Determination of the Trajectory of a Fireball Using Seismic Data

Details Determination of the Trajectory of a Fireball Using Seismic Data Determination of the Trajectory of a Fireball Using Seismic Data

Dec 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005agufm.p51a0912p&link_type=abstract

American Geophysical Union, Fall Meeting 2005, abstract #P51A-0912

Computer Science

Sound

6099 General Or Miscellaneous, 6299 General Or Miscellaneous

Scientific paper

We developed two methods to determine the trajectory of a fireball using the arrival times of the shock waves recorded by a seismic network. One method is analytical and the other is graphical. The analytical method is based on the assumption that the trajectory is straight and that the fireball velocity and speed of sound are constant. The unknown parameters are the azimuth and inclination angle of the trajectory, the coordinates of the intersection of the trajectory with the earth's surface, and the intersection time (t_0). As the problem is non-linear in all but one of the parameters (t_0), it is linearized by means of a Taylor expansion about a set of initial estimates and solved iteratively using damped least squares. This method was applied to fireballs recorded in the U.S.A. (Arkansas), Japan (Miyako and Kanto) and the Czech Republic (Morávka). Testing of the method with actual and synthetic data shows that the fireball velocity cannot be determined uniquely, and trades off with t_0. The parameters of the Morávka fireball were determined by others using video recordings and are highly reliable; comparison with our results show that the errors in the determination of the azimuth and inclination angle are 1.7° and 1.3°, respectively, which are not too large given the unfavorable distribution of stations. The Arkansas fireball was recorded by three-component seismometers and the observed and predicted horizontal polarizations are in good agreement. The graphical method is based on the drawing of contours of arrival times. Ideally, the contours should be elliptical for fireball shock waves but this constraint is not used when contouring the data. If the distribution of seismic stations is appropriate, the azimuth of the trajectory is obtained from the axis of symmetry of the contours, while the inclination angle is estimated from the contour spacing. Application of the methods to the four fireballs shows that the graphically derived parameters can be within a few degrees of the analytical parameters. For the Arkansas fireball the agreement between the analytical and graphical contours is excellent, and because there is no assumption behind the drawing of the graphical contours, this agreement provides additional evidence in support of the analytical method.

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