Great Circle Path Research Articles

Application of Propagation Modeling to Verify and Discriminate Ground-Truth Infrasound Signals at Regional Distances

An infrasound field campaign was performed in 2011/2012 utilizing single infrasound sensors along the great circle path between a known ground-truth source (Ariane 5 engine test facility, Lampoldshausen, Germany) and a regional receiver (German infrasound array IS26, Bavarian Forest) covering a distance of rough 320 km in total. The gathered recordings provide new insights in the infrasonic wave propagation at regional and near-source distances by comparing measured signals with modeling results within this study. Ray-tracing and parabolic equation approaches are utilized to model infrasound propagation from the ground-truth source to the line profile sensors and explain the obtained detections and non-detections. Modeling and observation results are compared by estimating their amplitude, quantifying amplitude deviations and also considering observed and calculated travel times and celerities. Modeling results show a significant influence of small-scale atmospheric variations in effective sound speed profiles on the propagation pattern, which results in varying tropospheric and stratospheric ducting behavior. A large number of gravity wave profiles are tested to investigate the influences of atmospheric dynamics on the infrasound wave field and improve the modeling results. The modeling is furthermore applied to a case of two potential, contemporaneous and closely spaced infrasound sources. Propagation modeling is used here to resolve the source ambiguity between a ground-based and a higher altitude source giving a strong preference to the latter with respect to the observed infrasonic signatures. The good agreement between modeling and observation results within this study successfully shows the benefit of applying infrasound propagation modeling to the validation of infrasound measurements, verification of ducting behavior and discrimination of infrasound sources.

Azimuthal anisotropy in the mantle transition zone beneath the Tibetan Plateau: Evidence from normal mode coupling

We investigate strong coupling between spheroidal mode 0S25 and toroidal mode 0T25 observed at LSA, a permanent seismic station located on the southern Tibetan Plateau, after some large earthquakes, such as the 2001/06/23 Mw=8.4 Peru earthquake and the 2011/09/18 Mw=7.2 Sikkim earthquake. Earth's rotation cannot cause coupling of 0S25–0T25 according to coupling selection rules. Our extensive observations indicate that the local azimuthal anisotropy is the dominant cause for strong coupling of 0S25–0T25. It is noted that the coupling is noticeable when the great circle paths connecting epicenters and LSA intersect an East–West line at about 45°, but not observed when paths are parallel or perpendicular to the East–West line. This result suggests that the local azimuthal anisotropy has a horizontal symmetry axis oriented nearly eastward. Our estimation of coupling kernels for the coupled modes 0S25–0T25 shows a peak sensitivity to the depth range of 400–650km, suggesting the existence of azimuthal anisotropy in the upper mantle transition zone beneath the Tibetan Plateau. Our observations also indicate that local anisotropy, rather than Earth's rotation, plays a leading role in causing strong coupling of 0S17–0T18 at LSA after the 2006/04/20 Mw=7.7 Siberia earthquake, suggesting the anisotropic coupling between fundamental spheroidal and toroidal modes is more important than previously realized. The work of this paper proposed that observations of anisotropic coupling below 3.5mHz may provide constraints on the azimuthal anisotropy in the upper mantle transition zone beneath the seismic station.

Shallow seismic source parameter determination using intermediate-period surface wave amplitude spectra

SUMMARY Estimating reliable depths for shallow seismic sources is important in both seismo-tectonic studies and in seismic discrimination studies. Surface wave excitation is sensitive to source depth, especially at intermediate and short-periods, owing to the approximate exponential decay of surface wave displacements with depth. A new method is presented here to retrieve earthquake source parameters from regional and teleseismic intermediate period (100–15s) fundamental-mode surface wave recordings. This method makes use of advances in mapping globaldispersiontoallowhigherfrequencysurfacewaverecordingsatregionalandteleseismic distances to be used with more confidence than in previous studies and hence improve the resolution of depth estimates. Synthetic amplitude spectra are generated using surface wave theory combined with a great circle path approximation, and a grid of double–couple sources are compared with the data. Source parameters producing the best-fitting amplitude spectra are identified by minimizing the least-squares misfit in logarithmic amplitude space. The F-test is used to search the solution space for statistically acceptable parameters and the ranges of these variables are used to place constraints on the best-fitting source. Estimates of focal mechanism, depth and scalar seismic moment are determined for 20 small to moderate sized (4.3 ≤ Mw ≤ 6.4) earthquakes. These earthquakes are situated across a wide range of geographic and tectonic locations and describe a range of faulting styles over the depth range 4–29km. For the larger earthquakes, comparisons with other studies are favourable, however existing source determination procedures, such as the CMT technique, cannot be performed for the smaller events. By reducing the magnitude threshold at which robust source parameters can be determined, the accuracy, especially at shallow depths, of seismo-tectonic studies, seismic hazard assessments, and seismic discrimination investigations can be improved by the application of this methodology.

