METHOD AND APPARATUS FOR SEISMIC EXPLORATION USING NON-LINEAR SWEEPS

METHODE ET DISPOSITIF DE PROSPECTION SISMIQUE A BALAYAGE NON LINEAIRE

English Abstract

A B S T R A C T
The invention is for a method of seismic exploration
involving the generation of a nonlinear signal of predetermined
shape at the output of a sweep generator which comprises the
steps of dividing the sweep time of the output signal into a
plurality of preselected time intervals, calculating the rate
of change of the frequency of the output signal for each time
interval to realize the predetermined shape based on the range
of the sweep, the sweep time, the starting frequency and the
predetermined shape, and using each value in the calculating
step to change the rate of change of frequency of the sweep
signal, and the invention includes the apparatus specifically
adapted to carry out the inventive method.

Claims

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The embodiments of the invention in which an exclusive
property or privilege is claimed are defined as follows:
1. A method of seismic exploration, comprising the steps
of:
establishing at least one seismic array at a
location on the earth's surface, each said
seismic array containing seismic detectors;
establishing at least one vibrator at a location
on the earth's surface, each said vibrator
having the capability of sweeping through a
range of frequencies during a preselected
sweep time and each said vibrator including
a sweep generator;
generating an output signal from the sweep gener-
ator which varies as a function of time
during the sweep time as follows:
<IMG>
where:
t is the instantaneous value of time during the
sweep in seconds;
Fo is the frequency at which the sweep starts
in Hz;
R is the range of frequencies over which the
sweep varies during the sweep time;

-13-
Ao is the initial rate of change of frequency
with respect to time; and
C is the logarithm to the base 10 of the ratio of
the response at high frequency to the response
at low frequency, where C is chosen to provide
compensation for any attenuation which exists
to a particular impedance boundary over the
range R.
receiving seismic data with the arrays of detectors
located on the earth's surface; and
recording the received seismic data.
2. The method of claim 1, wherein the frequency of the
sweep signal varies from 10 Hz to 110 Hz during a sweep
time of 10 seconds, and wherein the output signal from
the sweep generator varies as a function of time during
the sweep time as follows:
fi(t) = 10 + 43.43 1n [0.9t+1],
in order to compensate for an earth attenuation of 20
decibels over the frequency range of 10 to 110 HZ.
3. A method of generating one of a plurality of possible
non-linear sweep signals of predetermined time and shape at
the output of a sweep generator in a seismic exploration system,
comprising the steps of:
(a) dividing the sweep time of the output signal into
a plurality of preselected time intervals;

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(b) calculating the rate of change of the fre-
quency of the output signal for each time
interval to realize said predetermined shape
based on the range of the sweep, the sweep
time, the starting frequency and the prede-
termined shape; and
(c) using each said value calculated in step (b)
to change the rate of change of frequency of
the sweep signal.
4. Apparatus for producing a nonlinear sweep signal,
comprising:
means for generating signals representative of
the rate of change of frequency of the
sweep signal for each of a plurality of
time intervals of the sweep time;
means for storing said rate of change signals in
a memory; and
means for commencing the sweep signal at the
starting frequency; and
means for changing the frequency of the sweep
signal during each time interval of the sweep
at the rate stored in said memory for each
said time interval.

Description

7S~i
METHOD AND APPARATUS FOR SEISMIC
EXPLORATION USING NONLINEAR SWEEPS
The present invention relates to method and apparatus
for seismic exploration, and, more particularly, to pro-
viding a nonlinear sweep signal to a vibrator in a seismic
system.
In seismic exploration, seismic waves are commonly
used to probe the earth's crust as a means of determining
the type and location of subsurace formations. The
earth's crust can be considered a transmission medium or
filter whose characteristics are to be determined by pass-
ing seismic waves through that medium. In the reflection
seismic method, seismic waves or impulses are generated at
a point at or near the earth's surface, and the compres-
sional mode of these waves is reflected from subsurface
acoustic impedance boundaries and detected by arrays of
seismic detectors located at the earth's crust. The
seismic detectors convert the received waves into electri-
cal signals which are sensed and recorded in a form which
permits analysis~ Skilled interpreters can discern from
such an analysis the shape and depth of subsurface refiec-
tion boundaries and the likelihood of finding an accumula-
tion of minerals, such as oil and gas.

