Method for reducing noise effects in acoustic signals transmitted along a pipe structure

A method of analyzing vibrations transmitted along a structure such as a drill string is disclosed. The detected vibrations include both axial and torsional vibrations generated from the same location, so that the time delay between the two, due to the difference in axial and torsional velocities, can be determined. After deconvolution to take into account the non-ideal frequency response of the structure, such deconvolution preferably retaining the values of the transmission time for each component, one of the time series is shifted by the amount of the time delay, so that the vibrations generated from the same location coincide. A weighted sum of the two representations will provide reinforcement of the desired signal. The method may be used in determining a seismic source signature in prospecting where a drill bit is the source, in analyzing drilling parameters from drill string vibrations, and in stress wave telemetry.

This invention is in the field of signal processing, and is more 
specifically directed to reducing the effects of noise in signals 
transmitted along a pipe structure. 
BACKGROUND OF THE INVENTION 
The petroleum industry relies heavily on the operation of drilling into the 
earth, both on land and offshore, in the exploration for and production of 
petroleum products. Over the years, the more readily found and accessible 
petroleum reservoirs have of course been discovered and depleted first. As 
a result, the exploration and production operations must necessarily 
concentrate to a greater degree on less accessible and less readily 
discoverable reserves. In order to reach these locations, the depths of 
drilling have increased, the locations at which drilling takes place have 
become increasingly difficult and less accessible, and the drilling 
operations have necessarily become more complex. Accordingly, drilling 
operations in the search for and production of petroleum products have 
become more expensive, with this trend likely to continue in the future. 
Because of this increasing cost, the accuracy and efficiency of the 
drilling operation is becoming even more important. 
The success and efficiency of the drilling operation depends to a large 
degree on the quantity and quality of information that the drilling 
operator has about the sub-surface structure into which the drilling is 
taking place, and also about parameters concerning the operation of the 
drill bit as it proceeds into the earth. Many techniques for acquisition 
and communication of such information have been tried and used in the 
industry. Recent work has been done, as will be discussed hereinbelow, in 
acquiring information from the acoustical vibrations in the drill string 
itself during drilling. In such an application, the drill string serves 
not only to power and guide the drilling, but also as a communication 
medium for such acoustic signals. These signals are inherently generated 
during the drilling operation and communicated via the drill string to 
detectors. Analysis of the signals provides information about the drilling 
parameters and the drilling operation itself, and also about the geology 
into which the 
An example of a system and method using acoustic vibrations transmitted 
along the drill string itself to communicate various drilling parameters 
is described in U.S. Pat. No. 4,715,451, issued Dec. 29, 1987, assigned to 
Atlantic Richfield Company, said U.S. Patent incorporated herein by this 
reference. This system measures the motion of, and the strains on, a 
drillstem in various directions, by way of monitoring such indications as 
axial, torsional and lateral vibrations, and deflections of the 
drillstring. The strain generated on the drill string during drilling is 
indicative of such factors as the impact and rotation of the drill bit, 
its interaction with the formation into which the drilling is taking 
place, and the interaction with portions of the drill string above the bit 
with the surrounding formation. In this system, measurements are made by 
way of detectors, such as accelerometers and strain gages, which are 
located in a sub near the top of the drill string and which generate 
electrical signals corresponding to the vibration and motion detected 
thereby. Analysis of the electrical signals provides real-time information 
on parameters such as drillstem vibration and deflection, the location of 
interaction between the casing and the drillstem, the speed of and load on 
the drill bit, and other drill bit operating characteristics. Such 
real-time operating information is quite useful in efficiently and 
accurately performing the drilling operation. 
As disclosed in said U.S. Pat. No. 4,715,451 at column 5, lines 59 through 
68, in Rector III, et al., "Extending VSP to 3-D and MWD: Using the drill 
bit as downhole seismic source", Oil and Gas Journal, (Jun. 19, 1989), pp. 
55-58, and in Rector, Marion and Widrow, "Use of Drill-Bit Energy as a 
Downhole Seismic Source", 58th International Meeting of SEG, paper DEV 
2.7, pp. 161-164, analysis of the vibrations communicated along the drill 
string during drilling is useful in the seismic prospecting area, where 
the vibrations generated by the drill bit into the earth are the seismic 
source signals. Relative to the TOMEX.RTM. (Trademark of Western Atlas 
International Inc.) system disclosed by Rector III et al., seismic 
detectors such as geophones or hydrophones detect the reflections of these 
vibrations near the surface at a location distant from the drilling 
operation. Detection of the vibrations at the wellhead, as communicated by 
the drill string, can provide a signature of the source vibrations. 
Conventional time-domain cross-correlation of the vibrations detected by 
the geophones or hydrophones with the source vibrations communicated 
through the drill string provides data concerning the location of 
sub-surface strata and interfaces. 
Another system which utilizes the drill string as a medium for the 
transmission of data is referred to as stress wave telemetry. Stress wave 
telemetry systems are, disclosed, in copending U.S. Patent Applications 
Ser. No. 188,231 filed Apr. 21, 1988, now U.S. Pat. No. 4,992,997, issued 
Feb. 12, 1991, Ser. No. 554,030 filed Jul. 16, 1990, and in Ser. No. 
554,022 filed Jul. 16, 1990, all applications also assigned to Atlantic 
Richfield Company, and incorporated herein by this reference. This system 
includes transmitters, such as solenoids eccentric motors, and 
piezoelectric transducers, which intentionally vibrate the drill string in 
a manner corresponding to the desired data. This data may include 
information concerning drilling parameters, such as in the 
above-referenced U.S Pat. No. 4,715,451. In the of stress telemetry, 
however, the information is not extrapolated from analyzing the naturally 
occurring vibrations, but vibrations are generated which are in addition 
to the naturally occurring vibrations, these generated vibrations 
corresponding to the drilling parameter and other information transmitted 
along the drill string. 
It has been discovered, however, that vibrations, whether from the drill 
bit itself or intentionally generated by transmitters, are not 
communicated through the drill string in an ideal manner, due to the 
non-ideal response of the drill string to such vibrations. As described in 
Drumheller, "Acoustical Properties of Drillstrings", J. Acoustic Society 
of America. 85(3) (March, 1989), pp. 1048-1064, conventional drill 
strings, which consist of a number of lengths of drill pipe joined by pipe 
joints, inherently have frequency domain stopbands which attenuate 
acoustical signals at the stopband frequencies. This frequency-dependent 
attenuation can severely distort some signals. While simple deconvolution 
of the reflective effects of the ends of the drill string and the 
bottomhole assembly has been done, such deconvolution has accounted only 
for effects dependent upon the total length of the drill string and the 
construction of the bottomhole assemble, and has not accounted for the 
frequency dependent transmission of the drill string due to such factors 
as the tool joints between sections of the drill string. 
Furthermore, it has been discovered that other factors also distort the 
vibrations communicated along a drill string from downhole to the surface. 
Such factors include noise generated by the drilling fluid, or mud, which 
is conventionally pumped through the drill string at relatively high 
pressures. This high pressure flow of fluid causes significant vibrations 
in the drill string. Other apparatus in the drilling operation, such as 
bearings in the swivels at the top of the drill string, the rattling of 
chains which turn the kelly bushing, or the motor in a top drive drilling 
arrangement, and the slap of the casing against the drill string or well 
bore, also generate significant acoustical vibrations which are received 
by and transmitted along the drill string. These vibrations are 
superimposed upon the vibrations generated by the drill bit, and will 
accordingly be detected at the top of the drill string by such detectors 
as are attempting to detect the vibrations which are induced by the drill 
bit. 