Evidence for P′P′ asymmetrical scattering at near podal distances

We report strong short period (0.5–1.2 Hz) precursors to P′P′df at podal to short distances (0–50°) with advance time around 60s. From FK analysis, we find that the precursors at epicentral distance of ∼35° arrive along back‐azimuth about +/−120° off the great circle paths (asymmetrical path) with slowness between 2–4 sec/deg, arguing against propagation path in the inner core. Polarization analysis also supports wave propagation in the outer core. Timing and shape of the precursors' waveform envelopes are well matched with synthetic envelopes taking into account the scattering from the rough free surface and volumetric heterogeneities inside the Earth along asymmetrical propagation path. Therefore the precursors are very probably generated with asymmetrical scattering mechanism. This interpretation does not require extra discontinuities or a layer of strong small scale heterogeneities in the upper mantle, which are inferred from P′P′ precursors when only symmetrical scattering is assumed.

Possible precursor to the March 11, 2011, Japan earthquake: ionospheric perturbations as seen by subionospheric very low frequency/low frequency propagation

This study reports on a possible very low frequency/low frequency (VLF/LF) subionospheric precursor to a recent earthquake in Japan. As the epicenter of this large Japanese earthquake on March 11, 2011, was located just on the great-circle path from one of our VLF/LF network stations (Chofu) to the NLK US transmitter, we examined the propagation characteristics mainly associated with the signals from the NLK transmitter, as observed at three of the stations in Japan (Chofu, Kasugai and Kochi). On March 5 and 6, 2011, a remarkable anomaly was found on the path from NLK to Chofu, which is highly likely to have been a precursor to this earthquake. The anomaly in the night-time average amplitude at Chofu was characterized by a serious decrease in the signal that exceeded −4v (v: standard deviations). The anomaly was found on the same days on the other propagation paths (from NLK to both Kasugai and Kochi), although it was less enhanced. Finally, this propagation anomaly is extensively discussed with respect to the geomagnetic activity, and we also compare this anomaly with the properties related to the former 2004 Sumatra earthquake that had nearly the same magnitude as this March 11, 2011, earthquake.

Longitudinal dependence of lightning-induced electron precipitation

[1] Observations of lightning-induced electron precipitation (LEP) events at three geographic regions show characteristics which systematically vary with both longitude and hemisphere. These observations are quantitatively interpreted using a novel atmospheric interaction model designed to predict the characteristics of LEP events at any longitude and midlatitude L-shell by accounting for the effects of precipitating electrons which are backscattered from the atmosphere. The model of atmospheric backscatter (ABS) calculates atmospheric backscatter responses for individual monoenergetic electron beams with a single incident pitch angle using a Monte Carlo model of atmospheric interactions. The ABS model also includes an asymmetric (non-ideal dipole) geomagnetic field model in calculations of the pitch angle of backscattered electrons entering the conjugate hemisphere. Using a realistic distribution of precipitating electrons, the results of this backscatter calculation at three separate longitudes are compared with VLF remote sensing data collected on nearly north-south great circle paths (GCPs). Results predicted by the model and confirmed by data indicate that all four primary LEP characteristics exhibit longitudinal and hemispheric dependence which can be explained in terms of precipitating electrons backscattered from the atmosphere. By combining these effects with previously calculated radiation belt electron loss rates due to lightning at a single location it is possible to estimate the global loss of radiation belt electrons due to lightning.

