Great Circle Propagation Research Articles

Green’s Function, Earthquakes, and a Fast Ambient Noise Tomography Methodology

Green’s function plays an important role in the relationship of a future strong earthquake epicenter to the average earthquake potential score. In the frame of the latter, the fractal dimension of the unified scaling law for earthquakes naturally arises. Here it is also shown to be a cornerstone for the development of a new ambient noise tomography methodology, which is applied for example to the west coast of Central Greece. In particular, we show that a fast and reliable 3D shear velocity model extraction is possible without the need for a large amount of data, great-circle propagation assumptions, or the intermediate step of inverting for group velocity maps. The tomography results are consistent with previous studies conducted in the neighboring region.

Global empirical models for infrasonic celerity and backazimuth

SUMMARY Global empirical models for infrasound signal celerity (where celerity is defined as the epicentral distance divided by the total traveltime) and backazimuth deviation (the difference between the measured and predicted backazimuth assuming great circle propagation), can be used for the association of infrasound automatic detections, for event location and for the validation of acoustic propagation simulations. Using software developed to consistently analyse a global ground truth database, we observe 296 detections in the 0.32–1.28 Hz passband; predominantly stratospheric arrivals, with a smaller number of tropospheric and thermospheric arrivals, in agreement with previous studies. We develop an updated global celerity-range model and introduce a global backazimuth deviation model. These new models suggest that the variation in backazimuth deviation is not range-dependent; 93 per cent of the 296 detections studied have a deviation magnitude ≤5°. The maximum deviation observed is 8.9°. The variation in celerity, however, is range-dependent. An exponential range-dependent celerity model with bounds calculated using a quantile regression fit to the traveltime residuals is determined. This traveltime residual model, with uncertainties that increase with range, produces bounds on the celerity consistent with both the observations and current understanding of infrasound propagation. The traveltime residual model derived celerity bounds are not symmetric around the celerity model, which further reflects the physical processes. At long ranges (>3000 km), maximum peak-to-trough amplitude arrivals are not observed with celerities <280 ms−1, but even at long ranges, we occasionally observe celerities (>320 −1) more usually consistent with tropospheric arrivals.

Updates to global empirical models for infrasonic signal celerity and backazimuth from ground truth data

Global empirical models for infrasonic signal celerity (the epicentral distance divided by the total travel time) and backazimuth deviation (the difference between the measured and predicted backazimuth assuming great circle propagation), are used for the association of infrasound automatic detections, event location and acoustic propagation simulation validation. Following a previous methodology to develop a regional celerity-range model (Nippress et al., 2014), we developed a software suite for consistent analysis of a global ground truth database, allowing estimation of empirical models for celerity and backazimuth. We observe 304 detections in the 0.32–1.28 Hz passband, with propagation path lengths of between 25 and 6280 km. Models derived from these observations suggest the backazimuth deviation distribution is range-independent, 92% of the detections studied have a deviation ≤ ±5º. However, the celerity model, produced through fitting the travel-times with a linear regression model, is range-dependent. The celerity model bounds are determined using a quantile regression fit to the travel-time residuals, and are consistent with the current understanding of infrasound propagation. At 10 + years since the publication of the last global celerity-range model, this study provides a timely update.UK Ministry of Defence © Crown Owned Copyright 2022/AWE

Refraction of swell by surface currents

Using recordings of swell from pitch-and-roll buoys, we have reproduced the classic observations of long-range surface wave propagation originally made by Munk et al. (1963) using a triangular array of bottom pressure measurements. In the modern data, the direction of the incoming swell fluctuates by about ±10∘ on a time scale of one hour. But if the incoming direction is averaged over the duration of an event then, in contrast with the observations by Munk et al. (1963), the sources inferred by great-circle backtracking are most often in good agreement with the location of large storms on weather maps of the Southern Ocean. However there are a few puzzling failures of great-circle backtracking e.g., in one case, the direct great-circle route is blocked by the Tuamoto Islands and the inferred source falls on New Zealand. Mirages like this occur more frequently in the bottom-pressure observations of Munk et al. (1963), where several inferred sources fell on the Antarctic continent. Using spherical ray tracing we investigate the hypothesis that the refraction of waves by surface currents produces the mirages. With reconstructions of surface currents inferred from satellite altimetry, we show that mesoscale vorticity significantly deflects swell away from great-circle propagation so that the source and receiver are connected by a bundle of many rays, none of which precisely follow a great circle. The ±10∘ directional fluctuations at the receiver result from the arrival of wave packets that have travelled along the different rays within this multipath. The occasional failure of great-circle backtracking, and the associated mirages, probably results from partial topographic obstruction of the multipath, which biases the directional average at the receiver.

