Borehole surveying employing ring laser gyroscope

A borehole mapping apparatus which employs a ring laser gyroscope. The path of the laser is defined by looping paths of laser beam travel having long and short stretches of travel. The ratio of the stretches being substantially greater than two.

BACKGROUND OF THE INVENTION 
This invention relates generally to the usage of ring laser gyroscopes in 
the determination of azimuth information in a borehole or well. More 
particularly, it relates to the optimum design and methods of usage of a 
ring laser gyroscope in the azimuth determination application, in ways to 
obtain the best possible accuracy along with minimum cost. 
The use of one or more angular rate sensors along with one or more suitable 
acceleration sensors in borehole azimuth determination is well know. U.S. 
Pat. No. 3,753,296 describes the use of a single angular rate sensor, and 
U.S. Pat. No. 4,199,869 describes the use of two angular rate sensors, 
each having two axes of measurement sensitivity. In each of these patents, 
suitable acceleration sensors are provided to complete the required 
sensing functions. U.S. Pat. No. 4,197,654 describes the use of a single 
angular rate sensor having its axis of sensitivity canted so that a 
component of the input axis of sensitivity lies along the borehole axis. 
The environmental and physical limitations of borehole surveying or 
direction measurement create significant problems for high accuracy 
measurements using conventional gyroscopes or other conventional angular 
rate sensors. Wide temperature ranges, acceleration sensitive gyroscope 
errors, and often severe vibration inputs react to cause measurement 
errors. The ring laser gyroscope has been shown to approach theoretically 
ideal gyroscope performance with very accurate rate measuring scale 
factor, very low temperature and acceleration sensitive errors in 
gyroscope output, extremely rugged construction, and random errors limited 
only by the quantum limits of the gyroscopes laser action. These 
attributes make a ring laser gyroscope highly desirable and attractive for 
use in the borehole surveying problem. 
SUMMARY OF THE INVENTION 
It is a major object of the invention to provide improved accuracy along 
with reduced cost and complexity in borehole surveying by using a ring 
laser gyroscope of unique configuration in specific manners so as to 
achieve the desired results including optimized performance. 
Basically, the apparatus of the invention comprises: 
(a) a first ring laser gyroscope sized for travel in a direction lengthwise 
of and within the hole, the laser gyroscope characterized by two laser 
beams traveling along looping paths in opposite directions, and 
(b) means mounting said gyroscope for travel in the hole and for rotation 
about an axis extending generally in said direction, the looping paths 
having long and short stretches, the long stretches extending generally in 
the direction of the borehole. 
As will appear, the looping paths, which define the optical path or paths 
of the gyroscope, are generally rectangular, the long stretches of such 
rectangular paths extending in the direction of the borehole. The 
gyroscope has an axis of sensitivity which may be substantially normal to 
the axis of rotation of the instrument, or may be canted from the normal 
to that axis, so as to provide a component of sensitivity along that axis. 
A further aspect of the invention concerns the provision of a second ring 
laser gyroscope sized for travel with the first laser gyroscope, the two 
gyroscopes having axes of sensitivity which are non-parallel. Typically, 
both may have rectangular optical paths with long stretches extending in 
the borehole direction; and the axes of sensitivity of the two gyroscopes 
may extend in generally orthogonal relation (i.e. the planes defined by 
the two gyroscopes optical paths may extend mutually orthogonally). Also, 
one or both axes of sensitivity of the two gyroscopes may be canted 
relative to a normal, or normals, to a common axis of rotation. 
Finally, rotation of the laser gyroscope, or two laser gyroscopes, may be 
carried out, as will be seen, in a manner as to reduce the tendency for 
locking (natural "dead zone" or "lockband") of the laser gyroscope output 
or outputs.

DETAILED DESCRIPTION 
Consider first an arrangement as shown in FIG. 1. It includes an angular 
rate sensor 10, in the form of a laser gyroscope, whose output is 
proportional to a component of the earth's rotation rate vector. Also, it 
includes an acceleration sensing device 11 whose output is proportional to 
a component of a local gravity vector, and means 12 to rotate these 
devices about an axis 13, which will generally be along a borehole axis. 
The means 12 may be a geared timing type motor to provide continuous 
rotation, or a servoed type motor working with an angle sensor about the 
rotation axis to provide either a continuous rotation or discrete 
positioning. These devices, along with resolver 14, are located in a 
container or carrier 18 that is suspended by cable 15 in a borehole 16, 
and traveled therein by surface means 17. Motor output shaft 19 has 
extensions at 19a and 19b to rotate devices 10 and 11, and provide input 
to the resolver which is also tied to the container 18. See also U.S. Pat. 
No. 3,753,296, wherein a non-laser type gyroscope is employed. 