Considering the vibrations (generated by the drill bit, or alternatively 
the vibrations generated by a transmitter in the stress wave telemetry 
case, as "signal", and considering the other vibrations caused by drilling 
mud flow and the mechanical sources discussed in the prior paragraph as 
"noise", it has been found that the amplitude of the noise can be 1000 
times greater than the signal amplitude. Noise at this level not only 
clouds the analysis of the information, but indeed drowns out the 
information itself. This is true in the contexts of determining real-time 
drilling parameters, producing a source signature from the drill bit for 
seismic prospecting, and in the case of stress wave telemetry. 
The presence of such noise and distortion has been observed in field tests 
of the TOMEX.RTM. system described hereinabove, by J. P. DiSiena et al., 
"VSP While Drilling: Evaluation of TOMEX", Exploration Technology Report 
(Atlantic Richfield Company, Fall 1989), pp. 13-20, incorporated herein by 
this reference. While recovery of the drill-bit signal in the seismic 
prospecting context could be done in drilling operations using tricone 
bits and rotary drive, the signal-to-noise ratio for operations using PDC 
(Polycrystalline Diamond Compact) bits or a downhole mud motor was so low 
that no seismic source record could be detected in the drill string 
vibrations. The signal-to-noise ratio of the drill-bit energy as 
transmitted along the drill string must therefore be improved in order for 
such seismic prospecting analysis to be feasible during drilling, when 
using such important drilling equipment. 
It is therefore an object of this invention to provide a method of reducing 
the effects of noise on information communicated along a pipe structure 
such as a drill string. 
It is a further object of this invention to provide such a method which 
also includes the deconvolution of the pipe string response in 
accomplishing the noise reduction. 
It is a further object of this invention to provide such a method together 
with an improved deconvolution, taking into account the passbands and 
deadbands of a jointed pipe structure. 
Other objects and advantages of the invention will be apparent to those of 
ordinary skill in the art having reference to this specification, together 
with the drawings. 
SUMMARY OF THE INVENTION 
The invention may be incorporated into a method for processing signals 
corresponding to vibrations in a pipe structure. Measured axial and 
torsional vibrational signals as a function of time are received at an end 
of the structure. The torsional component is generally delayed in time 
from the axial component, due to the lower velocity of torsional waves 
along the structure. The time series of the vibration signals are shifted 
in time by approximately the difference in the axial and torsional 
velocities times the distance between the detector and the drill bit, or 
such other source of the vibrations in interest. In cases where the axial 
and torsional vibrations are substantially proportional to one another, 
such as when the vibration source is the drill bit, and since the noise is 
substantially random, addition of the axial and torsional signals will 
cause the vibration signals to reinforce one another. As a result, an 
improved signal to noise ratio in the detected vibration signals is 
achieved.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring now to FIG. 1, a drilling operation with which a preferred 
embodiment of the invention is used will be described. A conventional 
drilling rig 2 is shown as powering drill string 4, which conventionally 
consists of multiple sections 6 of drill pipe. Sections 6 are connected to 
one another by tool joints 8 in the conventional manner. Drill bit 10 is 
connected at the distal end of drill string 4, and can be a rotary bit, 
jet or spud bit, or other type of drill bit conventional in the art. As 
shown in FIG. 1, drill bit 10 is connected to bottomhole assembly 11, 
which in turn is connected to sections 6 of drill string 4. Provision of 
such a bottomhole assembly 11 is conventional in the drilling art, and is 
useful for housing such equipment as detectors for sensing attributes of 
the drilling operation, as well as for other conventional functions. While 
such a bottomhole assembly 11 is shown in FIG. 1, it should be noted that 
the presence of bottomhole assembly 11 is not required for purposes of the 
instant invention, such presence depending upon the particular drilling 
operation being performed. However, for purposes of stress wave telemetry 
as will be described hereinbelow, transducers for vibrating drill string 
4, according to information to be transmitted from downhole to the 
surface, are preferably located in such a bottomhole assembly 11. 
It is contemplated that the rotary bit, due to its mode of operation in 
drilling, will generate quite complex vibrational information, such 
information being transmitted, and capable of being subsequently analyzed 
according to this embodiment of the invention. The vibrational information 
utilized by this embodiment of the invention include axial compressional 
vibrations and torsional vibrations in drill string 4, such vibrations 
being generated by the powering of drill bit 10 and its interaction (as 
well as the interaction of drill string 4) with the formations encountered 
in the earth. The powering of drill bit 10, of whatever type, can be done 
either from the surface or via a downhole motor, according to the type of 
drill bit 10 used and the particular drilling operation undertaken. 
Sub 12 is connected within drill string 4 near the surface of the earth. 
Sub 12 contains detectors, such as accelerometers, strain gages, 
piezoelectric transducers, and the like, for detecting vibrations in drill 
string 4 and generating a signal, such as an electrical signal, 
corresponding to the detected vibrations. Examples of such detectors and 
their placement in sub 12 are described in U.S. Pat. No. 4,715,451 issued 
Dec. 29, 1987, assigned to the Atlantic Richfield Company, and 
incorporated herein by this reference. For purposes of this invention, 
since both axial and torsional vibrations are detected and used in the 
analysis, such detectors must accordingly be placed and oriented to detect 
both axial and torsional vibrations. The electrical signals generated from 
the detectors within sub 12 are communicated to computer system 19 for 
analysis of the signals corresponding to the vibrations of drill string 4, 
according to the embodiment of the invention described hereinbelow. 
As described in said U.S. Pat. No. 4,715,451, the vibrations detected by 
the detectors in sub 12 are representative of certain drilling parameters. 
Analysis of these vibrations, as communicated electrically from the 
detectors in sub 12, can quantify these drilling parameters, assuming that 
those vibrations from drill bit 10 can be sufficiently separated from such 
other vibrations along drill string 4 which are not generated from drill 
bit 10. Accordingly, an important application of the invention as 
described herein relative to its preferred embodiment is the reduction of 
the effects of the vibrations from sources not of interest (i.e., the 
"noise") on the vibrations generated by the operation of drill bit 10 and 
drill string 4 on the sub-surface formations which are of interest (i.e., 
the "signal"). As a result of such improvement of the signal-to-noise 
ratio, it is contemplated that the drilling operation can be more 
efficiently performed and controlled, as the quality of real-time 
information about important drilling parameters is improved by the use of 
this invention. 
Alternatively, or in addition, to the above utilization of this 
information, the vibrations sensed by detectors in sub 12 can be used in 
seismic prospecting. As described in the Rector III et al. article cited 
hereinabove, the vibrations generated by drill bit 10 during the drilling 
operation are transmitted through the earth. It is believed that the 
vibrations which are transmitted axially along drill string 4 from drill 
bit 10 correspond to pressure ("P") waves which drill bit 10 imparts into 
the earth. These vibrations, when reflected below the surface of the earth 
and received at locations remote from the drilling operation, are 
indicative of the attributes of these sub-surface strata and their 
interfaces. 
As shown in FIG. 1, the vibrations generated by drill bit 10 are 
transmitted acoustically through the earth. For example, vibrations may 
follow path 15 downwardly from drill bit 10, reflecting from interface 12 
between strata 14 and 16 to the surface, at which the vibrations are 
detected by detector 18. Vibrations may also directly travel from drill 
bit 10 along path 13 to detector 18. Detector 18 may be a conventional 
geophone, or other conventional apparatus useful in the detection of 
vibrations at the surface of the earth (or water, as the case may be). 
While a single detector 18 is illustrated in FIG. 1, it should be noted 
that, of course, multiple detectors 18 are conventionally placed along the 
surface of the earth during seismic prospecting. The use of an array of 
multiple detectors 18 provides detailed information about the sub-surface 
geology of the region under analysis. The analysis of the detected 
vibrations by each of such multiple detectors 18 is done in much the same 
manner as for a single detector 18, with the differences in travel times 
among the detectors 18 in the array indicative of the strata and 
interfaces at different locations. The vibrations detected by detector 18, 
as well as those detected by detectors in sub 12, are communicated in the 
conventional manner via field electronics 21 to computer system 19 for 
analysis according to the method to be described hereinbelow. 
