Geology Reference
In-Depth Information
600
500
400
300
200
0
(a)
10
20
30
40
50
Distance (m)
Fig. 2.1
(a) A graph showing a typical
magnetic field strength variation which
may be measured along a profile. (b) A
graph of a typical seismogram, showing
variation of particle velocities in the
ground as a function of time during the
passage of a seismic wave.
15
10
5
0
-5
-10
10
20
30
40
50
60
70
80
(b)
Time (milliseconds)
fine electrical power ratios: the ratio of two power values
P
1
and
P
2
is given by 10 log
10
(
P
1
/
P
2
) dB. Since
power
is
proportional to the square of
signal amplitude A
(a)
f
(
t
)
1.0
2
10
log
(
PP
) =
10
20
log
log
(
A A
AA
)
10
1
2
10
1
2
(2.1)
=
(
)
0
10
1
2
t
Thus, if a digital sampling scheme measures ampli-
tudes over the range from 1 to 1024 units of amplitude,
the dynamic range is given by
-1.0
20
log
AA
)
=
20
log
1024
ª
60
dB
(
10
max
min
10
(b)
g
(
t
)
1.0
1.0
In digital computers, digital samples are expressed in
binary form (i.e. they are composed of a sequence of dig-
its that have the value of either 0 or 1). Each binary digit
is known as a
bit
and the sequence of bits representing the
sample value is known as a
word
. The number of bits in
each word determines the dynamic range of a digitized
waveform. For example, a dynamic range of 60 dB
requires 11-bit words since the appropriate amplitude
ratio of 1024 (= 2
10
) is rendered as 10000000000 in
binary form. A dynamic range of 84 dB represents an
amplitude ratio of 2
14
and, hence, requires sampling
with 15-bit words. Thus, increasing the number of bits
in each word in digital sampling increases the dynamic
range of the digital function.
Sampling frequency
is the number of sampling points in
unit time or unit distance. Intuitively, it may appear that
the digital sampling of a continuous function inevitably
leads to a loss of information in the resultant digital func-
tion, since the latter is only specified by discrete values
at a series of points. Again intuitively, there will be no
0.9
0.9
0.5
0.5
0
τ
2
τ
3
τ
0.0
t
-0.5
-0.5
-1.0
-0.9
-0.9
-1.0
Fig. 2.2
(a) Analogue representation of a sinusoidal function.
(b) Digital representation of the same function.
dynamic range, the more faithfully the amplitude
variations in the analogue waveform will be represented
in the digitized version of the waveform. Dynamic range
is normally expressed in the
decibel
(dB) scale used to de-