Monitoring and analysis of ocean swell fields from space: New methods for routine observations

Satellite synthetic aperture radar (SAR) observations can provide a global view of ocean swell fields when using a specific “wave mode” sampling. A methodology is presented to routinely derive integral properties of the longer‐wavelength (swell) portion of the wave spectrum from SAR level 2 products and both monitor and predict their evolution across ocean basins. SAR‐derived estimates of swell height and energy‐weighted peak period and direction are validated against buoy observations, and the peak directions are used to project the peak periods in one dimension along the corresponding great circle route, both forward and back in time, using the peak period group velocity. The resulting real‐time data set of great circle–projected peak periods produces two‐dimensional maps that can be used to monitor and predict the spatial extent and temporal evolution of individual ocean swell fields as they propagate from their source region to distant coastlines. The result is found to be consistent with the dispersive arrival of peak swell periods at a midocean buoy. The simple great circle propagation method cannot project the swell heights in space like the peak periods, because energy evolution along a great circle is a function of the source storm characteristics and the unknown swell dissipation rate. A more general geometric optics model is thus proposed for the far field of the storms. This model is applied here to determine the attenuation over long distances. For one of the largest recorded storms, observations of 15 s period swells are consistent with a constant dissipation rate that corresponds to a 3300 km e‐folding scale for the energy. In this case, swell dissipation is a significant term in the wave energy balance at global scales.

Observations of HF propagation on a path aligned along the mid-latitude trough

Observations of the direction of arrival and time of flight of HF signals propagating on a 1400 km path oriented along the mid-latitude trough are presented. At night, the signal commonly arrives from directions offset from the great circle bearing by up to 80° and these events have been categorised into five main types. Statistics indicating how often these categories of propagation were observed in the period August 2006 to September 2007 are presented. The physical mechanisms which result in the off great circle propagation are also discussed.

Impacts of non-plane waves on two-station measurements of phase velocities

SUMMARY To determine the regional shear wave velocities in the lithosphere it is frequently necessary to use two-station dispersion curves. We investigate the influence of non-plane wave energy on such dispersion curves, and compare them to two other better known sources of error: deviations from great-circle paths and uncorrelated noise. To study the influence of nonplane waves created from distant heterogeneities we create complex wavefields in a laterally homogeneous medium by adding interfering waves to a main plane wave. We then calculate the apparent phase velocity between two seismic stations located 100–400 km apart. Using realistic values for the sources of error, we conclude that the contribution of each is similar for 200-km-long profiles. Our conclusions on non-plane waves are made under the assumption that non-plane energy from distant heterogeneities varies randomly with hypocentre location. If this is correct, then only five to 10 events with different hypocentres are required to obtain a stable dispersion curve with less than 1 per cent error. The influence of uncorrelated noise and non-plane waves diminish for longer profiles, while the errors due to great-circle deviations are independent of profile length and systematically bias the dispersion curve to higher velocities. We recommend the inclusion of some off-profile broad-band stations for surface wave studies on a regional scale, because such supplementary stations make it possible to apply first-order corrections for off great-circle propagation. The strong influence from the different sources of error, combined with our lack of precise knowledge of the nature and amplitude of non-plane energy, implies that the interpretation of two-station measurements should be restricted to major changes in regional earth structure.

A ray‐tracing model to account for off–great circle HF propagation over northerly paths

Off–great circle HF propagation effects are a common feature of the northerly ionosphere (i.e., the subauroral trough region, the auroral zone, and the polar cap). In addition to their importance in radiolocation applications where deviations from the great circle path may result in significant triangulation errors, they are also important in two other respects: (1) In systems employing directional antennas pointed along the great circle path, the signal quality may be degraded at times when propagation is via off–great circle propagation modes; and (2) the off–great circle propagation mechanisms may result in propagation at times when the signal frequency exceeds the maximum usable frequency along the great circle path. A ray‐tracing model covering the northerly ionosphere is described in this paper. The results obtained using the model are very reminiscent of the directional characteristics observed in various experimental measurement programs, and consequently, it is believed that the model may be employed to enable the nature of off–great circle propagation effects to be estimated for paths which were not subject to experimental investigation. Although it is not possible to predict individual off–great circle propagation events, it is possible to predict the periods during which large deviations are likely to occur and their magnitudes and directions.