As described in the article by Rector III, et al. cited hereinabove, 
seismic prospecting using drill bit 10 as the seismic source, as with any 
seismic source, requires knowledge of the input signal so that reflections 
and other information can be gleaned from the reflected signal received by 
geophone 18. Conventional methods, such as cross-correlation of the 
received signal with the input signal as in the well-known Vibroseis.RTM. 
(Registered trademark of Continental Oil Company) technique, and performed 
by computing system 19 either on location in the field, or alternatively 
at an off-site computing center, identify such important parameters in the 
received information such as transit time from the source (i.e,. drill bit 
10) to the geophone 18, which will indicate the location of reflecting 
strata or interfaces. 
However, where drill bit 10 is the seismic source and where detectors, for 
example in sub 12, are used to measure the source signal as transmitted 
through drill string 4, the vibrations received via transmission through 
drill string 4 will include any effects of the response of the drill 
string 4 upon the vibrations generated by drill bit 10. As noted in the 
Drumheller article noted hereinabove, the response of a drill string to 
vibrations passing therethrough is such that severe distortions of the 
acoustic signal will occur as the signal travels to and is received by the 
detectors in sub 12, at or near the surface of the earth. In the seismic 
prospecting application, it should be noted that the signal received by 
geophone 18 will not have the distortions generated by the acoustic 
response of drill string 4, but will be subject to distortions presented 
by the earth. Of course, in the seismic prospecting application, such 
distortions are the very information which is sought by the process, as 
the distortions (e.g., reflections) correspond to the geology of the 
drilling location. Furthermore, as noted hereinabove, the vibrations from 
drill bit 10 which are transmitted along drill string 4 will have 
superimposed thereupon such "noise" vibrations resulting from the flow of 
drilling mud at high pressure, and the operation of various mechanical 
elements on drill string 4, as discussed hereinabove. 
As is well known in the field of seismic prospecting, correlation 
techniques determine the time delay between the source signal and the 
receipt of the reflected signal; from this time delay, the depth and 
location of reflecting strata and interfaces between strata can be 
calculated. The accuracy of these calculations depends upon how well the 
analysis can recognize the point in time at which the reflected signal is 
detected. Due to the presence of noise in the measurements, as well as the 
weakness of the seismic signal, especially those resulting from partial 
reflections from very deep strata, this identification of the receipt of 
the measured signal is often not easily accomplished. This process is made 
even more difficult where the signature of the source signal is not known, 
is distorted, or is otherwise inaccurate due to additional noise 
superimposed thereupon. As noted above, where the vibrations are distorted 
in transmission through drill string 4 in a way in which the vibrations 
traveling through the earth are not distorted, and where significant noise 
is generated by the flow of drilling mud and other mechanical 
interactions, the ability to accurately cross-correlate the source signal 
with the reflected waveforms becomes even more reduced. 
Also as noted above, stress wave telemetry is another application in which 
vibrations of a drill string 4 are analyzed for their informational 
content. Of course, whether the signals are inherent in the vibrations 
generated during drilling, as discussed above, or induced by additional 
equipment such as transducers located in downhole assembly 11, as in the 
case of stress wave telemetry, noise and distortion of the signal occur 
during transmission through drill string 4. Furthermore, considering the 
amplitude of signals which can be generated by downhole transducer 
apparatus as are described in said copending application Ser. No. 188,231 
filed Apr. 21, 1988, now U.S. Pat. No. 4,992,997, issued Feb. 12, 1991, 
where such transmitting apparatus is of limited size and power due to its 
installation downhole, signal-to-noise ratio and distortion is a serious 
problem, even where the frequencies of transmission may be known in 
advance, as is the case in stress wave telemetry. 
Referring now to FIG. 2, a method for reducing the effects of noise on 
detected vibrations transmitted through a pipe structure such as drill 
string 4 according to the preferred embodiment of the invention will now 
be described. The method begins at process 20, at which both axial and 
torsional vibrations in drill string 4 are measured by detectors in sub 12 
near the surface of drill string 4. As described hereinabove, these 
detectors are conventional accelerometers, strain gages, piezoelectric 
transducers and the like; an example of a system including such detectors 
is described in the above-referenced U.S. Pat. No. 4,715,451. 
It is contemplated that conventional computer equipment, programmed 
according to the method according to this embodiment of the invention, may 
be used in performing this preferred embodiment of the invention. An 
example of a conventional computer system particularly adapted to the task 
of seismic prospecting using the drill bit as a seismic source is the 
TOMEX.RTM. Field System manufactured and sold by Western Atlas 
International. Other conventional computer systems such as 
microcomputer-based workstations may of course be used in performing this 
embodiment of the method, as well. In particular, certain special purpose 
microprocessor circuits, commonly referred to as digital signal processors 
(DSPs), are constructed to rapidly perform operations useful in digitally 
performing Fourier transforms, such transforms accomplished according to 
the class of methods conventionally referred to as Discrete Fourier 
Transforms (DFTs), an important type of which are commonly referred to as 
Fast Fourier Transforms (FFTs). Readily available add-on circuit boards 
containing such DSP processors, for use in a microcomputer-based 
workstation, are particularly well-suited for performing the process steps 
of FIG. 2, including the deconvolution operation discussed herein. 
Referring to FIG. 8, a block diagram of an example of a computing system 19 
for performing the analysis according to this embodiment of the invention 
will now be described. Computing system 19 of FIG. 8 receives information 
both from detectors in sub 12, and also from geophones 18 via field 
electronics 21, and accordingly is applicable for analysis of information 
from seismic prospecting where drill bit 10 is the seismic source and 
geophones 18 receive the reflected signals, as in FIG. 1. Of course, 
computing system 19 may be constructed to receive only input from 
detectors in sub 12, for analyzing vibrations in drill string 4 to 
determine certain drilling parameters, or in the stress wave telemetry 
application, as described hereinabove. 
Detectors in sub 12 provide analog electrical input responsive to torsional 
and axial vibrations detected in drill string 4, to analog-to-digital 
converters (ADC) 82. ADCs 82 convert the analog signals received from each 
of the detectors in sub 12 into digital form in the conventional manner. 
ADCs 82 communicate the digital representations of the vibrations, either 
from each of the detectors or in a multiplexed manner, to coding circuit 
84 which converts the digital data into signals suitable for transmission 
to computing system 19. The conversion by coding circuit 84 is according 
to conventional data transmission techniques, for example by coding the 
information into frequency shift keyed (FSK) digital data, phase shift 
keyed (PSK) digital data, or another conventional coding scheme. Coding 
circuit 84 then transmits the coded information concerning the vibrations 
detected at sub 12 to computing system 19; such transmission may be by way 
of synchronous digital data transmission, or by microwave or infrared 
transmission, all of which being conventional for the transmission of 
digital data. 
Similarly, field electronics 21 includes ADCs 86 for receiving and 
digitizing analog signals received from geophones 18. ADCs 86 communicate 
the digital signals to multiplexer and coding circuit 88, which 
multiplexes the data received from the multiple geophones 18, and 
transmits the data to computing system in similar manner as coding circuit 
84 described hereinabove. As noted above, in the stress wave telemetry and 
drilling parameter communication applications, field electronics 21 need 
not be provided, as no inputs from geophones 18 are necessary in such 
analysis. 
Computing system 19 includes interface 90 for receiving the coded and 
transmitted signals from coding circuit 84 and from multiplexer and coding 
circuit 88, and for communicating the received signals to computer 92 in a 
manner which can be stored and manipulated thereby. Computer 92 is a 
conventional high speed PC-based workstation, for example based on 80386 
or 80486 microprocessors. Due to the nature of the method to be described 
hereinbelow, it is also preferable that computer 92 include one or more 
DSP add-on boards as described above; a preferred DSP board is the Spirit 
30 DSP board manufactured and sold by Sonitec. Computer 92, as mentioned 
above, includes conventional hardware, including the DSP boards, but is 
programmed to perform the analysis to be described according to the 
preferred embodiment of the invention hereinbelow. Computer 92 may be 
connected to monitor 94, tape drive 96, printer 98 or interface 99, for 
communication and storage of the results in the conventional manner. 