Anisotropy as cause for polarity reversals of D″ reflections

Recordings of seismic events that sample the deep mantle can test different hypotheses of mantle processes and composition. Seismic reflections from structures in the D″ region — the bottom 200–400 km of the Earth's mantle — can provide information on the velocity contrasts in this region. By studying the waveforms and polarities of the D″ reflections in P and S-waves, we can potentially distinguish between different explanations for the observed structures, such as phase transitions, mineral texture or thermal anomalies. Here we use source–receiver combinations that contain reflections from D″ in two different regions that are both characterised by fast seismic velocities in tomographic models. Beneath the Caribbean a positive S-velocity contrast but negative P-wave velocity contrast across the D″ reflector has been reported previously, consistent with a model of a phase change in MgSiO 3. In the second fast velocity region (Eurasia) we detect positive P- and S-wave velocity contrasts in two orthogonal paths crossing in the lowermost mantle indicating a different scenario for D″. A path that crosses this region in 45° to the other two great circle paths shows evidence for a negative P velocity contrast. One explanation to reconcile observations in both regions is a phase transition from perovskite to post-perovskite with a fraction of 12% preferred crystal alignment in the post-perovskite phase. Depending on the travel direction of the waves with respect to the flow direction in the lower mantle, positive or negative velocity jumps can be expected. Other anisotropic models are considered but cannot fully explain the range of observations we find in the data.

Upper-mantle structure in southern Norway from beamforming of Rayleigh wave data presenting multipathing

SUMMARY A model for the upper mantle SV-wave velocity under southern Norway is obtained by depth inversion of the average phase velocity of the Rayleigh wave fundamental mode in the area. The average dispersion curve is obtained in the period range 22–200 s by beamforming of 190 Rayleigh waves recorded by the MAGNUS network, a temporary regional network of 41 broad-band stations. Resolution of the beamforming procedure is increased by deconvolving the original beams from the array response function using the Lucy–Richardson algorithm. In addition to an average phase velocity, beamforming gives us some information concerning the nature of the incoming wavefield. We detect deviations of the wave propagation direction from the great-circle paths which commonly reach 10° at a period of 25 s for the teleseismic events. The amplitude of the deviations decreases with increasing period and with decreasing epicentral distance, as expected. The phase velocity measured by beamforming does not show any correlation with the deviation from great circle path, suggesting that deviation does not bias phase velocity measurements. We detect also significant multipathing with characteristics that vary rapidly with frequency. The obtained SV-wave velocity profile clearly shows that southern Norway is underlain by a low-velocity zone in the upper mantle and does not have shield-like characteristics, despite its location in the Baltic shield. These findings support the hypothesis that the high topography of southern Norway is sustained by anomalous upper-mantle material.

Space‐time structure of long ocean swell fields

The space‐time structure of long‐period ocean swell fields is investigated, with particular attention given to features in the direction orthogonal to the propagation direction. This study combines space‐borne synthetic aperture radar (SAR) data with numerical model hindcasts and time series recorded by in situ instruments. In each data set the swell field is defined by a common storm source. The correlation of swell height time series is very high along a single great circle path with a time shift given by the deep water dispersion relation of the dominant swells. This correlation is also high for locations situated on different great circles in entire ocean basins. Given the Earth radiusR, we define the distance from the sourceRαand the transversal angleβso thatαandβwould be equal the colatitude and longitude for a storm centered on the North Pole. Outside of land influence, the swell height field at timet,Hss(α,β,t) is well approximated by a functionHss,0(t ‐ Rα/Cg)/times another functionr2(β), whereCgis a representative group speed. Herer2(β) derived from SAR data is very broad, with a width at half the maximum that is larger than 70°, and varies significantly from storm to storm. Land shadows introduce further modifications so that in generalr2is a function ofβandα. This separation of variables and the smoothness of theHssfield, allows the estimation of the full field ofHssfrom sparse measurements, such as wave mode SAR data, combined with one time series, such as that provided by a single buoy. A first crude estimation of a syntheticHssfield based on this principle already shows that swell hindcasts and forecasts can be improved by assimilating such synthetic observations.