Measurements of the Doppler and multipath spread of HF signals received over a path oriented along the midlatitude trough

The presence of the midlatitude trough can severely impact on HF radio systems since the electron density depletion within the trough reduces the maximum frequency which can be reflected by the ionosphere along the great circle path. Furthermore, the associated horizontal gradients in the electron density distribution frequently result in propagation well displaced from the great circle path. The signal characteristics associated with this type of propagation have been investigated for a 1400 km link oriented along the midlatitude trough between Sweden and the UK. As anticipated, the observed delay and Doppler spread characteristics are strongly dependent upon time of day and season since the trough is a nighttime feature which occurs predominantly during the winter. In particular, the Doppler spread is often large when great circle propagation has been suppressed and reflections are from the north of the great circle path (i.e., from the poleward wall of the trough or from gradients and/or irregularities associated with the auroral zone).

The effect of the mid-latitude trough on the direction of arrival and time-of-flight of HF radio signals

Ray tracing has been used for the investigation of the off great circle propagation of radio signals in a 4490 km West-East path in presence of the mid-latitude trough. Two propagation mechanisms were studied, non-specular scatter from the sea and reflection from the walls of the trough. The results assuming sea scatter are generally in good agreement with observations at a number of frequencies, while ray tracing simulations of reflection from the equatorward wall of the trough do not reproduce the large bearing deviations observed. For additional information about the trough in northern Europe, an experiment between Uppsala, Sweden and Leister U.K. has been established, in which measurement of the elevation angle and time-of-flight characteristics are included to improve and develop ionospheric trough models for this region.

Determination of the influence zone for surface wave paths

SUMMARY An approximate description of the zone of influence around the propagation path for a surface wave is provided by investigating the Fresnel zones for the frequency range of interest. The influence zone about surface wave paths, over which surface waves are coherent in phase, is identified as approximately one-third of the width of the first Fresnel zone. A technique called Fresnel-area ray tracing (FRT) for surface waves has been used to estimate this region around the ray path for each frequency. The FRT technique is developed by combining two standard ray tracing methods, i.e. kinematic ray tracing (KRT) and dynamic ray tracing (DRT). To obtain the exact Fresnel area in a laterally heterogeneous structure would require the solution of a large number of KRT equations. In contrast, the FRT approach requires just a few ray tracing calculations. In the first step, the trajectory of the surface wave is computed by solving the KRT system for the phase-velocity distribution at the required frequency. In the next step, the behaviour of rays in the zone surrounding the KRT path is calculated by solving the DRT system twice; once from the source to the receiver and once more from the receiver to the source along the same trajectory. Finally, combining the solutions of these ray tracing systems using paraxial ray theory, the Fresnel area around a central ray can be estimated. Using FRT, stationary-phase fields can be constructed around a central ray path in a laterally heterogeneous structure. The influence zone around the ray path is then estimated from the stationary-phase function with simple assumptions concerning the perturbed wavefield. The estimate of the influence zone can be efficiently calculated in laterally heterogeneous structure by using the FRT technique, and allows an extension of current methods of surface wave analysis, which have commonly been based on geometrical ray theory and on the approximation of great-circle propagation. This approach allows the treatment of finite-width rays as well as deviations in propagation from the great circle induced by moderate lateral heterogeneity as revealed by recent tomography models. Such finite-width rays should be of major benefit in enhancing ray-based surface wave tomography.

VLF and LF signatures of mesospheric/lower ionospheric response to lightning discharges

New evidence is presented of disturbances of the electrical conductivity of the nighttime mesosphere and the lower ionosphere in association with lightning discharges. In addition to extensive documentation of the characteristics of a class of events heretofore referred to as early/fast VLF events [Inan et al., 1993], our data reveal a new feature of these events, consisting of a postonset peak that typically lasts for 1–2 s. We also report the observation of short‐duration VLF or LF perturbations, in which the amplitude of the subionospheric signal exhibits a sudden change within 20 ms of the causative lightning discharge, and recovers back to its original level in < 3 s. These short‐duration events have characteristics similar to the previously observed rapid onset, rapid decay VLF signatures [Dowden et al.., 1994]. Both the typical and rapidly recovering events are observed primarily when the causative lightning discharge is within ±50 km of the VLF or LF great circle propagation path, indicating that the scattering from the localized disturbance is highly collimated in the forward direction. The latter in turn implies that for the parameters in hand, the transverse extent of the disturbance must be at least ∼ 100–150 km. The measured VLF signatures are compared with the predictions of a three‐dimensional model of subionospheric VLF propagation and scattering in the presence of localized ionospheric disturbances produced by electromagnetic impulses and quasi‐electrostatic (QE) fields produced by lightning discharges. The rapidly recovering or short‐duration events are consistent with the heating of the ambient electrons by quasi‐static electric fields, in cases when heating is not intense enough to exceed the attachment or ionization thresholds. When no significant electron density changes occur, the conductivity changes due to heating alone last only as long as the QE fields, typically less than a few seconds. When heating is intense enough so that attachment or ionization thresholds are exceeded, reductions or enhancements in electron density can respectively occur, in which case the medium would relax back to the ambient conditions with the time scales of the local D region chemistry, typically 10–100 s.

