## 1. Introduction

[2] Perturbations in the height and electron density of the ionosphere have been studied for decades. The amplitudes of these disturbances are typically small compared with the diurnal variation in the ionosphere. Use of a band-pass filter, combined with some test for signal coherence, is thus necessary in order to detect these disturbances in the presence of the much larger long-period variations.

[3] Short period (less than 10 min) disturbances, propagating near the speed of sound (700–1800 m/s), have been associated with shock acoustic waves generated by impulsive sources in the neutral atmosphere. Some sources include large earthquakes [*Calais and Minster*, 1995; *Afraimovich et al.*, 2001b; *Ducic et al.*, 2003; *Wolcott et al.*, 1984; *Otsuka et al.*, 2006], rocket launches [*Calais and Minster*, 1996; *Afraimovich et al.*, 2002; *Jacobson and Carlos*, 1994], large chemical explosions [*Calais et al.*, 1998; *Blanc and Jacobson*, 1989; *Fitzgerald*, 1997], and nuclear weapon tests [*Hines*, 1967].

[4] *Calais et al.* [2003] applied an array processing technique, using a 3–10 min band-pass filter, to GPS measurements from the Southern California Integrated GPS Network (SCIGN) [*Hudnut et al.*, 2001] to search for disturbances following the 16 October 1999 Hector Mines earthquake. Several waves were detected in that experiment. None of them, however, occurred at times that were compatible with the earthquake as a source. Those findings motivated the research which is presented in the present paper.

[5] The first step in determining the origin of these disturbances, which do not appear to be associated with known impulsive events in the atmosphere or the solid Earth, is to characterize the statistics of their occurrence.

[6] The following research was undertaken to develop an automated method for processing large sets of GPS measurements (one or more years) to detect these disturbances and estimate their speeds and directions of propagation. The time and propagation vector for individual disturbances could then be used to search for possible sources. A large ensemble of disturbances could also be studied to look for variations which are, for example, seasonally dependent or correlated with geomagnetic conditions.

[7] Dual-frequency GPS receivers are commonly used to measure the integrated electron content (IEC) through a linear combination of the pseudorange and carrier phase from the L1 and L2 frequencies (1575.42 MHz and 1227.6 MHz, respectively) [*Mannucci et al.*, 1998]. A network of hundreds of GPS receivers, such as SCIGN, provides for a dense sampling of the ionosphere and thus offers the possibility of detection and study of these disturbances through the optimal fusion of many measurements.

[8] Algorithms for the processing of an entire array of data must be computationally efficient, given the large number of stations presently available (250 in SCIGN). Thresholds for the detection of a disturbance and quality control of the data must be set autonomously to allow the processing of data over a long period of time without operator intervention. Both of these requirements were important considerations in this research.

[9] One previously developed method for the detection of ionospheric disturbances in GPS data is the Statistical Angle-of-Arrival and Doppler Method (SADM-GPS) [*Afraimovich et al.*, 1998, 2000, 2003]. SADM-GPS computes the gradient in IEC measurements from three stations and projects this vector onto a two-dimensional plane to yield a time series of instantaneous propagation velocities. The velocity measurements are then time-averaged to reduce the noise and produce the propagation speed and direction, assuming a plane wave model. The detection threshold in *Afraimovich et al.* [2003] was based on the amplitude of the IEC variation. The width of the main lobe of the disturbance spectrum was used as a test of the quasi-monochromatic assumption.

[10] The method to be presented in this paper uses the cross-correlation between many pairs of IEC time series produced from receivers in the network. These cross-correlation measurements are constrained by a geometric model that is inverted to estimate the speed and direction of a propagating disturbance.

[11] The remainder of this paper is organized as follows: The method for estimating velocity from the filtered IEC time series is described in section 2. Section 3 introduces the statistical tests applied to determine the quality of the velocity estimate and the method for removing the effects of satellite motion to reconstruct undistorted IEC waveforms. Section 4 contains simulation results and sensitivity studies, and section 5 presents the experimental results. Section 6 compares the results in this paper with other published findings and makes recommendations on the use and limitation of our method for studying short-period disturbances in the ionosphere.