1. Introduction

[2]  Many papers have been dedicated to studies of the ionospheric response to disturbances generated at the pulse impact on the terrestrial atmosphere [Ahmadov and Kunitsyn, 2003, 2004; Calais and Minster, 1995; Golitsyn and Klyatskin, 1967; Orlov and Uralov, 1984; Pavlov, 1986; Row, 1967; Rudenko and Uralov, 1995]. Nuclear tests, industrial explosions, and large earthquakes may be considered as sources of such impacts. The shift of the Earth surface leads to generation of acoustic gravity waves (AGW) propagating in the atmosphere with an increase of the amplitude up to high altitudes where they are able to initiate the plasma motion due to the collision interaction of neutral and charged particles.

[3]  The ionospheric irregularity influences significantly the evolution of the acoustic wave. At the upward propagation there occurs an increase of the wave amplitude and in the case of weak dissipation nonlinear effects appear [Pavlov, 1986]. A shock wave is formed and at the accent its profile gets a triangle shape [Uizem, 1977].

[4]  The specific mechanism of formation of such disturbances is not yet clear. There are a few models explaining ionospheric disturbances: generation of infrasonic waves [Calais et al., 1998], generation of IGW [Francis, 1975], eddy motions of the neural atmospheric constituents excited after a passage of the acoustic pulse [Andreeva et al., 2001], generation of shock-acoustic waves (SAW) [Afraimovich et al., 2001a, 2001b; Nagorsky and Taraschuk, 1992], and so on. Various terms different by physical interpretation are used in the publications for the ionospheric response of the shock wave including the term shock-acoustic wave [Nagorsky, 1985; Nagorsky and Taraschuk, 1992]. For the sake of convenience in this paper we will use this term as well as the more general term "ionospheric disturbance" (ID).

[5]  The approach to solution of the problem of ionospheric disturbance generation during earthquakes is present even in early publications and includes a substitution of the epicenter emitter by a ground-based point source of velocity or by an explosion. The substitution of the earthquake zone by a point source is fruitful describing long-period AGW at very long (thousands of km) distances from the epicenter [Row, 1967]. Visual similarity of ionospheric disturbances at small (hundreds of km) distances from the epicenter to disturbances from ground-based explosions was discussed by Calais et al. [1998].

[6]  Barry et al. [1966] showed that according to the theory of the linear acoustics a large ground-based surface explosion is able to generate a pressure wave with the amplitude reaching a few percents of the background atmospheric pressure at a height of 200 km over the explosion epicenter. The analysis of the interaction of this wave to the ionosphere makes it possible to assume that such a wave can be detected by the ionospheric diagnosis methods. Measurements conducted in July 1964 by a high-quality vertical sounding during the 500-t explosion (Suffield, Alberta, Canada) confirmed this hypothesis. The amplitude and duration of the detected phase disturbances were 100 rad and 2 min, respectively, the disturbance phase corresponding to the modeling results for the acoustic wave.

[7]  Fitzgerald [1997] 565 s after the surface explosion in New Mexico with the efficient energy of 2 kt ( 8.5 10¹² J) detected by the method of the GPS monitoring of the total electron content (TEC) a disturbance with an amplitude of 0.14 TECU ( 10¹⁶ el m^-2 ) and duration of 80 s. The acoustic disturbance needed to produce such ionospheric disturbance is well modeled as an N wave with the spatial dimensions and relative amplitude of 35 km and 12%, respectively, propagating with a radial velocity 700 m s^-1. Similar results concerning the ionospheric response of this explosion have been earlier obtained registering TEC by the measurements of rotation of the polarization plane of the signal from the geostationary satellite GOES [Massey et al., 1994].

[8]  During conducting three powerful explosions in eastern Wyoming (United States) in July and August 1996 five GPS receivers were installed [Calais et al., 1998]. Ionospheric disturbances what began 10-15 min after the explosion and lasted about 30 min propagating with a horizontal velocity of 1200 m s^-1 were registered. These irregularities were interpreted as disturbances formed by the direct acoustic wave generated by the explosion.

[9]  Using the GPS receivers, Calais and Minster [1995] 10-30 min after the earthquake in California on 17 January 1994 (with a magnitude of 6.7) observed in the time series of TEC anomalous signal in the period range 3-10 min. The frequency and propagation phase velocity (300-600 m s^-1 ) agree to the results of numerical simulation for atmospheric AGW caused by a strong shift of the Earth surface during the earthquake.

[10]  It should be noted that despite the above mentioned similarity in ionospheric disturbances caused by industrial ground-based and underground nuclear explosions, the generation mechanisms are principally different [Rudenko and Uralov, 1995]. The Earth surface disturbed by the explosion is a source of emission at an underground nuclear test as well as at an earthquake. The intensity and spectral composition of the generated acoustic signal demonstrate (unlike a surface explosion) a strong dependence on the zenith angle and are completely determined by the form, dimensions, and characteristics of the Earth surface motion in the epicenter of the underground explosion zone. The width of the "directivity diagram" of the acoustic signal propagating from the disturbed Earth surface is very narrow: Dq 5^o. The shape and duration of the signal depend strongly on the zenith angle q of the acoustic ray from the epicenter [Rudenko and Uralov, 1995].