It should be noted that the time series of vibrational signals which are 
analyzed according to this embodiment of the invention may be a continuing 
series of signals, so that the analysis occurs periodically, but on 
substantially a real-time basis. Computing system 19 thus can be located 
in the field for iterative analysis during drilling. Such analysis is 
preferable for the application discussed hereinabove relating to the 
real-time receipt of drilling parameters during the drilling operation, as 
described in said U.S. Pat. No. 4,715,451. Alternatively, a time series of 
vibrations may be received and analyzed later, together with such other 
information as the received reflections from geophone 18. Such computation 
may be done by computer system 19 located at the drilling site, or 
alternatively may be done by a computing system located remote from the 
drilling site, at a time after the drilling is complete, so long as the 
raw time series data is retained or transmitted. 
FIG. 2 illustrates the steps in the method according to this embodiment of 
the invention. For purposes of describing the benefits of the invention 
and its theory of operation, time domain and frequency domain waveforms 
will be used hereinbelow. Referring to FIGS. 3a through 3c, time domain 
representations of a typical signal as transmitted near drill bit 10, and 
as detected for both axial and torsional components near the top of drill 
string 4, will be discussed. FIG. 3a illustrates an example of signal 22 
as generated by, or near, drill bit 10, with signal 22 represented in the 
time domain. This signal is substantially an impulse beginning at time 
t.sub.0 and, for purposes of this discussion, is presumed to generate 
substantial vibrations both axially and torsionally along drill string 4. 
For a drill string 4 having a given length between drill bit 10 and the 
location of sub 12, including detectors for both axial and torsional 
vibrations, near the surface, the source signal illustrated in FIG. 3a 
will be detected (process 20 of FIG. 2) at a point in time delayed from 
the generation of the signal. It is known that axial compressional 
vibrations have a higher velocity in a pipe structure such as drill string 
4 than do torsional vibrations. In conventional steel drill pipe, for 
example, the velocity of axial vibrations is approximately 16,850 ft/sec, 
while the velocity of torsional vibrations is approximately 10,650 ft/sec. 
Accordingly, the torsional vibrations induced by the same event as axial 
vibrations will exhibit a time shift dependent upon this difference in 
velocity and the length of drill string 4 between drill bit 10 (or such 
other apparatus which causes the vibration) and sub 12, at which the 
vibrations are detected. 
The result of the measurement is a time series of vibration amplitude over 
time, an example of which is shown in FIG. 3b for axial compressional 
vibrations and in FIG. 3c for torsional vibrations. FIG. 3b illustrates a 
time domain representation of detected signal 24a, which begins at a time 
t.sub.a, delayed from time t.sub.0 by the length of drill string 4 times 
the axial velocity of vibrations in drill string 4. FIG. 3c similarly 
illustrates a time domain representation of detected signal 24b, beginning 
at a time t.sub.b equal to the torsional velocity of vibrations in drill 
string 4 times the length of drill string 4. It should be noted that the 
amplitude of the signals 24a and 24b represented in FIGS. 3a and 3b is not 
necessarily at the same scale as the source signal, as significant 
attenuation is likely through drill string 4. 
It should also be noted that the representation of signals 24a and 24b in 
FIGS. 3b and 3c are not in the form that they would be actually detected 
by detectors in sub 12, but instead separately illustrate signal 
components 24a and 24b,and noise components 26a and 26b. Of course, the 
actual time series of the vibrations detected by detectors in sub 12 would 
not have the signal and noise components separated as shown in FIGS. 3b 
and 3c, but would be the sum of the two components 24 and 26 for each of 
the Figures. For purposes of explanation of the method of this embodiment 
of the invention, however, the two components will be separately 
illustrated, even though in practice, at this step, the shape of the 
signal component 24 is not known. 
Noise components 26a and 26b,generated from the factors discussed above, 
have an amplitude which is quite significant relative to the amplitude of 
the signal 24a and 24b.While these relative amplitudes are illustrative of 
the noise problem encountered, it should be noted that observed values of 
the amplitude of the noise components 26 have been on the order of one 
thousand times the amplitude of the signal components 24; accordingly, the 
illustrated relative amplitudes of FIGS. 3b and 3c are not to scale. 
It should also be noted that noise components 26a and 26b are broadband 
noise, i.e., a wide range of frequencies. The noise generated along drill 
string 4 also may have periodic and non-periodic components, depending of 
course upon the physical cause of the particular component of the noise. 
For example, the flow of drilling mud may generate relatively periodic 
noise, although at multiple frequencies and harmonics of such frequencies. 
Other events, such as casing slap, may not be periodic and will generate 
noise accordingly. Due to these factors, noise components 26, illustrated 
in FIGS. 3b and 3c for purpose of explanation, may not be representative 
of actual noise detected by detectors in sub 12. 
The method of this embodiment of the invention treats noise components 26a 
and 26b as random noise. Of course, such noise is not truly random, since 
physical events generate the axial and torsional noise vibrations. As will 
be discussed below in further detail, the torsional and axial signal 
components 24 can be treated as proportional to one another at the times 
of interest, while the torsional and axial noise components 26 do not have 
this relationship. This may be seen intuitively by considering that axial 
signal component 24a and torsional signal component 24b are proportional, 
as generated by the same physical events at the same time, but time 
shifted as measured due to the velocity difference. On the other hand, 
axial noise component 26a and torsional noise component 26b,although also 
generated by same physical events and traveling at different velocities, 
are generated at points along drill string 4 other than that of interest 
for the signal (i.e., not at drill bit 10). It will be seen that by 
"zooming" in to a particular location of interest such as the location of 
drill bit 10, according to this embodiment of the invention, noise 
components 26a and 26b will not coincide with one another, and will appear 
as random noise in the analysis. 
It should further be noted from a comparison of torsional noise component 
26b to axial noise component 26a that, in this example, torsional noise 
component 26b has a relatively lower amplitude than axial noise component 
26a. It has been found that it is not uncommon for vibrational noise of 
one component to have a relatively larger amplitude than that of another 
component; of course, depending on the particular situation, the relative 
amplitudes of the noise may be substantially equal for both the axial and 
torsional components. The method according to this embodiment of the 
invention, as will be described hereinbelow, can take into account such 
differences in the relative amplitudes of noise components 26a and 26b,in 
reducing the effects of such noise in analysis of the desired signal. 
It is apparent from a comparison of FIGS. 3b and 3c to each other, and to 
FIG. 3a, that not only is the noise component 26 significant, but also 
that the signal components 24 are distorted from the source signal of FIG. 
3a, and distorted differently for axial vibrations relative to torsional 
vibrations. Referring to FIGS. 4a and 4b,the frequency response of a 
typical drill string 4 to impulse inputs of axial and torsional 
vibrations, respectively. Comparison of the axial and torsional frequency 
response characteristics of FIGS. 4a and 4b will illustrate this differing 
distortion. 
FIG. 4a shows the frequency response of a drill string 10 to compressional 
axial vibrations. The actual data taken for this frequency response 
characteristic is the response of a drill string 4 consisting of sixteen 
sections 6 of 31/2 inch pipe, each section approximately 31 feet in 
length. The input used to measure this frequency response is a hammer 
blow, which easily provides a wide band of frequencies an above-ground 
testing mode. The frequency range for this plot is from 0 Hz to 800 Hz, 
although it should be noted that higher frequency vibrations generated by 
the hammer blow impulse will also pass along such a drill string 4, 
although attenuation of these vibrations increases with the frequency of 
the vibration. 