Si95
Various sources of seismic energy have been utilized
in the art to impart the seismic waves into the earth's
crust. Such sources have included dynamite and weight-
drop apparatus.
Another source of seismic energy is a vibrator
which, ~hen energized, imparts relatively low level
energy signals into the earth's crust. Typically, the
impartation of energy with vibrator devices is for a
preselected energization interval, and data are recorded
during the energiæation interval and a subsequent "lis-
tening 17 interval.
Often it is desirable for the vibrator to impart
energies of varying frequencies into the earth's crust
during the energization interval. In such instances,
energy at a starting frequency is first imparted into
the earth, and the frequency of energization changes over
the energization interval at some rate until tl~e stopping
frequency is reached at the end of the interval. The
difference between the starting and stopping frequencies
of the sweep generator is known as the range of the
sweep, and the length of time in which the generator has
to sweep through those frequencies is know~ as the sweep
time.
Vibrators typically employ a sweep generator t and
the output of the sweep generator is coupled to the inpu~
of the vibrating type device. The output of the sweep
ge~erator dictates the manner in which the frequency
of the energization signal which is imparted into the
earth's crust varies as a function of time~

` 1~l~75~fi~
~3--
Several methods of e~fecting the rate of change of
the frequency of the sweep generator during the sweep
time have been proposed. For example, in the case of a
linear sweep, the frequency output of the sweep generator
changes linearly over the sweep time at the rate dictated
by the starting and stopping frequencies and the sweep
time. Further, nonlinear sweeps have been proposed in
which ~he rate o~ change of the frequency of the sweep
generator varies nonlinearly between the starting and
stopping frequencies over the sweep time. Examples of
nonlinear sweeps have been quadratic sweeps and square
root sweeps.
It is known in the seismic exploration art that the
higher frequencies of energization signals are attenuated
to a greater degree than lower frequency energization
signals, and most authorities have concluded that the
attenuation of the earth in decibels is directly propor-
tional to the frequency of the energization signal.
Further, the total attenuation of any specific signal
is known to ~e dependent upon the velocity, layering,
thickness and attenuation coefficients of each layer
traversed, as well as the frequency range.
Even though the earth attenuation is known to in-
crease with increasing frequency of the energi~ation
signals, linear sweeps have been extensively used in
vibrators. Techniques for emphasizing the lower ampli-
tude higher frequenc~ responses are well-known and have
been employed to account for the attenuation applied to
these higher frequency seismic signals by the earth.
Nonlinear sweep signals have been suggested but
have not achieved acceptance by the industry due to
poor performance.

~ ~7S915
--4--
The shortcomings of the prior art are overcome with
the method and apparatus of the present invention.
In accordance with the present invention, a method
of seismic exploration is provided wherein an optimal
nonlinear sweep signal is presented to the source of
vibrating seismic energy.
In accordance with the method of the present inven-
tion, at least one array of seismic detectors is estab-
lished at a location on the earth's surface and at least
one vibrator is also established on the earth's surface.
The vibrator includes a sweep generator. which generates
an output signal. The output signal of the sweep genera-
tor is nonlinear, and preferably, varies as a function of
time during the sweep time as follows:
Fo+0.43429 R [ln (2.3026CAot+1)]
C R
where:
t is the instantaneous value of time during the
sweep in seconds;
Fo is the frequency at which the sweep starts
in Hz;
R is the range of frequencies over which the sweep
varies during the sweep time;
Ao is the initial rate of change of frequency
with respect to time; and
C is the logarithm to the base lO of ~he ratio of the
3,

7595
--5--
response at high frequency to the response at low
frequency. C is chosen to provide compensation for
any attenuation which exists to a particular impedance
boundary over the range R.
In one embodiment wherein the starting frequency of the
swcep is 10 ~Iz, the stopping frequency of the sweep is 110
Hz, the sweep time is 10 seconds, and the attenuation of the
earth is a total of 20 db, the frequency of the sweep signal
which will exactly compensate for this attenuation, varies
over the sweep time as follows:
10+43.~3 ln (.9t+1).
In accordance with the present invention, a method of
generating an output signal of a predetermined shape is also
provided. The method comprises dividing the sweep time of
the output signal into a plurality of preselected time
intervals. The method also comprises calculating the rate of
change of the frequency of the output signal for each time
interval to reali~e said predetermined shape based on the range
of the sweep, the sweep time, the starting frequency of the
sweep and the predetermined shape of the output signal. The
signals representative of the rate of change of the output
frequency are then fed to a frequency generator, which generates
the output signal.
The invention also pertains to apparatus for producing
a non-linear sweep signal, comprising means for generating
signals representative of the rate of change of frequency of
the sweep signal for each of a plurality of time intervals
of the sweep time, means for storing the rate of change signals
in a memory, means for commencing the sweep signal at the
starting frequency, and means for changing the frequency of
the sweep signal during each time interval of the sweep at
the rate stored in the memory for each time interval.
In the accompanying drawings:
Figure 1 is a pictorial diagram which illustrates component
parts of a seismic exploration system.
, ~ ~