[11]  The scheme of formation and propagation of an ionospheric disturbance from a swallow underground source was presented by Rudenko and Uralov [1995]. The underground point of explosion e generates a spherical elastic wave in the rocks. Its appearance on the Earth surface ( z = 0 ) one can compare to a strong shock. As a result the rock pieces A-G are "separated" [Rodionov et al., 1971], then slightly lifted and then return to the initial position. This process is accompanied by generation in the atmosphere of an acoustic wave. Because of strong nonlinearity of the characteristics (parameters) of the air near the "lithosphere-atmosphere" boundary high-frequency seismic signals may generate air streams inducing low-frequency waves in the atmosphere. The nonlinear flow plays the role of an energetic connection between the high-frequency seismic motions and low-frequency atmospheric waves.

[12]  In some papers [Ahmadov and Kunitsyn, 2003, 2004; Pavlov, 1979, 1986; Row, 1967] a grounding of the model is presented. In this model the ionospheric response to an earthquake is caused by a wave disturbance from the secondary source located not in the epicenter but at ionospheric heights over the epicenter. However, no confirmation of such mechanism has been presented in publications.

[13]  Currently, the principal time parameters characterizing ionospheric response to SAW (shape, amplitude, and period) are studied fairly well. In publications, there is a strong scatter of the data on the main parameters of SAW generated during earthquakes. The oscillation period and propagation velocity of the ionospheric response to SAW vary from 30 to 300 s and from 700 to 1200 m s^-1, respectively [Afraimovich et al., 1984; Blanc and Jacobson, 1989; Calais et al., 1998; Fitzgerald, 1997]. Determination of spatial-time characteristics of ionospheric disturbances (ID) still stays an actual problem. This problem includes a wide set of tasks, in particular: calculation of the phase and group velocity of ID, determination of the direction of its propagation and location of the disturbance source, and also a wider problem of studying of the shape and dynamics of the SAW front propagation.

[14]  The absence of complete and reliable data on the SAW parameters is due mainly to the defects of the existing radiophysical methods and detection means. The main amount of the data has been obtained by measurements of the Doppler frequency shift at the vertical and oblique radiosounding of the ionosphere in the HF range [Afraimovich et al., 1984; Li et al., 1994; Nagorsky and Taraschuk, 1992]. The sensitivity of this method in some cases is sufficient for detecting SAW; however, difficulties arise with localization of the formation region of the detected signal, the latter fact being due to the multihop character of HF signal propagation.

[15]  The need for information on the time of the event (industrial explosion or earthquake) is the common defect of the above described methods because the disturbance propagation velocity is calculated using the SAW delay relative the event beginning and assuming the constancy of the velocity along the propagation path (which does not always correspond to the reality).

[16]  Afraimovich et al. [1998, 2001b, 2004] developed a method of determination of the phase velocity and propagation direction of ID using three spatially diverse GPS receivers in the plain front approximation. Unlike the radiophysical methods known earlier, the proposed method provides an estimation of the SAW parameters without a priori information on the place and time of the pulse impact. The period of detected shock-acoustic waves was 180-390 s, and the amplitude exceeded the standard deviation of the background fluctuations of TEC in this range of periods in quiet and moderately disturbed geomagnetic conditions as a minimum by a factor of 2. The elongation angle of the wave vector varied in the limits 20^o - 44^o and the horizontal component of the phase velocity (1100-1300 m s^-1 ) was close to the sound speed at heights of the maximum of the ionospheric F region. These data agree to the available ideas on the generation of shock-acoustic waves caused by piston-like motions of the Earth surface in the epicenter zone of the earthquake.

[17]  Afraimovich et al. [2001a] developed a method of determination of the phase velocity and arrival direction of ID based on the spatial-temporal processing of the TEC variations in the ionosphere on the grating of GPS stations with number higher than three. However, this method is applicable only in the case of a small deviation of the wave front from the plain one. Afraimovich et al. [2002a] proposed a method of calculation of ID characteristics (the phase velocity and source location) in the near zone of the earthquake epicenter, that is, when one cannot neglect the spherical character of the wave front.

[18]  Both these methods [Afraimovich et al., 2001a, 2002a] are based on the concept of using networks of GPS receivers as a nonequidistant phased antenna grating (PAG) proposed by Afraimovich [2000]. The coherent processing of variations in TEC measured simultaneously for all rays at the satellite at all stations of the GPS grating selected for the analysis is based on the known PAG algorithms. Depending on the type of the analyzed disturbance the form of the PAG complex characteristic is chosen corresponding to the spatial-time properties of the given disturbance.

[19]  Using GPS gratings in the remote zone of the source in the approximation of the plain front makes it possible to determine the horizontal component of the phase velocity and the direction of the wave vector of the disturbance, but neither the time of switching nor coordinates of the point source. Determination of the coordinates in the horizontal plane becomes possible in this approximation in the regions with a dense network of GPS stations when one can select widely spaced relative to the assumed source various GRS gratings.

[20]  In the approximation of a spherical front vice versa the coordinates and the switching-on time may be determined in the near zone of the source; however, a problem of determination of the source height (and so of determination of the phase velocity) appears. Only joint complex use of these approximations proposed in this paper makes it possible to estimate the velocity, coordinates, and switching-on time of the disturbance source.

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