Delay, Doppler, and amplitude characteristics of HF signals received over a 1300‐km transauroral sky wave channel

Channel probe observations of propagation conditions along a 1294‐km transauroral path between Sondrestrom, Greenland, and Keflavik, Iceland, were made during the period from March 13 to April 2, 1992. The midpoint of this path was located at a corrected geomagnetic latitude of 72°. The objective of these measurements was to supplement the existing data base describing propagation conditions on the HF transauroral channel with data pertaining to a period around the time of solar maximum. Received signals for this path fell into three distinct groups depending on their amplitude and delay and Doppler spread characteristics. These are (1) strong, specularly reflected ionospheric returns characteristic of a quiescent daytime ionospheric channel during magnetically quiet conditions; (2) strong specular multipath signals reflected from horizontal gradients of electron density and regularly encountered at night; and (3) weak scatter returns that are also a persistent nighttime phenomenon. The scatter returns are usually observed at delays exceeding those anticipated for the one‐hop return and, very often, at frequencies that are well above the MUF for the great circle propagation path. The multipath and scatter returns exhibit large delay and Doppler spreads indicative of spatially extensive distributions of drifting and randomly moving irregularities. Two measurement events are discussed which illustrate these conclusions: a noontime measurement with Kp = 3, and a midnight measurement with Kp = 2. The noontime measurement exhibited a scatter return from an isolated irregularity region in addition to the usual ionospheric reflected signals. A simple irregularity drift model produced delay and Doppler shift curves that were consistent with those observed for the scatter component of the received signal and supported a hypothesis of an irregularity region drift speed of 1200 m s−1 parallel to the great circle propagation path.

Frequency-dependent polarization measurements of long-period surface waves and their implications for global phase-velocity maps

Abstract Surface-wave dispersion maps provide important constraints on global models of shear-wave velocity structure. Current surface-wave dispersion maps show significant differences from researcher to researcher, and it is clear that further work is required. In addition to dispersion data, polarization measurements obtained from long-period (100 s or more) three-component recordings from the various global networks can also be used to constrain dispersion maps. The off great circle propagation of the surface-wave packets is relatively easy to interpret within a ray-theoretic framework, and provides sensitivity to higher-order structure. The polarization angles as a function of frequency are readily measured using a multi-taper technique, which also has the benefit of providing an error estimate for the measurements. Application of the technique to three-component seismograms from the global GEOSCOPE array reveals large deviations from great circle propagation (up to 15° for low-orbit Love waves and 10° for Rayleigh waves in the frequency band 5–12.5 mHz). On a more regional scale, an analysis of seismograms from the German Regional Seismic Network (GRSN) reveals even larger, strongly frequency-dependent deviations from great circle propagation in the frequency range 10–50 mHz.

Global acoustic propagation modeling using MaCh1

MaCh1 is a broadband, range-dependent acoustic propagation model based on the one-way form of the Maslov integral representation of the wave field. The one-way propagation assumption may—but need not—be combined with a parabolic approximation. MaCh1 model predictions along multi-megameter great circle propagation paths using climatological sound-speed structure and coarse resolution bathymetry will be shown. Model predictions will be compared to preliminary ATOC (acoustic thermometry of ocean climate) program measurements if the latter are available.