As shown in FIG. 4a, it should be noted that dead bands occur at 
approximately 260 Hz, 520 Hz, and 780 Hz. These dead bands result from 
reflections of the compressional axial vibrations within a single section 
6 of drill string 4. One can calculate an approximate base dead band 
frequency for a single section of pipe by dividing the velocity of 
compressional axial vibrations (approximately 16,000 ft/sec) by twice the 
length of the section. Accordingly, for a section approximately 31 feet 
long, the dead band frequencies for compressional vibrations is on the 
order of 260 Hz. For a drill string 4 having multiple sections 6, each of 
approximately the same length, the dead band frequencies, including the 
base dead band frequency and its integral harmonics, will align 
substantially with each other in the frequency response characteristic, as 
is evident in FIG. 4a. Based on other measurements, it is believed that 
the major deadbands shown in FIG. 4a for axial vibrations (i.e,. at 
integral multiples of 260 Hz) are substantially independent of the number 
of sections 6 in the drill string 4, so long as the lengths of the 
sections 6 are substantially the same, as is conventionally the case in 
the drilling art. It has also been determined that the frequencies of the 
major deadbands to axial vibrations is also substantially independent of 
the size of the drill pipe of sections 6. 
Between the major dead band frequencies at multiples of 260 Hz, the 
frequency response characteristic of FIG. 4a has pass bands of relatively 
high amplitude. Accordingly, a compressional axial vibration at a 
frequency between the dead band frequencies passes along drill string 4 
relatively well. However, between the major deadbands at integral 
multiples of 260 Hz, smaller local deadbands and passbands are also 
present. In the characteristic of FIG. 4a, the passbands manifest as 
sixteen peaks in the characteristic. These sixteen peaks correspond to the 
number of sections 6 in drill string 4, with the number of local passbands 
increasing with the number of sections 6 in drill string 4. It should be 
noted that the local deadbands between the major deadbands in the 
characteristic of FIG. 4a attenuate the vibrations at those frequencies to 
a lesser degree than occurs in the major deadbands. 
FIG. 4b illustrates the frequency response characteristic to torsional 
vibrations of drill string 4, having sixteen sections 6 of 31/2 inch drill 
pipe. Comparison of this characteristic with that of FIG. 4a shows that 
the shape of the frequency response characteristic is similar for the two 
components of vibration, but that the major deadband frequencies are 
different. As discussed above, for a pipe of a given length, the deadband 
frequency depends on the length of the pipe and also on the velocity of 
the vibrations. Since the velocity of torsional vibrations is lower than 
that of axial vibrations, the deadband frequencies for the same drill 
string will be lower for torsional vibrations than for axial vibrations. 
Specifically, the first dead band is in the neighborhood of 180 Hz, and at 
roughly integral multiples thereof. 
Similarly as in the case of axial vibrational frequency response, it is 
believed that the major deadband frequencies for torsional vibrations are 
substantially independent of the size of the pipe and of the number of 
sections 6 in drill string 4, so long as the individual lengths of 
sections 6 are substantially the same. Also similarly to the axial 
vibration case, local deadbands and passbands are present in the frequency 
response characteristic for torsional vibrations. 
Due to the difference in the major deadband frequencies for axial and 
torsional vibrations in a drill string 4, the distortion presented to a 
source signal as it travels along drill string 4 will be different for the 
axial component than for the torsional component. This is indicated by 
comparison of axial signal component 24a and torsional signal component 
24b in FIGS. 3b and 3c, both of which are distorted from the source 
signal, and are distorted in different ways relative to one another. 
Referring again to FIG. 2, after process 20 in which the vibrations are 
detected by detectors in sub 12, it is therefore preferably to perform 
process 30 for the removal of the effects of drill string 4 on the 
transmitted vibrations. Deconvolution of the impulse response of drill 
string 4 from the measured axial and torsional vibrations at sub 12 is the 
preferred method for removing these effects, using separate deconvolution 
operators for the axial and torsional components. While process 30, 
particularly deconvolution of the two signal components 24, is not 
essential for benefits to be obtained from the method according to the 
invention, the difference in distortion for the two vibration components 
clearly indicates that separate deconvolution for the two components will 
be beneficial in the method according to this embodiment of the invention. 
It should be noted that prior deconvolution methods, as noted in the 
Rector, Marion and Widrow paper cited hereinabove, have taken into account 
only such distortion as results from the ends of the drill string and the 
bottomhole assembly. Such coarse deconvolution thus only is dependent upon 
the total length of the drill string and upon parameters concerning the 
bottomhole assembly; such important factors as the reflective effects of 
the tool joints 8 in drill string 4 have not been taken into account by 
such prior methods. As noted by the above-cited Drumheller article and as 
evident from the frequency response characteristics of FIGS. 4a and 4b, 
drill string 4 introduces severe distortion to waves transmitted 
therethrough, particularly due to the construction of drill string 4 from 
a number of sections 6 joined by tool joints 8. Further with reference to 
FIGS. 4a and 4b, this distortion is especially true for vibrations which 
are at a frequency above 100 Hz, since such vibrations are subject to the 
major deadbands in the characteristics. Accordingly, this preferred 
embodiment of the invention includes a method for determining a 
deconvolution operator which takes into account the reflective and other 
distorting effects of the construction of drill string 4. 
It should be noted that the coarse deconvolution noted above, which takes 
into account only the length of drill string 4 and the bottomhole 
assembly, may be used in this embodiment of the invention. It is 
preferred, however, especially in improving the accuracy of the analysis 
of the higher frequency components of the axial and torsional vibrations, 
such higher frequency components containing important information in both 
the drilling parameter monitoring and seismic prospecting applications, 
that the deconvolution operator be determined according to the description 
of the embodiment to follow hereinbelow. 
Furthermore, as is evident from the representations of Figures 3b and 3c, 
and as will be made further evident hereinbelow, the value of the time 
delays t.sub.a for axial vibrations and t.sub.b for torsional vibrations 
are important in the method according to this embodiment of the invention. 
Referring to FIG. 5, a preferred method of deconvolution in which the 
deconvolution operators retain the time delay values will be described. 
The retained time delay values are beneficial in the subsequent operations 
of reducing the effects of the random noise. 
As noted above, the frequency domain impulse response of drill string 4 may 
be known from experimentation or modeling; FIGS. 4a and 4b illustrate the 
magnitude of the frequency response (phase is not illustrated). A 
preferred method for acquiring the impulse response for drill string 4 is 
by way of applying vibrational signals at the top of drill string 4, for 
example with a hammer blow (i.e., substantially an impulse input) or with 
some other wideband stimulus, to present an axial vibrational input into 
drill string 4. These vibrations will travel downhole along drill string 
4, and reflect from the distal end thereof (e.g., at drill bit 10) back to 
the surface. Detectors such as in sub 12 described hereinabove detect the 
transmitted vibrations, with the detected vibrations used to determine the 
response of drill string 4 to the axial vibrations generated by the axial 
hammer blow (of course, accounting for travel in both directions). 
Torsional vibrations may be applied by a hammer blow to a flange located 
near the top of drill string 4, in a direction which produces torsional 
vibrations along drill string 4, such vibrations also traveling down drill 
string 4, reflecting from drill bit 10 and traveling back up drill string 
and detected by the detectors in sub 12. After analysis, a representation 
of the response of drill string 4 is stored by conventional computing 
equipment. Referring to FIG. 5, process 31 indicates the retrieval of the 
axial vibration frequency response I.sub.a (f) and torsional vibration 
frequency response I.sub.b (f) from the memory of the computing equipment 
performing the method according to this embodiment of the invention. 
The values of the time delays are preferably combined with the FFTs of the 
impulse response operators, according to this embodiment of the method. 