For this configuration, both the sensing devices 10 and 11 (i.e. LG and A) 
have single axes of sensitivity, nominally positioned parallel to each 
other and normal to the rotation axis 13. As the combination of sensing 
devices is rotated about its rotation axis 13 in a borehole 16, both the 
sensing devices 10 and 11 will produce variable output indications 
proportional to the vector dot product of a unit vector along the 
respective input axis and the earth's rotation rate vector and gravity 
vector, respectively. For continuous rotation operation at a fixed 
location in the borehole, these signals will be sinusoidal in nature. For 
discrete step rotation, the sensor output will be just the equivalent of 
sampling points on the above mentioned sinusoidal signals. Thus, from a 
knowledge of sample point amplitudes and position along the sinusoid, the 
character of an equivalent sinusoid in amplitude and phase may be 
determined. 
The output sinusoidal signals from the sensing devices may be combined and 
processed as in circuitry indicated at 22, and which may be located in 
carrier 18 or at the surface to provide the azimuth direction of the 
borehole axis with respect to the vertical plane containing the direction 
of the earth's inertial rotation rate vector. The output signal from the 
acceleration sensing device 11 alone may be used to determine the tilt or 
drift of the borehole axis with respect to the local gravity field vector. 
Such determination of directional azimuth .psi. and tilt .phi. or drift 
from vertical are free of any constant or bias type errors of the sensing 
devices. 
Note in this regard that the present configuration provides azimuthal 
direction with respect to true north as defined by the earth's rotation 
rate vector. Circuitry 28 connected in feedback relation between resolver 
14 and motor 12 controls the latter in response to resolver output. 
The laser gyroscope LG is of the general type shown in FIG. 2. A body 30 
defines four beam channels 31-34 which define a rectangular ring. The 
channels contain a gas or gasses suitable for laser operation, examples 
being neon and helium. Cathode 35 and anodes 36 and 37 produce two laser 
beams which travel oppositely along the rectangularly shaped optical 
paths, defined by legs 31a-34a. Legs or stretches 31a and 33a are 
substantially longer than legs or stretches 32a and 34a, and legs 31a and 
33a extend parallel to axis 13. Four mirrors 41-44 are located at the four 
corners associated with such legs, for reflecting the monochromatic beams 
around the rectangular optical paths. As the gyro rotates about an axis 
normal to the plane of the optical path, the effective path length for one 
beam is increased, and the effective path length for the other beam is 
decreased, due to Doppler shifting. A beat frequency is produced in 
response to heterodyning of the two beams, as with a combining prism; and 
the beat frequency produces a fringe pattern which is typically detected 
as with a photodiode. Such detecting means is indicated generally at 49. 
See for example U.S. Pat. No. 4,281,930 to Hutchings. 
At very low rates of rotation of the gyro, the difference in frequency 
between the two beams is small, and it is found that the two beams tend to 
resonate together, or "lock-in", so that the two beams oscillate at only 
one frequency. Thus it becomes difficult to detect low rotational rates. 
It is well known that for a ring laser gyroscope the so called "lock band" 
or "dead zone", the incremental pulse angular scale factor, and the 
theoretical error limits depend upon the ratio of the area enclosed by the 
light path to the length of the light path. For the closed path, this is 
usually referred to as the area to perimeter ratio. It is desirable for 
accurate surveying to maximize this ratio within the available dimensions 
of the survey tool. Since the diameter of the survey tool (normal to the 
borehole axis) must be kept small (on the order of 1" to 2.5") for broad 
application this dimension is controlling for any ring laser gyroscope. 
Ring laser gyroscopes have generally been developed using either nominally 
equilateral triangular shape or nominally square shape for the optical 
path. It can be shown that the important area to perimeter ratio for a 
nominally square optical path is approximately 1.75 times greater than 
that for a nominally equilateral triangle of equal side lengths. 
Accordingly, the use of the nominally square path in the limited diameter 
borehole is preferred compared to the nominally triangular path for equal 
side lengths. FIG. 3 shows the comparison of equal side lengths for a 
square and triangular path for a ring laser gyroscope in a fixed diameter 
borehole 16. 
The important area to perimeter ratio is further improved in the limited 
diameter borehole application by elongating the optical path of the ring 
laser gyroscope along the borehole axis. FIG. 4 shows this relationship 
for the four sided and three sided optical path cases. Note the elongation 
in the borehole direction of sides 50 and 51 in FIG. 4(a), and sides 50a 
and 51a in FIG. 4(b). 
FIG. 5 shows computed values for normalized area to perimeter ratios for 
both the rectangular and triangular shapes vs the elongation ratio, k, 
which is defined as the ratio of the long side to the short side 
dimension. This shows clearly the previously cited superiority of the 
basic square shape as well as the benefit derived by elongation in a 
dimension limited borehole as per FIG. 4. It is apparent that 
significantly improved area to perimeter ratios are obtained for values of 
k greater than 1 and that a "point-of-diminishing returns" is reached 
between k=5 and k=10 such that values above k=5 may not in practice be of 
great value. However, the basic improvement obtained by elongation in 
limited diameter installation is a significant benefit in performance for 
all elongations. Significant advantage is obtained when k is greater than 
2. 