~;~7S9~ .
--6--
Figure 2 is a block diagram of some of the component
parts of the vibrator depicted in Figure 1.
Figure 3 is a graphical illustration of an experimen-
tal frequency response using a linear sweepO
Figure 4 is a graphical illustration of an experimen-
tal frequency response using a nonlinear sweep in accor-
dance with the present invention.
Figure 5 is an electrical schematic in block diagram
form of apparatus for generating a nonlinear sweep signalO
Figure 6 is an electrical schematic in block diagram
form of a programmer apparatus.
Figure 7 is a more detailed electrical schematic of
portions of the circuitry illustrated in Figures 5 and 6.
It will be appreciated that the present invention can
take many forms and embodiments. Some embodiments of the
invention are described so as to give an understanding of
the invention. It is not intended, however, that the
embodiments described herein should in any way limit the
true scope and spirit of the invention.
Referring first to Figure 1, portions of a seismic
exploration system are illustrated. ~s shown, the system
comprises a plurality of seismic arrays 101. Each seismic
array 101 contains a plurality of seismic detectors 102.
The seismic arrays 101 are preferably located at regularly
spaced intervals along the earth's surface.

--7--
The system illustrated in Figure 1 also includes
recording cable 104, which is preferably a multi-pair of
cable. A pair of wires 103 is ~taken out" of cable 104
and is connected to the output of each seismic array 101.
Electrical signals generated by the seismic deteetors 102
in seismic arrays 101 are conveyed via the multi pair of
cable 104 to recording truck 105, where appropriate field
recording of the signals takes place.
The system illustrated in Figure 1 also includes
a source of seismic energy, which is shown as vibrator
1~7. Periodically, vibrator 107 imparts low `level seismic
waves into the earth. The seismic arrays 101 produce
electrical si~nals in response to the reflected portions
of the sei~mic waves, and the electrical signals are then
conveyed to recording truck 105.
Now referring to FIG. 2, there are portions of the
elements of vibrator 107 of FIG. 1 are illustrated.
Vibrator 107 includes sweep generator 201, hydraulic
valve 202, hydraulic piston 203 and vibrator base plate
204. The output signal from sweep generator 201 is fed
to hydraulicValVe 202, which is preferably a solenoid-
actuated valve. Based on the input signal received
from sweep generator 201, hydraulic valve 202 controls
the movement of hydraulic piston 203, which in turn drives
the vibrator base plate 204~ Vibrator base plate 204 is
in contact with the earth and imparts seismic energy into
the earth's crust responsive to the movement of hydraulic
piston 203.
In many applications where vibrator units are utilized
as the source of seismic energy, energy is inputted into
the earth during an energization interval of time, and
seismic data are recorded during the energization interval
f~

7595
and for a listening interval following the energization
interval. During the energization interval, the frequency
of the input energy is often varied over a range of pre~
selected values. For example, vibrator 107 may input
energy at a frequency of 10 Hz at the start of the ener-
gization interval, and may change the input frequency at
some preselected rate over the energization interval. The
differences is known as the range of the sweep, and the
length of the energization interval is known as the sweep
time.
As noted above, it is well-known in the seismic
industry that the higher frequencies in a seismic signal
are subject to greater earth attenuation than the lower
ones and that this attenuation in decibels is directly
proportional to the frequency. Thus, the higher frequen-
cies inputted in the earth's crust by vibrator 107 will
suffer more attenuation than the lower frequency signals
inputted by vibrator 107.
In accordance with the present invention, sweep
generator 20~ is designed to provide a nonlinear signal to
hydraulic valve 202 to provide nonlinear control of the
frequencies inputted into the earth by vibrator 107, as
vibrator 107 sweeps through the range of frequencies which
are to be inputted at any given time. Preferably, the
frequency of the output signal from sweep generator 201
varies as a function of time during the sweep as follows:
Fo+0.43429 R lln (2.3026CAot-~1)] (1)
C R
where:
t is the instantaneous value of time during the
sweep in seconds;