Response of the equatorial lower ionosphere to the total solar eclipse of 22 July 2009 during sunrise transition period studied using VLF signal

Changes in equatorial D‐region electron density are studied using subionospherically propagating VLF signal at 18.2 kHz over a distance of 2200 km during the total solar eclipse of 22 July 2009. There are very few studies about the eclipse's effects on the equatorial lower ionosphere in the scientific literature. In the light of that, the objective of the present work is to study the effects of the eclipse on the dynamics of the equatorial lower ionosphere during ionospheric sunrise transition period. In the present case, great circle path between VLF transmitter and receiver falls totally in partial eclipse zone, having a maximum solar obscuration of 90% and an average obscuration of 74%. Results show an average decrease of 3.2 dB in signal strength compared to control days during peak solar obscuration over the path. A comparison with previous studies shows an increase both in lower ionosphere virtual reflection height (H′) and Wait inverse scale height parameter (β); the values estimated are 74.5 km and 0.46 km−1 compared to unperturbed ionosphere values of 71 km and 0.43 km−1, respectively. During maximum eclipse over the path, the model profile shows an average 80% drop in electron density at a height of 71 km at equatorial lower ionosphere. A nonlinear variation of lower ionosphere electron density with solar radiation is found as opposed to the model study proposed by previous workers.

Some Notes on Discrete Trains of Infrasonic Waves Produced by Point Sources

The most prominent trains of infrasonic waves are produced by strong point disturbances in the atmosphere, such as nuclear explosions in the megaton range. The infrasonic records at the La Paz Bolivia observatory indicate that the signals resulting from such explosions have a sharp beginning similar to seismic records. The results of analysing the data from four signals presumed to have resulted from nuclear explosions in the atmosphere are given in Table 1. The great circle path length from the source location to La Paz, and the arrival times for the short and long path arrivals are also given in the table. The long path arrival for all events, except that of 1968 August 24, was somewhat masked by the irregular noise at the tail of the short path signal. Readings on all received signals were taken at four distinct times. Values are not given for some readings on the long path arrivals, due to low signal conditions. The periods given in the table indicate normal dispersion properties, with the very long period gravity waves arriving first. The remaining readings appear irregular both in period and in travel time, with no distinct wave arrivals noted. The observed dispersion is somewhat dependent on the size of the explosion exciting the waves, but a greater influence is the wind and temperature variation with altitude. Seasonal effects are evidenced by observing the travel time for the events of 1968 December 27 and 1970 October 14. The difference between the short and long path arrivals is changing, probably due to different seasonal wind profiles.

More evidence for a one‐to‐one correlation between Sprites and Early VLF perturbations

Past studies have shown a correlation between sprites and early VLF perturbations, but the reported correlation varies widely from ∼50% to 100%. The present study resolves these large discrepancies by analyzing several case studies of sprite and narrowband VLF observations, in which multiple transmitter‐receiver VLF pairs with great circle paths (GCPs) passing near a sprite‐producing thunderstorm were available. In this setup, the multiple paths act in a complementary way that makes the detection of early VLF perturbations much more probable compared to a single VLF path that can miss several of them, a fact that was overlooked in past studies. The evidence shows that visible sprite occurrences are accompanied by early VLF perturbations in a one‐to‐one correspondence. This implies that the sprite generation mechanism may cause also sub‐ionospheric conductivity disturbances that produce early VLF events. However, the one‐to‐one visible sprite to early VLF event correspondence, if viewed conversely, appears not to be always reciprocal. This is because the number of early events detected in some case studies was considerably larger than the number of visible sprites. Since the great majority of the early events not accompanied by visible sprites appeared to be caused by positive cloud to ground (+CG) lightning discharges, it is possible that sprites or sprite halos were concurrently present in these events as well but were missed by the sprite‐watch camera detection system. In order for this option to be resolved we need more studies using highly sensitive optical systems capable of detecting weaker sprites, sprite halos and elves.

USArray observations of quasi‐Love surface wave scattering: Orienting anisotropy in the Cascadia plate boundary

Quasi‐Love (QL) surface wave anomalies are observed along multiple great circle paths crossing the Pacific and through the mid‐ocean ridge and subduction zone associated with the Juan de Fuca plate. The long‐period QL waves observed on the USArray component of EarthScope arrive immediately after the fundamental Love wave arrival, suggesting that the QL waves were generated close to USArray and near the plate boundary. The dense USArray network allows the analysis of the azimuthal dependence of the QL surface wave scattering to determine the horizontal anisotropic axes of symmetry in Earth's upper mantle. We focus on the location, 42.5°N and 127.5°W just offshore of the southern Oregon coastline near the Gorda Ridge, and we analyze the QL scattering along 14 different great circle paths crossing through this location. We low‐pass filter the data to suppress overtones and crustal effects. QL amplitude and polarity constrains an anisotropic axis of symmetry that correlates well with the hot spot referenced Juan de Fuca plate motion and regional shear wave splitting. QL observations at multiple periods (50, 75, 100, 150, and 200 s) suggest a maximum Love‐to‐Rayleigh scattering at 100 s period, which is consistent with anisotropic lateral gradients in the asthenosphere beneath the Juan de Fuca and Gorda plates. Our observations do not follow the predictions of slab rollback and suggest the entrainment of asthenosphere with the overriding Juan de Fuca and Gorda plates.

