amount of westward tilt of the Sierra Nevada and can explain the pronounced eastward tilt of the White and Inyo mountains. The position where paleo and present drainages in the Sierra cross over in elevation is the most sensitive indicator of the elastic thickness required of the lithosphere. An effective elastic thickness of 50 km best fits the observed crossover distances and is consistent with the amount of post‐10 m.y. uplift. Calculated fiber and shear stresses suggest that actual extension of the crust is more important in permitting the uplift than the mere presence of normal faults. Part of the residual isostatic gravity anomaly pattern (high gravity over the eastern Great Valley and western Sierra Nevada, low residual gravity over the high Sierra) may be explained by the continuing flexural support of departure from local isostatic equilibrium. The model implies that before 10 m.y. ago the Sierra should have been marked by a negative isostatic gravity anomaly of more than −100 m Gal, flanked by isostatic gravity highs. Such large isostatic anomalies have not been observed to date over eroded arcs, but the Sierra has uniquely low heat flow and, presumably therefore, high lithospheric strength, and the Sierran root is at the upper limit of size that could be isostatically suppressed.

Inheritance and activity of some esterases associated with organophosphate resistance in mosquitoes of the complex ofCulex pipiensL. (Diptera: Cnlicidae)

AbstractEighteen strains of the complex ofCulex pipiensL. from Africa, Asia and Europe were bioassayed for resistance to chlorpyrifos and electro-phoresed and stained for esterases. Susceptible strains showed only low activity esterase bands. The resistant strains ofC. quinquefasciatusSay from hot countries (Liberia, Nigeria, Sri Lanka, Tanzania, Thailand) all showed the same two high intensity esterase bands (Rm 0·60 + 0·82). Different patterns of high esterase were found in resistantC. pipiensstrains from cooler localities in Nairobi, Kenya (Rm 100), and Mont-pellier, France (Rm 0–50). Selection experiments on strains originally polymorphic for resistance and esterase pattern showed, without exception, that high esterase remained associated with resistance, and it is concluded that the association is almost certainly causal and not merely due to genetic linkage. The high intensity esterase bands were probably due to alleles of the loci Est-l, Est-2 and Est-3, separated by crossover distances of approximately 2·4 and 5·5 units, respectively. Strains monomorphic for what appeared to be the same high esterase pattern varied markedly in resistance level. Enzyme assays showed a direct relationship between levels of enzyme activity and resistance. Bioassays with fenthion and chlorpyrifos revealed differences in the relative resistance ofC. quinquefasciatusfrom Colombo (Sri Lanka) and Dar-es-Salaam (Tanzania). Despite these differential degrees of cross-effectiveness, it is concluded that high intensity esterases are reliable indicators of organophosphate resistance in mosquitoes of theC. pipienscomplex, although the possibility of other resistance mechanisms means that the lack of abnormally active esterases does not necessarily indicate the absence of resistance.

Gray Code Generation for MPSK Signals

Presented here are techniques for generating desired gray codes with properties different from those of the standard binary reflected gray code. For communications using phase shift-keyed (PSK) signals with different significances for different phases, it is desirable to have such codes with different bit error probabilities. For some applications, it is important to have codes with arbitrary crossover Hamming distances. These techniques are suitable for generating codes with either or both of these properties. The codes generated may be far longer than those generated by current computer search techniques.

Upper mantle P structure on the ocean side of the Japan--Kurile Arc

Slowness measurements are made for the first and later arrivals of P waves from about seventy Kurile-Kamchatka earthquakes (13° < Δ < 30°) at the Wakayama Micro-Earthquake Observatory, Japan. The experimental error of dT/dd is not more than 3 per cent and the data points suffice to draw a dT/dΔ curve fairly uniquely. In the distance range 4° < Δ < 15° a travel-time curve, including a later arrival branch, is constructed for a specific Kurile event using the records along the Pacific coasts of the Japanese-Kurile islands. The results are inverted to obtain a velocity model for the upper 800 km of the mantle beneath the trench side of the Japan-Kurile Arc. The model includes a high-velocity lid extending down to 85 km depth. The low-velocity zone is of relatively high speed (8.1 km/s) and is terminated by a high-velocity gradient zone at depths 165-200 km, just below which the velocity is nearly constant with depth. The velocity increases very sharply near 400 km by about 6 per cent. An abrupt change in the slope of velocity occurs near 520 km. A major transition zone in the depth range 630-670 km consists of about 7 per cent increase in velocity and is sharp, especially near the base. A minor transition zone is tentatively suggested to exist around 740 km. Relative arrival times, crossover distances and qualitative amplitude behaviour calculated for this model are consistent with the observed data. Station residuals for the least-squares determination of dT/dΔ closely correlate with the local seismicity.

An array study of P-wave velocities in the upper mantle transition zone beneath northeastern Australia

abstract The use of a seismometer array in determining slowness and travel time greatly enhances the identification of later-arrival branches of the P -wave travel-time curve between 12° and 30°. An adaptive processing method has been used to determine travel times and slownesses for 494 P -wave arrivals, at the WRA medium aperture array in northern Australia, from earthquakes in the New Guinea-Solomon Islands region. Pronounced later arrivals are observed from 12° to 18° and from 21° to 24°. Abrupt changes in slowness are found near crossover distances of 19° and 24.5°. A velocity model, SMAK I, based on a combined interpretation of the travel-time and slowness data has a low gradient in velocity above 300 km, a gradual increase in velocity between 300 and 400 km, a minor zone of high-velocity gradient near 520 km, a low gradient in velocity from 550 to 680 km and an abrupt increase in velocity near 680 km. The main features in this model are in substantial agreement with the changes in physical properties expected from mineralogical variations in a pyrolite upper mantle. A comparison of the WRA data with the results of similar studies in North America suggests that significant differences in velocity between the western United States and northeastern Australia may exist to depths of 400 km, whereas below that depth the structure beneath the two regions may be similar.

Depth to sources of magnetic anomalies

The characteristics of several long magnetic total field intensity profiles have been determined. Only track lines which were nearly straight and longer than 2000 miles were considered. First, the centered dipole field total intensity was subtracted from the measured total intensity to obtain a real nondipole field. A smooth curve was then drawn through this nondipole field using a stiff spline curve. The distance between crossover points of the smooth field and the nondipole field was determined and a histogram of the results plotted. The results confirm the earlier results of Serson and Hannaford that most of the anomalies have a very short wavelength. Ninety-three per cent of the cases had crossover distances less than 60 nautical miles. The simple form of the smooth curves indicated a nearly sinusoidal departure from a dipole field having crossover points between 2100 and 5200 nautical miles. The most natural unforced explanation of the above results is that short-wavelength anomalies are due to crustal effects and the long-wavelength anomalies are due to causes within the core of the earth. The large gap between the short- and long-wavelength groupings supports the hypothesis that the mantle is a forbidden region for magnetic sources. This conclusion is illustrated by calculations based on simple models.