7S95
_9_
Fo is the frequency at which the sweep starts
in Hz;
R is the range of frequencies over which the sweep
varies during the sweep time;
Ao is the initial rate of change of frequency
with respect to time; and
lQ C is the logarithm to the base 10 of the ratio of
the response at high frequency to the response
at low frequency. We have discovered that the
value of C may be chosen to provide compensa-
tion for any attenuation which exists to a
particular acoustic boundary over the range R.
In a specific embodiment where the frequency of the
signals inputted into the earth are to vary between 10 H~
and 110 Hz over a sweep time of 10 seconds and assuming
that the attenuation of the earth is a total of 20 db
between 10 ~z and 110 Hz, ~he frequency of the output
signal from sweep generator 201, which will exactly
compensate for this attenuation, varies over the sweep
time as follows:
10+43.43 ln (0.9t+1).
For example given above, experimental responses have
been generated for not only the instance where the output
signal of sweep generator 201 is linear, but also for the
instance where the output signal from sweep generator 201
is in accordance with the generalized logarithmic expres-
sion above. The experimental results for the linear sweep
are shown in Figure 3, while the experimental results for
the logarithmic sweep are shown in Figure 4~ It will be
. .

7595
--1 o-- .
observed that, with the logarithmic sweep, the relative
frequency response in substantially flat over the range
of frequencies in question. Thus, with the method of the
present invention, the frequency response over the range
of frequencies in the sweep is markedly improved, and
compensation for earth attenuation has been obtained.
In accordance with the present invention, apparatus
is also provided for generating a nonlinear signal at the
output of a sweep generator. Referring to Figure 5, such
apparatus includes nonlinear range generator 50t, frequency
generator 502 and sine function generator 503. Nonlinear
range generator 501 inputs signals representative of the
rate of change which is required in the frequency of the
15 SWEEP OUT signal. The rate of change of frequency signals
are provided at preselected time intervals during the
sweep. Frequency generator 502 responds to the rate of
change in frequency signals to produce output signals
representative of the new frequency. Sine function
generator 503 converts the digital output of frequency
generator 502 to an analog signal of the desired frequency
at its output (SWEEP O~T ) .
A significant feature of the apparatus of the present
invention is that nonlinear range generator 501 provides
rate of change of frequency signals to frequency generator
502. By this technique, relatively smooth transistions in
the frequency of SWEEP OUT are realized. On the other
hand, prior attempts to provide a nonlinear output have
attempted to provide change in frequency information to
the sweep generator. With this latter approach, ~mooth
transitions in output frequency have not been achieved.

7S95
- 1 1 -
Referring now to Figure 6, the rate of change of
frequency signals over the sweep are generated as follows.
Programmer 600 includes processor 602 and front panel
control 601. The values of the starting frequency of the
sweep, the range of the sweep, the sweep time, and the
desired shape of the nonlinear output are programmed in
front panel control 601. Processor 602 reads this pro-
grammed information. Processor 602 also divides the sweep
time into small intervals of time, and i~ a preferred
embodiment, these intervals of time are four milliseconds.
For each four millisecond interval, processor 602 calcu-
lates the rate of change of frequency required to realize
the desired output of the sweep generator. The rate of
change of frequency is then stored in non-volatile storage
device 603, which is preferably an electrically erasable
programmable read only memory (EEPROM) card. Preferably,
the EEPROMs of non-volatile memory storage device 603 has
a storage capacity of 4,096, eight-bit words. The con-
tents of non-volatile storage device 603 thus contains the
information necessary for the SWEEP OUT signal ~o move
from the starting frequency to the stopping frequency in
the sweep time according to the nonlinear function desired.
Preferably, the nonlinear function realized is as set
forth in expression (1) above.
~5
Now referring to Figure 7, there is illust~ated a
detailed implementation of the nonlinear range generator
501, frequency generator 502 and sine function generator
503 of Figure 5.