Noise removal on Shearer's data

Professor Peter Shearer gathered the earthquakes from the IDA network, an array of about 25 widely distributed gravimeters, donated by Cecil Green, and Shearer selected most of the shallow-depth earthquakes of magnitude greater than about 6 over the 1981-91 time interval, and sorted them by epicentral distance into bins $1^\circ$ wide and stacked them. He generously shared his edited data with me and I have been restacking it, compensating for amplitude in various ways, and planning time and filtering compensations.

Figure  shows a test of noise subtraction by multidip narrow-pass filtering on the Shearer-IDA stack. As with prediction there is a general reduction of the noise. Unlike with prediction, weak events are preserved and noise is subtracted from them too.

 

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Figure 14 Stack of Shearer's IDA data (left). Multidip filtered (right). It is pleasing that the noise is reduced while weak events are preserved.

Besides the difference in theory, the separation filters are much smaller because their size is determined by the concept that ``two dips will fit anything locally'' (a2=3), versus the prediction filters ``needing a sizeable window to do statistical averaging.'' The same aspect ratio a1/a2 is kept and the page is now divided into 11 vertical patches and 24 horizontal patches (whereas previously the page was divided in $3\times 4$ patches). In both cases the patches overlap about 50%. In both cases I chose to have about ten times as many equations as unknowns on each axis in the estimation. The ten degrees of freedom could be distributed differently along the two axes, but I saw no reason to do so.