1.000 A501 B501 C501 … YY501 ZZ501 1.002 A502 B502 C502 … YY502 ZZ502 Multiplexed order: A001, B001, C001 etc.
De-Multiplexed order: A001, A002, A003 etc.
When data is stored in de-multiplexed format (often known as a trace sequential format), the groups of numbers are (logically) referred to as "traces".
For multiplexed formats, the group of numbers are often referred to as a "scan" - the data from all channels at one time.
Recording filters
Before we get deep into the business of recording filters, we need to define a couple of terms.
Filters are applied to the seismic data before it is digitised to remove (among other things) frequencies above the Nyquist frequency for the sample rate we are using.
These filters are, of necessity, analogue filters (somewhat more
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complicated than the one shown here!), with cut-off frequencies defined in Hertz, and "slopes" that are usually specified in dB's per octave.
Decibels
A bel (named after Alexander Graham, not ding-dong!), is defined as the logarithm (to the base 10) of a power difference.
For example, one of the fastest piston-engined aircraft, the North American P-51D Mustang, has flown with an engine that develops 3000 hp. This compares with the 0.85 hp of Karl-Friedrich Benz's first car in 1885.
The power ratio here is 3000 ÷ 0.85, or about 3530:1. Taking the logarithm of this ratio, we can express this difference as "3.55 bels".
The bel was soon found to be a somewhat unwieldy unit. The total range of sound audible to humans, from the flap of a butterfly's wings to the threshold of pain (or the average rock concert) represents a power difference of about 1,000,000,000,000 to 1, or about 12 bels.
In order to be able to use a unit with more meaning, the decibel (dB), or one tenth of a bel has come into general use. Thus the range of human hearing is usually expressed as about 120 dB.
The dB is a power ratio. If we are dealing with amplitudes (of, for example, a seismic trace) then, as power equates to the amplitude squared, we can define the decibel as:-
120 Where A1 and A2 are amplitudes.
Here's some typical amplitude ratios expressed in the logarithmic scale of dB:-
Amplitude Ratio Log10 dB Approx.
1:1 0 0 0
1.4:1 0.14613 2.92256 +3dB
2:1 0.30103 6.0206 +6dB
4:1 0.60206 12.0412 +12dB 8:1 0.90309 18.0618 +18dB
10:1 1 20 +20dB
100:1 2 40 +40dB
0.7:1 -0.1549 -3.098 -3dB 0.5:1 -0.301 -6.0206 -6dB
0.1:1 -1 -20 -20dB
Octaves
We're probably familiar with the concept of octaves in a musical sense.
Here's the centre three octaves of a piano keyboard (middle "C" marked in red), with a plot showing the frequency of each note (including the black ones!).
Use the buttons to switch the frequency axis to a logarithmic scale. It should now be obvious that the frequency for each note is a constant factor (about 1.0595) times the frequency for the previous note; a geometric progression.
The ratio is actually equal to the 12th root of 2 - each octave (12 notes) representing a doubling of
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frequency. (The "A" below middle "C" is a fixed point - 440 Hz.)
An octave is, once again, a logarithmic scale representing the ratio between two different frequencies (it comes out as about 3.322 x Log10 of the frequency ratio). This following shows some frequency ratios expressed in octaves:-
Frequency 1 Frequency 2 Ratio Octaves
10 15 1.5 0.58496
10 20 2 1
10 40 4 2
10 80 8 3
80 40 0.5 -1
80 10 0.125 -3
50 70.71 1.4142 0.5
dBs/Octave
It we put the two concepts of dBs and Octaves together, we get a "Log/Log" scale.
This plot shows some typical filter "slopes" specified in dBs per octave. I've used an amplitude of "1"
at 50 Hz as my starting point (remember that both dBs and octaves are relative measures).
As 6dB is about one half, a slope of 6dB per octave means we halve the amplitude at half the frequency - amplitude is proportional to frequency.
12dB per octave applies a scalar equal to frequency squared, and so on.
Switch the axes to log scales to see the different representations of the slopes - the only all appear linear on the log-log scale.
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Recording filters
Now we've worked our way through that lot, we can talk about recording filters!
Here's the amplitude response of a typical recording filter.
Plotted on a logarithmic amplitude scale (dB), this shows the frequency passband for a 8 to 77 Hz filter, with slopes of 18 dB/Oct. at the low end, and 70dB/Oct. on the high end.
This filter is designed for recording data at a 1 millisecond sample interval - if we recorded the data at 2 ms, the amplitudes present above 250 Hz would still alias - they are only about 25 dB down, or about 5% of the maximum
amplitude.
Another vital characteristic of a recording filter is its phase response. This shows the "shift"
introduced into each frequency component by the electronics.
A phase shift is inevitable in a recording filter, but, the best types of filters have a linear phase shift over the important (the strongest)
frequencies.
This curve is fairly linear over the region of highest amplitudes, this (as we will see later) will introduce an overall time shift in our data, but will not affect the timing of the individual frequency components in the seismic trace.
Although the high-cut filter is very important to prevent aliasing, a low-cut filter is not always applied
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(often referred to as "OUT"). This can cause some unwanted low frequency noise that can be removed in the processing, provided that it doesn't completely obliterate the signal!
It's important for the person processing the data to be aware of any changes in recording filters within one seismic survey. Because both the amplitude and phase characteristics of the recorded data are irreversibly affected by this filter, data recorded using different filters will not "tie".
It's usual for the signatures supplied to the processing centre by a marine vessel acquiring data to be recorded with the same filter as the seismic data - just make sure you use the right filter for the right data!
What is the effect of high-cut filters on the appearance of seismic data?
The small piece of (fully processed) seismic data shown here has been filtered with a whole range of high-cut filters.
These were applied in the processing as digital filters, which do not introduce any time shifts in the data.
Note the changes in fine detail as the high-cut moves lower. (The data are sampled at 4 ms so 125 Hz
= no filter.)
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