A multiple‐mode three‐dimensional model of VLF propagation in the Earth‐ionosphere waveguide in the presence of localized D region disturbances

Transient localized D region disturbances, such as those associated with lightning discharges, affect the characteristics of VLF waves propagating in the Earth‐ionosphere waveguide. In particular, both phase and amplitude changes in the subionospheric signal can be observed at receiving sites as a result of the wave scattering that takes place in the disturbed region. In the present paper we present a multiple‐mode three‐dimensional model of VLF propagation in the Earth‐ionosphere waveguide in the presence of localized D region disturbances. The model takes into account great circle (GC) propagation paths with realistic ground and ionospheric conductivity changes that result in mode conversion along the path. It is assumed that conductivity changes transverse to the GC paths are negligible except in the vicinity of the D region disturbance and that mode coupling is negligible within the disturbed region. This new model is applied to experimental observations and is found to be in general agreement. The diagnostics potential of the model for characterizing energetic particle precipitation events is discussed.

Signature of burst particle precipitation on VLF signals propagating in the Antarctic Earth‐ionosphere waveguide

The burst precipitation of energetic electrons (≥40 keV), induced by interactions with lightning‐generated whistler mode waves, has been observed to cause phase and amplitude perturbations on subionospheric VLF signals (“Trimpi” events). With a knowledge of the propagation characteristics of the subionospheric signal, analysis of the perturbation details can lead to estimates of the energy, extent, and location of the precipitation.Trimpi events have been observed on VLF signals propagating at high latitudes (L ≥ 4) over Antarctica, on 3.79‐kHz signals transmitted from the horizontal dipole at Siple station. A mode theory computer model for propagation of VLF waves in the Antarctic Earth‐ionosphere waveguide is used to illustrate the characteristics of 3.79‐kHz signals as they propagate from Siple toward VLF receivers at Halley and South Pole stations. To simulate the effects of precipitation, localized depressions in the ionospheric reflection height are introduced over the great circle propagation paths in the model, and it is seen that, while the amplitude and phase perturbations of some specific events are accurately reproduced, large positive amplitude (up to 6 dB) Trimpi events at Halley cannot be reproduced. Calculations are presented which show that signals echoing from precipitation patches located away from the great circle path could be the cause of such signatures.

Effects of off great-circle propagation on the phase of long-period surface waves

Summary. Surface wave phase corrections for departures from great-circle propagation are computed using two-point ray-tracing through the aspherical earth model M84C of Woodhouse & Dziewonski (1 984). For Rayleigh and Love waves with periods in the range 100-250 s, we determine whether these corrections provide significant variance reductions in source determinations compared with corrections calculated assuming great-circle propagation through the heterogeneous structure. For most source-receiver geometries, the off great-circle travel-time effects are small (< 10 s) for second and third orbits (e.g. R2 and R3), and their application in source determinations does not significantly reduce the data variance. This suggests that for the loworder heterogeneous models currently available the geometrical optics approximation is valid for long-period low orbit surface waves. Off greatcircle phase anomalies increase quasi-linearly with increasing orbit number, indicating that the geometrical optics approximation degrades for higher orbits, which emphasizes the importance of developing higher order approximations for free-oscillation studies.

Mantle wave deviations from ‘pure-path’ propagation on aspherical models of the Earth by Gaussian beam waveform synthesis

Departures from the classical approximations of geometrical optics and great circle propagation are investigated by surface wave ray-tracing on laterally heterogeneous models and computation of synthetic seismograms by the Gaussian beam method. Higher order deviations, such as time differences between odd and even orbits, residuals from great-circle average times, and fluctuations in the succession of eigenfrequencies in the spectra are sought for and compared with long-period great-circle observations. In the case of the Akita-Oki (Honshu) earthquake (1983) at the Geoscope station PAF, the deviations are of the order of the first order tomographic effect. They are interpreted by a transverse velocity gradient shifting the orbits. In other examples where great-circle propagation is nearly satisfied, geometrical effects of curvature are displayed. Frequency fluctuations due to lateral heterogeneity appear in the synthetic spectrum.

Schumann resonance—some properties of discrete events

The work described here is concerned with the background electromagnetic noise in the band from 6 Hz to 100 Hz, and was carried out during 1969. Within this band the Schumann resonances are to be observed and their main source of energy is the radiation produced by lightning. Each lightning stroke produces a single resonance event having a set of mode amplitudes which are dependent on the source spectrum, and frequencies which are dependent on the propagation azimuth. The work is concerned with the development of a method for examining discrete resonance events and evaluating some of the properties of these events as a function of propagation path. The apparatus used to record the noise has a very good mains rejector with 3 dB rejection bandwidth of less than 1 Hz at 50 Hz, and this provides a broad band in which to work. The sensors used are arranged so that some of the directional properties of the noise can be observed and this makes it possible to determine the great circle propagation path of some of the resonance events which are examined here.