# Mag1513 Results

In this experiment we looked at the event Mag1513, from the file mag_3_5_1513.asc.
The software used is documented here.

Here is a
plot of the event:

.
Note the 4 satellites are numbered 2 through 5.
We then applied a cross-correlation to the unsmoothed data.
For example, when we cross correlated the event on satellite 2

against the data from
satellites 2, 3, 4, and 5 we found this:

Please note that the cross correlations are normalized so that the values must lie in the
interval [-1,1]. (1 is a perfect match, and -1 is one function is the negative of the
other.)
The CrossCorrelation is documented here.

We next took the data, and removed the mean,
and then applied a Butterworth Filter.
(The theory of the Butterworth filter we used is here.)

After the filtering, the data looked like this:

We then extracted the events for each of the satellites:

Satellite | Event Range |

2 | Sample 1500-2500 |

3 | Sample 1500-2500 |

4 | Sample 1250-2250 |

5 | Sample 1500-2500 |

(The results will confirm this eye-ball estimate. The event occurs earlier on Satellite 4.)

Drum Role Please

The results are in the next four figures. Each plot is event x=2,3,4,or 5 cross
correlated with the filtered data from satellites 2, 3, 4, and 5. So for instance, if we are
using event 3 against data 2, 3, 4, and 5, we would expect the highest cross correlation to
occur on data 3. That is indeed the case. Here are the plots.

In each case the peak occurs when the event is measured against itself. Also the quality
of the events can be assessed:

The unfiltered data has a peak of .25 versus a much better .55 for the filtered data.

Finally when we ran the cross correlation, we recorded the sample number of the
peak. Thus we have this table:

## Lag of events with respect to the Location of Event 2

Event | Data 2 | Data 3 | Data 4 | Data 5 |

2 | 0 | 0 | 0 | 0 |

3 | -43 | 76 | -47 | -58 |

4 | 51 | 115 | 52 | 35 |

5 | -135 | -50 | -129 | -152 |

As you can see, the data (with the exception of Event 3 versus Data 3) are consistent.

In addition we see the lag of event 4 is evident. This confirms our eyeball estimate.

Of
course, this then leads to the puzzle of how the satellites are configured. But with this
information and with the location of the satellites we should be able to find out the direction of the incoming wave.

## Next

Next we will conduct the same process using the semblance, and we will process some other
events.
Wm P. Kamp