Such retention of the time delay values with the frequency response is 
preferred, as this representation is stored in the computing equipment 
performing the analysis, and is used repeatedly over time as the measured 
vibrations are monitored and analyzed. Time delay in the frequency domain, 
as is well known in the art, is expressed by multiplication by the phase 
shift terms. In this embodiment, these phase shift terms may be expressed 
as exp(-jt.sub.a 2.pi.f) and exp(-jt.sub.b 2.pi.f) for the axial and 
torsional cases, respectively. In this embodiment of the deconvolution 
operation, the complex frequency response of drill string 4 is thus 
expressed as: 
EQU I.sub.a (f,t.sub.a)=F[i.sub.a (t-t.sub.a)]=[I.sub.a (f)][exp(-jt.sub.a 2f)] 
EQU I.sub.b (f,t.sub.b)=F[i.sub.b (t-t.sub.b)]=[I.sub.b (f)][exp(-jt.sub.b 
2.pi.f)] 
where i.sub.a (t-t.sub.a) and i.sub.b (t-t.sub.b) are the time-shifted time 
domain impulse responses for axial and torsional vibrations, respectively, 
where F is the Fourier operator, and where I.sub.a (f) and I.sub.b (f) are 
the complex Fourier transforms of the impulse response for axial and 
torsional vibrations, respectively. FIG. 5 illustrates the performing of 
this operation in process 32. 
It should of course be noted that, if the distance between sub 12 
containing the detectors and the source of the signal is constant for 
multiple deconvolution operations, the result of process 32 may be stored 
in lieu of the non-shifted frequency response characteristics. It is 
contemplated, however, that the distance between sub 12 containing the 
detectors and the point at which the signal is to be analyzed may change 
over time. For example, the analysis may wish to "zoom" in on another 
location of drill string 4 for analysis of the signal coming therefrom. 
Also, the addition of sections 6 to drill string 4 as drilling progresses 
will also change the distance between drill bit 10 and sub 12, and 
accordingly the time delay values. For ease in performing such operations 
with varying delay times t.sub.a and t.sub.b, it is preferable to store 
and retrieve the frequency response characteristic, and to multiply each 
by the exponential phase shift term during the deconvolution. 
For purposes of explanation, the axial and torsional vibrations are 
expressed as time functions m.sub.a (t) for the measured m.sub.b (t) for 
the measured torsional vibrations, with the functions extending over all 
non-negative time t&gt;0. As noted above, each of these time series can be 
considered as the sum of signal and noise components, as follows: 
EQU m.sub.a (t)=s.sub.a (t)+n.sub.a (t) 
EQU m.sub.b (t)=s.sub.b (t)+n.sub.b (t) 
where s(t) and n(t) are the time domain representations of the signal and 
noise components, respectively, of the measured time series signals m(t). 
In FIG. 5, retrieval of the time series m.sub.a (t) and m.sub.b (t) from 
memory of the computer, or directly from the measurement apparatus, is 
indicated by process step 33. Since convolution in the time domain 
requires integration, but only requires multiplication (or division, in 
the case of deconvolution) in the frequency domain, Fourier transformation 
of the measured time series of signals into the frequency domain is 
preferred, and is performed in process 34 of FIG. 5. 
Since the frequency response operators retain the information relating to 
the time delay values t.sub.a and t.sub.b, the FFTs for the time series of 
the measured vibrations m.sub.a (t) and m.sub.b (t) may be done over a 
limited number of points in time. This is useful due to the limited number 
of points that many FFT algorithms (and hardware) can handle within 
reasonable computing time, making it useful to limit the range of points 
in time that are used in the FFT. Accordingly, for the time series m.sub.a 
(t), the points used in the FFT can begin at or closely before the time 
t.sub.a ; similarly, for the time series m.sub.b (t), the points used in 
the FFT can begin at or closely before the time t.sub.b. Since the time 
delay values are incorporated into the expressions hereinabove for 
frequency response of drill string 4, they need not be maintained in the 
FFT of the time series of the measured vibrations. The expressions for the 
frequency domain representations of the measured vibrations are as 
follows: 
EQU M.sub.a (f)=F[m.sub.a (t)] 
and 
EQU M.sub.b (f)=F[m.sub.b (t)] 
where M.sub.a (f) is the frequency domain representation of the measured 
axial vibrations, where M.sub.b (f) is the frequency domain representation 
of the measured torsional vibrations, and where F is the Fourier transform 
operator. 
Deconvolution is then accomplished, in process 35 of FIG. 5, by the 
division of the frequency domain representations M.sub.a (f) and M.sub.b 
(f) by the frequency response operators I.sub.a (f,t.sub.a) and I.sub.b 
(f,t.sub.b), respectively. This division can be done according to well 
known techniques in the computing art, for example by point-by-point 
division of the two representations at a series of discrete frequencies in 
the range of interest. In order to avoid divide-by-zero problems, it is 
preferred to add "white noise", i.e., small magnitude signals at all 
frequencies, to the representations of the frequency response operators 
I(f,t). The results of these division operations are then converted into 
time domain representations by performing the inverse FFTs, in process 36 
of FIG. 5, resulting in time domain representations m'.sub.a (t) and 
m'.sub.b (t). The sum of these representations of signal and noise 
components can be expressed as follows: 
EQU m'.sub.a (t)=s'.sub.a (t)+F.sup.-1 [N.sub.a (f)/I.sub.a (f)exp(-jt .sub.a 
2.pi.f)] 
EQU m'.sub.b (t)=s'.sub.b (t)+F.sup.-1 [N.sub.b (f)/I.sub.b (f)exp(-jt.sub.b 
2.pi.f)] 
where F.sup.-1 is the inverse Fourier operator, and where N(f) is the 
frequency domain representation of noise components 26. 
Referring to FIGS. 6a and 6b, representations m'.sub.a (t) and m'.sub.b (t) 
after deconvolution are illustrated for the axial and torsional measured 
vibrations, respectively, with noise components 26' and signal components 
24' shown separately as above. As a result of the deconvolution of process 
30, the signal components 24a' and 24b' more closely resemble one another, 
and more closely resemble the source signal 22 of FIG. 3a. This is due to 
the removal of the effects of drill string 4 on the vibrations transmitted 
through drill string 4 from the point of interest (e.g., drill bit 10) to 
the detectors in sub 12. The time delay values t.sub.a and t.sub.b have 
been retained after the deconvolution, as discussed hereinabove, as shown 
in FIGS. 6a and 6b. 
It should be noted that the deconvolution step described above will operate 
on both the noise and signal components of the measured time series of 
vibrations. However, since for purposes of this invention the noise is 
considered as random noise, the deconvolution of random noise results in 
random noise, and will be equally reducible according to the method 
described herein. 
Referring again to FIG. 2, upon the completion of the deconvolution of 
process 30, the next step in this embodiment of the invention is a time 
shift of the deconvolved axial and torsional time domain representations 
m'.sub.a (t) and m'.sub.b (t) relative to one another. This is performed 
in process 40 of FIG. 2. 
Referring again to FIGS. 6a and 6b, it should be noted that the signal 
components 24a ' and 24b' more closely resemble one another, with the 
torsional component 24b' delayed in time from the axial component 24a ' by 
the time t.sub.b -t.sub.a ; no such resemblance is present for the noise 
components 26' since, as discussed above, the noise signals are generated 
at various points along drill string 4, so that the time delay between the 
arrival of the axial noise component 26a' and the torsional noise 
component 26b' will not be a constant for all such noise, but will depend 
upon the individual noise source, many of which are summed together when 
considering the signal components 24' of interest. 
This embodiment of the invention takes advantage of the correlation between 
the signal components 24' and the lack of correlation between the noise 
components 26' to reduce the effects of the noise on the signal This is 
done in process 40 according to the invention, where the two 
representations m'.sub.a (t) and m'.sub.b (t) are made coincident in time 
and then summed. 