The ionospheric perturbations associated with Asian earthquakes as seen from the subionospheric propagation from NWC to Japanese stations

Abstract. Huge five earthquakes with magnitude greater than 6.0 took place in Asia (include Philippines, Indonesia, etc.) during the period from the beginning of August 2008 to the end of Junuary 2009, and the corresponding data of subionospheric VLF propagation between the NWC transmitter (Australia, 19.8 kHz) and a few Japanese stations (distance 6~8 Mm) are examined. As the result of our analysis by means of (1) trend (average nighttime amplitude), (2) dispersion, (3) nighttime fluctuation, and (4) atmospheric gravity wave enhancement, three earthquakes from the five taking place within the fifth Frenel zone are found to have accompanied a precursory signature in VLF propagation. On the other hand, there were observed no such precursory signatures for the remaing two earthquakes. One is too deep (>400 km) and another is too distant from the great-circle path. These characteristics of seismo-ionospheric perturbations would be of essential importance in studying the spatial/temporal properties of seismo-ionospheric perturbations for medium-distance propagation.

Propagation of HF radio waves over northerly paths: measurements,simulation and systems aspects

Large deviations in the direction of arrival of ionospherically propagating radio signals from the Great Circle Path (GCP) have serious implications for the planning and operation of communications and radiolocation systems operating within the HF-band. Very large deviations are particularly prevalent in the polar and sub-auroral regions where signals often arrive at the receiver with bearings displaced from the great circle direction by up to ±100° or more. Measurements made over several paths are presented in this paper, and the principle causes of off-great circle propagation outlined. Significant progress has been made in modelling the propagation effects and work is now in hand to incorporate the results into tools to aid the planning and operation of HF radio systems operating at northerly latitudes.

Considerations in Phase Estimation and Event Location Using Small-aperture Regional Seismic Arrays

The global monitoring of earthquakes and explosions at decreasing magnitudes necessitates the fully automatic detection, location and classification of an ever increasing number of seismic events. Many seismic stations of the International Monitoring System are small-aperture arrays designed to optimize the detection and measurement of regional phases. Collaboration with operators of mines within regional distances of the ARCES array, together with waveform correlation techniques, has provided an unparalleled opportunity to assess the ability of a small-aperture array to provide robust and accurate direction and slowness estimates for phase arrivals resulting from well-constrained events at sites of repeating seismicity. A significant reason for the inaccuracy of current fully-automatic event location estimates is the use of f−k slowness estimates measured in variable frequency bands. The variability of slowness and azimuth measurements for a given phase from a given source region is reduced by the application of almost any constant frequency band. However, the frequency band resulting in the most stable estimates varies greatly from site to site. Situations are observed in which regional P- arrivals from two sites, far closer than the theoretical resolution of the array, result in highly distinct populations in slowness space. This means that the f−k estimates, even at relatively low frequencies, can be sensitive to source and path-specific characteristics of the wavefield and should be treated with caution when inferring a geographical backazimuth under the assumption of a planar wavefront arriving along the great-circle path. Moreover, different frequency bands are associated with different biases meaning that slowness and azimuth station corrections (commonly denoted SASCs) cannot be calibrated, and should not be used, without reference to the frequency band employed. We demonstrate an example where fully-automatic locations based on a source-region specific fixed-parameter template are more stable than the corresponding analyst reviewed estimates. The reason is that the analyst selects a frequency band and analysis window which appears optimal for each event. In this case, the frequency band which produces the most consistent direction estimates has neither the best SNR or the greatest beam-gain, and is therefore unlikely to be chosen by an analyst without calibration data.

Waveguide Parameters of 19.8 kHz Signal Propagating over a Long Path

The amplitude and phase of 19.8 kHz signal from navigational transmitter located in North West Cape, Australia, recorded at Suva, Fiji, have been utilized to determine the waveguide mode parameters. The propagation path is mixed over land and sea having Transmitter-Receiver Great Circle Path distance 6.7 Mm. The experimental values of the parameters were found to be consistent with the theoretical values calculated using the mode theory of VLF wave propagation in the waveguide.

