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where  is the azimuth difference between the rock fall direction and the beam axis,  rf the
average angle of rock fall relative to the horizontal and  ant the elevation angle of the beam.
Approximate angle values determined from field observations (45°,  rf 35°, and  ant 22°
for the lowest part of the beam) lead to rock falls velocities equal to 1.45 times the measured
radial velocities. With maximum radial velocities commonly in the range 7-14 m/s, the
upper range of rock fall velocities is 10 to 20 m/s. Likewise, average rock fall speeds can be
estimated from the time delays of power onsets in successive range gates and the gate radial
resolution.
Fig. 17. Radar and seismic signals associated with rock falls at Arenal (02/02/2009). Bottom :
25 minute record of power from two range gates hitting the volcano upper slopes, where
rock falls are detected by VOLDORAD; middle : maximum radial velocity (component
towards radar) superimposed on a color spectrogram showing the seismic frequency
content associated with rock fall events; top : seismic trace of a large rock fall and view of
Arenal's summit from north showing lava flows and rock falls producing dust (seismic data
courtesy of M. Mora; photo © F. Donnadieu, 14/05/2006).
In theory, the volume of rock falls could be determined from the power measured by the
radar. In the case of Arenal, however, the size distribution of the fragments tumbling down
the flanks is unknown and challenging to measure. Also, rock falls occurring in corridors
can be masked by topographic obstacles or take place in other directions not visible to the
radar so that it is likely that not all the falling material is detected and some events can even
remain undetected by the radar. Nevertheless, as most rock falls are generated in
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