In practice, of course, the representations m'.sub.a (t) and m'.sub.b (t) 
are time series of measured vibrations, upon which the operations of 
process 30 have been performed, and the signal and noise components 24' 
and 26' are not known. However, the distance from drill bit 10 (or such 
other source of interest) is known, as are the relative velocities of the 
torsional and axial vibrations in drill string 4. Accordingly, the time 
shift of process 40 can be easily done by multiplying the distance between 
drill bit 10 and sub 12, in this example, by the difference in the axial 
and torsional velocities to determine the value t.sub.b -t.sub.4. Once 
t.sub.b -t.sub.a has been determined, either the axial or torsional time 
series can be shifted by this value in the computer performing the 
analysis. In this example, the representation of the torsional vibrations 
will be shifted to be considered earlier in time; the shifted 
representation will be referred to as m'.sub.b (t-(t.sub.b -t.sub.a)). 
Referring to FIGS. 7a and 7b,the time shifting of the torsional 
representation m'.sub.b (t-(t.sub.b -t.sub.4 a)) is illustrated, with time 
shifted signal component 24b" and time shifted noise component 26b". It 
should be noted, of course, that the axial representation may 
alternatively be shifted later in time to coincide with the torsional 
representation, if desired; further alternatively, both representations 
may be shifted in time to coincide at a third point in time. 
By virtue of the assumption that the axial and torsional signal components 
24 are similar, or substantially proportional to one another, the two 
time-shifted (and deconvolved, if desired) representations may be summed 
together to reinforce the signal portions. It is believed that this 
assumption is valid in at least the cases of vibrations generated by drill 
bit 10, vibrations generated by casing slap, and vibrations generated by 
axial and torsional transducers located in a bottomhole assembly 11 for 
the application of stress wave telemetry. Therefore, upon completion of 
the time shift of process 40, the two representations m'.sub.a (t) and 
m'.sub.b (t-(t.sub.b -t.sub.a)) are summed together in process 50. Since 
the signal components 24a ' and 24b" resemble one another, and since the 
noise C components 26a ' and 26b" do not (both being random, including 
after the time shift of the torsional representation), such a summation 
will tend to reinforce the signal components 24 while the noise components 
26 will randomly add to or subtract from one another. Accordingly, the 
signal-to-noise ratio will be improved, with the signal components 24 
reinforcing one another relative to the noise components 26 which will 
remain approximately the same, on the average over the time period of 
interest. The summing operation, in the case where the torsional 
representation is time-shifted, can be expressed as follows: 
##EQU1## 
However, as recognized above, the time-shifted torsional signal can be 
considered as proportional to the axial signal, i.e., 
EQU s'.sub.b (t-(t.sub.b -t.sub.a))=Ks'.sub.a (t) 
Accordingly, the sum of the axial and time-shifted components can be 
expressed as follows: 
EQU m'.sub.a (t)+m'.sub.b (t-(t.sub.b -t.sub.a))=(K+1)s'.sub.a (t)+n'(t) 
where n'(t) is a noise component consisting of the sum of the deconvolved 
axial and time-shifted torsional noise components. As noted hereinabove, 
since the noise components can accurately be considered as random for 
purposes of this method, the factors making up n'(t) need not be retained. 
It should be noted that the time shifting operation of process 40 may be 
done in conjunction with the summation of process 50, rather than as a 
separate step prior to the summation, if the computing process is more 
easily done in this way. For example, if the number of samples in the time 
series of measured vibrations are the same for the axial and torsional 
vibrations, an ordered summation may be done merely by adding the 
amplitude of the first axial sample (at about time t.sub.a) with the first 
torsional sample (at about time t.sub.b), continuing over the range of 
time of interest. Such a method would necessarily incorporate the time 
shift, since the vibrations would coincide in time due to the summation 
operation performed, and without an additional step of time-shifting 
performed for one of the time series of measured vibrations. 
It should also be noted that the signal-to-noise ratio is now improved by 
the method according to this embodiment of the invention. Considering the 
signal-to-noise ratio of each of the axial and torsional components, as 
measured, as follows: 
EQU S/N.sub.a =s.sub.a (t)/n.sub.a (t) 
EQU S/N.sub.b =s.sub.b (t)/n.sub.b (t) 
the signal-to-noise ratio after the method of this embodiment of the 
invention thus can be on the order of K+1 times that each of the original 
ratios, if the assumption that there is, on the average, no additive 
reinforcement of the noise components in the summation so that the 
amplitude of the noise components remains relatively constant. For the 
case where the amplitudes of the noise components in the axial and 
torsional vibrations are approximately equal, it is believed that the 
improvement in the signal-to-noise ratio is on the order of the square 
root of two. 
It should further be noted, however, that the amplitude of the axial noise 
component n.sub.a (t) is generally significantly larger than the amplitude 
of the torsional noise component n.sub.b (t), as in most drilling 
applications more axial noise than torsional noise is generated. 
Accordingly, the increase in the signal-to-noise ratio can be maximized if 
the amplitude of the noise components are approximately the same prior to 
the summation operation in process 50. This can be accomplished be 
performing a weighted summation where one of the components, generally the 
torsional component, has its amplitude multiplied by a constant which is 
the ratio of the amplitude of the axial noise to the ratio of the 
torsional noise. Accordingly, the summing operation would be as follows: 
EQU m'.sub.a (t)+m'.sub.b (t-(t.sub.b -t.sub.a))=[s'.sub.a (t)+n'.sub.a 
(t)]+(N.sub.a /N.sub.b)[s'.sub.b (t-(t.sub.b -t.sub.a))+n'.sub.b 
(t-(t.sub.b -t.sub.a))] 
where n'(t) represents the deconvolved noise components, as described 
hereinabove, and where N.sub.a and N.sub.b represent the root-mean-square 
amplitude of the axial and torsional noise components, respectively, over 
the time period of interest. This weighted summation is preferable in the 
case where the relative amplitudes of the noise components differ between 
the axial and torsional vibrations, as it provides the ability of the two 
noise components to cancel out one another to a greater extent than in the 
case where one is much larger than the other. Such cancellation is, of 
course, helpful in improving the signal-to-noise ratio. 
The result of the weighted (or unweighted, as the case may be) summation is 
a signal in which the signal component can be more easily identified and 
analyzed for the particular operation. Referring to FIG. 2, the case of 
seismic prospecting using drill bit 10 as the source is completed by 
process 60, in which the source signal is correlated with the reflected 
signals detected by geophone 18 of the system of FIG. 1. Methods of 
performing such correlation are conventional in the art, and include, for 
example, the Vibroseis.RTM. technique. For purposes of performing such 
correlation, the time delay resulting from transmission of the vibrations 
along drill string 4 must, of course, be taken into account. A method for 
performing such correlation, in the particular case where the drill bit 
energy serves as the seismic source waves, is described in the Rector, 
Marion and Widrow article "Use of Drill-Bit Energy as a Downhole Seismic 
Source" cited hereinabove. 
In the application described in U.S. Pat. No. 4,715,451 cited hereinabove, 
where the vibrations are indicative of certain drilling parameters, as a 
result of the method described hereinabove the vibrations at the location 
of drill bit 10 can be more easily identified and analyzed, than in the 
case where the signal-to-noise ratio remains low. In addition, by changing 
the distance of interest, i.e., changing the value of time used in the 
relative time shift between the axial and torsional vibrations after 
deconvolution, different locations of drill string 4 can be separately 
analyzed. This allows analysis of the vibrations originating at any point 
along drill string 4, and allows for the detection of the location of 
casing slap or other vibration generating events, without requiring 
additional steps of detecting the vibrations; the originally detected time 
series data can be used, and reanalyzed, with the change in the relative 
time delay. 
The noise reduction technique of this invention can also be used in the 
application of stress wave, telemetry, such as described in said copending 
applications Ser. No. 188,231 filed Apr. 21, 1988, now U.S. Pat. No. 