Array Analysis of Regional-Distance P-Coda in South Asia

Abstract We present a comprehensive study of regional distance P -coda recorded by a medium-aperture array station located in Chiang Mai, Thailand (CMAR). Using array processing techniques, we analyzed data from 955 events that occurred at distances of 13°–30° with primarily continental paths. Nearly all significant, coherent arrivals in the P -coda traveled along the great circle path with ray parameters within of the direct arrival. Most of this energy was created near the source, probably via ( L g , R g )→ P scattering. This was especially true at the larger distances of 28°–30° in which coda decay rates decreased and large-amplitude significant arrivals occurred throughout the first 30 sec of the coda. The codas from approximately 40 intermediate-depth events in our data set were generally less energetic than shallow-event coda at comparable distances. In some cases, the coherent later arrivals we observed were related to upper mantle triplications. At distances of 14°–17° we observed clear secondary arrivals related to the 410 km discontinuity. They appeared on average 2 sec later than expected relative to the first arrivals, which may be partially explained by a depressed 410 beneath Burma. We isolated the diffuse component of the P -coda by subtracting array beams from individual elements to create residual seismograms. The diffuse, residual energy was highly variable from trace to trace and became equal in amplitude to the coherent component after only 20–30 sec of lapse time. We used a high-resolution maximum-likelihood technique to compute frequency–wavenumber spectra of the residual seismograms but did not conclusively observe any deterministic P → R g scatterer locations. The majority of the diffuse energy is created quite close to CMAR and does not travel as a plane wave across the array.

Seismic tomography of crustalPandSacross Eurasia

SUMMARY In this paper, we present inversion results for regional Pg and Sg phases for the Eurasian continent to explore its use for understanding upper crustal velocity structure. Tomographic inversion of traveltimes from first arriving compressional and shear waves for velocity structure has been applied with great success at all length scales, ranging from the laboratory benchtop to the entire Earth, while inversion of later arriving phases has been much more limited. Our inversion is performed using a damped, smoothed LSQR implementation that solves for site and event terms as well as for velocity along great circle paths between the source and receiver. Results are broadly consistent with published upper crustal velocities for Eurasia, with predominantly high velocities in cratonic regions. Generally, but not always, lower velocities are observed in orogenic and extensional areas and in deep sedimentary basins. A spotcomparison of VP/VS from local and regional studies compares well with the ratio of observed Pg to Sg velocities from our study where resolution is high. Resolution is determined through the use of checkerboard tests, and these suggest that in regions where data density is high we can resolve features down to at least 2 ◦ , with 4 ◦ possible over broader areas. rms residual reductions are on the order of 25 per cent for Sg and 30 per cent for Pg.

Long-Distance Propagation of VHF Radio Waves due to the Effect of the Equatorial Anomaly

Observation of 48.25-MHz radio waves transmitted from Bangkok, Thailand, was carried out at Tateyama, Japan, during 2001. Since the radio wave propagates through a crest of equatorial anomaly, which disturbs stratified structure of the ionosphere, it is conceivable that the propagation of the radio wave is affected by three-dimensional structure of the ionosphere. Seasonal and diurnal variations of the signal intensity are quite similar to ƒ0F2 above Guangzhou and also Okinawa, which are located on the great circle path between Bangkok and Tateyama. Using ray-tracing calculations with the distribution of the electron density determined by IRI model, it is also confirmed that the radio wave propagates to Tateyama because of one-hop reflection in the ionosphere and that MUF is mainly dependent on ƒ0F2 above the midpoint between Bangkok and Tateyama. Although the value of ƒ0F2 is almost constant, MUF calculated by the ray-tracing treatment decreases around 14 JST in fall and winter. This decrease is also detected in the observational result of the signal intensity of the radio wave received at Tateyama. The ray tracing calculation shows that the decrease of MUF is due to tilt of the distribution of electron density, which is noticeable in developing the equatorial anomaly. Then discussing the propagation characteristics of 48.25-MHz radio waves crossing equatorial anomaly region, it is important to consider not only the parameters of the ionosphere, e.g. ƒ0F2, but also the tilt of the distribution of electron density.