A suitable ring laser gyroscope having the properties described above is 
the Optical Technologies Laboratories, Inc., Newbury Park, Calif., Model 
L1717 which has a rectangular path with an elongation ratio, k, of 
approximately 5, and a total optical path length of approximately 17 cm. 
Such a ring laser gyroscope can be used in a survey instrument generally 
similar to that disclosed in U.S. Pat. No. 3,753,296, which includes a 
rate measuring gyroscope having an axis of rate measurement sensitivity 
normal to the borehole axis. FIG. 6 shows such a configuration, with a 
ring laser gyroscope having its axis 52 of rate measurement sensitivity 
normal to the borehole axis 53. The numbered components are as described 
in U.S. Pat. No. 3,753,296. 
As referred to above, ring laser gyroscopes are subject to "locking" at low 
input angular rates such that no output is obtained until the "locking 
rate" is exceeded. Any of the well known methods of "unlocking" a ring 
laser gyroscope for other uses can be applied to the borehole survey 
usage. Known methods include continuous or oscillatory rotational bias 
about the input axis, various optical biasing based on Kerr or Faraday 
magneto-optics effects, and the differential or multioscillator approach. 
See for example U.S. Pat. No. 3,467,472 to Killpatrick. Any of these 
methods can be used in a survey tool of the configuration of FIG. 6. Such 
devices or methods require added apparatus and may provide some bias, 
which is of disadvantage in borehole applications. 
In the borehole suryey application a unique opportunity exists to obtain 
the required unlocking without the addition of any hardware to the 
gyroscope. 
As shown in FIG. 1a if the sensing axis 56a is canted through some small 
angle .alpha., from a normal 56 to the borehole axis, then either a 
continuous rotation or a cyclical reversing motion of the survey tool 
gimbal can provide the required "unlocking rate". Values of .alpha. 
between about 1 degree and 45 degrees are usable. Trade-offs exist between 
cant angle .alpha., and the previously discussed ring laser gyroscope 
elongation factor, k, for fixed borehole diameter. For such a fixed 
diameter, the greater the value of "k", the smaller the value of .alpha. 
must be to physically stay within the fixed diameter. This has a trend 
toward self-compensation, since in general the "locking rate" will 
decrease as "k" is increased, and therefore a smaller .alpha. is required 
for unlocking with fixed gimbal rate magnitude. 
Referring to FIG. 1, control of the angular rate of rotation of shaft 19 
about axis 13 may be from control equipment 28, which may be at the 
surface, or at the locus of the instrument, and connected as at 80 with 
the motor.12. FIG. 7 shows details of circuitry to be used for such 
control of angular rate. As referred to above, the rate control may be 
varied in speed and direction so that a series of discrete positions can 
be obtained as well as constant angular rate of any speed and either 
direction. In FIG. 7, a basic rate command at 82 is summed at 83 with an 
unlocking rate command 84 and the result 85 amplified at 86 in a signal 
amplifier, frequency compensated as required for closed loop dynamics 
stability in a servo compensation network 87, and amplified in the power 
amplifier 88 to a sufficient level to drive the motor M shown in FIG. 1. 
The signal at 89 from the resolver R (such as shaft angle transducer 14 in 
FIG. 1) is passed through the signal conditioner 90 (providing a 
derivative function) and then subtracted from the summed rate command, at 
83. 
The unlocking rate command may be a continuous command, causing continuous 
rotation, or it may be cyclical at any desired amplitude and direction vs 
time function. Possible waveforms for such cyclical rate commands include 
sinusoidal, or square wave, or a zero mean random noise process. 
If unlocking by cyclical motion of the survey tool gimbal is employed, the 
magnitude of the required reversing rate may be reduced by mounting the 
ring laser gyroscope to the tool gimbal by a torsional spring allowing 
rotational motion of the gyroscope about its sensing axis. See FIG. 8, 
wherein a frame 91 interconnects shafts 19 and 19a (corresponding to these 
same shafts in FIG. 1). Mounted within or to the frame, as by torsional 
spring components 94 and 95, is the ring laser gyroscope 10. It is allowed 
to rotate about sensing axis 56 against resistance imposed by the 
torsional springs. When the torsional effective spring constant is 
selected such that the natural frequency of the mount determined by the 
spring constant and the gyroscope moment of inertia is the same frequency 
as the reversing gimbal rotation, only a very small gimbal rate magnitude 
is required to provide the unlocking rate. Arrow 110' indicates gimbal 
rotation. 
FIG. 9 is a view like FIG. 1a, but showing two laser gyroscopes 111' and 
112' slowly rotated by a motor 113' about axis 114', in housing 115, in a 
borehole. Upper laser gyroscope 111 has its sensitive axis 111a canted in 
the "xz" plane, and lower laser gyroscope 112' has its sensitive axis 112a 
canted in the "yz" plane; thus axes 111a and 112a are in planes which are 
orthogonal, and if the cant angles (relative to normals to axis 114) are 
zero, the sensitive axes are nominally orthogonal. One of the axes 111a 
and 112a may be along the borehole axis 114', and the other normal 
thereto.