4,992,997, issued Feb. 12, 1991, Ser. No. 554,030 filed Jul. 16, 1990, and 
Ser. No. 554,022 filed Jul. 16, 1990, incorporated herein by this 
reference. In stress wave telemetry, however, a different method of 
deconvolution may alternatively be used, taking advantage of prior 
knowledge of the frequencies at which the information is being 
transmitted. FIG. 9 illustrates a flow diagram for the deconvolution of 
stress wave telemetry information, in the example where the information is 
frequency shift keyed, such deconvolution being performed as process 30 of 
FIG. 2 discussed hereinabove. 
Referring now to FIG. 9, process 30' for the deconvolution of stress wave 
telemetry data will now be described. Conventional computing equipment, 
such as described relative to FIG. 8 hereinabove, can be programmed to 
perform the calculations and operations in the flow of FIG. 9. It should 
be noted that process 30' of FIG. 9 is to be performed separately on axial 
and torsional vibration data, according to the axial and torsional 
frequency response of drill string 4 illustrated in FIGS. 4a and 4b 
described hereinabove, similarly as the separate deconvolution for axial 
and torsional vibrations in process 30 described hereinabove relative to 
FIG. 5. 
Similarly as in process 30 of FIG. 5, the frequency response of the drill 
string I(f) is retrieved from memory, in process 71. Since deconvolution 
in the time domain corresponds to division in the frequency domain, and 
since process 30' performs the deconvolution by way of a convolution 
operation (as will be described hereinbelow), the reciprocal of the 
frequency response I(f) is calculated in process 73. It is preferable to 
eliminate the potential for divide-by-zero problems by adding a small 
level of "white noise" to the frequency response characteristic I(f) prior 
to its division into unity. Accordingly, the reciprocal frequency response 
characteristic A(f) may be calculated in process 73 as: 
EQU A(f)=1/[I(f)+e] 
where e is a small constant relative to the amplitude of I(f), and is 
independent of frequency. Such division may be done in conventional 
computing equipment in the conventional manner, for example by iterative 
addition and division at a series of desired frequency values. 
Since the frequencies of transmission are known in the stress wave 
telemetry application, the frequency response of drill string 4 outside of 
the transmission frequencies is neither useful nor relevant in the 
deconvolution process 30'. Accordingly, in process 75, the reciprocal 
frequency response A(f) calculated in process 71 is bandpass filtered 
about the frequencies of transmission. For example, if frequency shift 
keyed (FSK) digital data is being transmitted by vibrations at 920 Hz (for 
a "0") and at 1180 Hz (for a "1"), the reciprocal frequency response A(f) 
can be filtered so that frequencies near the transmission frequencies 
(e.g., plus or minus 50 Hz from each of the transmission frequencies) will 
be passed with unity gain, with frequencies outside of the bands fully 
attenuated by the filter. The result of process 75 is thus a filtered 
reciprocal frequency response B(f): 
EQU B(f)=bandpass[A(f), 870-970 Hz, 1130-1230 Hz] 
where the bandpass function, performed by computing system 19, is a 
conventional digital bandpass filter as can be performed by conventional 
computing equipment. It should be noted that the DSP boards discussed 
hereinabove are also especially adapted for the performing of digital 
filter operations, as is well known in the art. 
Process 77 calculates the inverse Fourier transform of the bandpassed 
reciprocal frequency response B(f) in the conventional manner. The result 
is a time domain operator b(t), which represents the reciprocal of the 
impulse response of drill string 4, at frequencies near the transmission 
frequencies of the FSK data. It may be useful to further filter the time 
domain operator b(t) in such a manner that only the portions thereof which 
are above a certain amplitude are used in the convolution operation, with 
the lower amplitude portions set to zero; such filtering will reduce the 
number of calculations in the convolution operation with minimal effect on 
the result. 
In process 74, the time series data m(t) upon which the deconvolution 
operation is to be performed is retrieved from process 20 of FIG. 2. Such 
time series data can, of course, be received directly from sub 12, may be 
alternatively retrieved from the memory of computing system 19 if 
previously received data is to be analyzed, or may be received from such 
other appropriate source. Process 78 performs a time domain convolution of 
the time series data m(t) with the reciprocal filtered impulse response 
operator b(t). Since the operator b(t) is derived from the reciprocal of 
the frequency response, the time domain convolution of process 78 
corresponds to deconvolution with the impulse response of drill string 4. 
The result of process 74 is thus a time series m'(t) which, as in the case 
of process 30 described hereinabove, is the measured vibration data with 
the distortions from the non-ideal transmission of drill string 4 removed 
therefrom. 
It should be noted that, for repeated transmissions at constant frequencies 
from the same location in drill string 4, the result b(t) from processes 
71, 73, 75, and 77 may be stored in the memory of computing system 19 for 
convolution with multiple time series m(t) over the length of the 
transmission. This is possible due to the dependence of operator b(t) 
solely on the construction of drill string 4 between the transmitting and 
receiving locations, and on the frequency of transmission. Accordingly, 
the deconvolution of process 30' can be most efficiently performed by 
computing system 19 by avoiding recalculation of the repetitive steps. 
After deconvolution of both of the axial and torsional vibration time 
series m.sub.a (t) and m.sub.b (t) according to process 30', in the stress 
wave telemetry application, the process of FIG. 2 can be continued, with 
the time shifting step of process 40. 
As a result of the method according to the above-described embodiments of 
the invention, the improved signal-to-noise ratio provides enhanced 
ability to analyze and use data transmitted by vibrations along a 
structure such as a drill string. Such improvement in the definition of 
the signal components of the vibrations allows for better quantification 
of drilling parameters, in the application where inherent vibrations are 
analyzed to determine such parameters as in the example of the 
above-referenced U.S. Pat. No. 4,715,451. The method also provides 
improved receipt of vibration signals which are sent in stress wave 
telemetry. Such improved receipt allows not only more accurate 
communication by way of stress wave telemetry, but also enables the data 
transmission to take place at higher frequencies, since additional 
attenuation can be tolerated with an improved signal-to-noise ratio. 
Furthermore, the improved signal-to-noise ratio, and also the improved 
deconvolution technique, allows for more accurate determination of the 
seismic source signature in the application of seismic prospecting using 
the drill bit as the seismic source. Since the accuracy of the correlation 
results depend upon the accuracy of the seismic source signature, the 
accuracy of the seismic analysis will be improved by use of the method 
according to the preferred embodiment of the invention. Furthermore, as 
noted above in the Background of the Invention, currently available 
systems for detecting the seismic source signature from drill string 
vibrations have been observed to be ineffective for particular drilling 
operations, such as those using PDC bits and downhole motors, since the 
noise amplitude is apparently larger for these operations. It should be 
noted that the choice of drill bit, and the choice of downhole motor 
versus top drive, depends in large part upon the type of formations into 
which the drilling is occurring. Accordingly, the method according to this 
embodiment of the invention can enable seismic prospecting in such 
formations which require the use of such drilling equipment, as the method 
provides for reduction of the effects of noise in the vibrations 
transmitted along the drill string. 
It should be noted that the methods according to the above-described 
embodiments of the invention are applicable not only to axial and 
torsional vibrations transmitted along a drill string or other structure, 
but may also be applied to other acoustic signals transmitted or traveling 
along a structure, where such signals are generated at a particular 
location and have components of differing velocities which are 
substantially proportional to one another. 
While the invention has been described herein relative to its preferred 
embodiments, it is of course contemplated that modifications of, and 
alternatives to, these embodiments, such modifications and alternatives 
obtaining the advantages and benefits of this invention, will be apparent 
to those of ordinary skill in the art having reference to this 
specification and its drawings. It is contemplated that such modifications 
and alternatives are within the scope of this invention as claimed 
hereinbelow.