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Fraser filter

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A Fraser filter, named after Douglas Fraser, is typically used in geophysics when displaying VLF data. It is effectively the first derivative of the data.

If f ( i ) = f i {\displaystyle f(i)=f_{i}} represents the collected data then a v e r a g e 12 = f 1 + f 2 2 {\displaystyle average_{12}={\frac {f_{1}+f_{2}}{2}}} is the average of two values. Consider this value to be plotted between point 1 and point 2 and do the same with points 3 and 4: a v e r a g e 34 = f 3 + f 4 2 {\displaystyle average_{34}={\frac {f_{3}+f_{4}}{2}}}

If Δ x {\displaystyle \Delta x} represents the space between each station along the line then a v e r a g e 12 − a v e r a g e 34 2 Δ x = ( f 1 + f 2 ) − ( f 3 + f 4 ) 4 Δ x {\displaystyle {\frac {average_{12}-average_{34}}{2\Delta x}}={\frac {(f_{1}+f_{2})-(f_{3}+f_{4})}{4\Delta x}}} is the Fraser Filter of those four values.

Since 4 Δ x {\displaystyle 4\Delta x} is constant, it can be ignored and the Fraser filter considered to be ( f 1 + f 2 ) − ( f 3 + f 4 ) {\displaystyle (f_{1}+f_{2})-(f_{3}+f_{4})} .

References

Telford, W.M.; L.P. Geldart; R.E. Sheriff. Applied Geophyisics (2nd ed.).


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