Classifications

• • E—FIXED CONSTRUCTIONS
  • E21—EARTH OR ROCK DRILLING; MINING
  • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
  • E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
  • E21B43/11—Perforators; Permeators
  • E21B43/116—Gun or shaped-charge perforators
  • E21B43/1185—Ignition systems
  • E21B43/11857—Ignition systems firing indication systems
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
  • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
  • G01V1/40—Seismology; Seismic or acoustic prospecting or detecting specially adapted for well-logging
  • G01V1/42—Seismology; Seismic or acoustic prospecting or detecting specially adapted for well-logging using generators in one well and receivers elsewhere or vice versa

Definitions

• the present invention relates to subterranean well drilling, well completion and maintenance. More particularly, the invention relates to procedures for enhancing well production and for verification of production zone perforation by shaped charge explosives.
• Those in the petroleum industry are particularly concerned with extracting petroleum by boring holes into deep underground rock formations.
• explosive devices are placed in the borehole and detonated, causing piercement and fracturing of the rock.
• These explosive devices are called Perforating Guns and contain a series of shaped charges, each with a primer connected by explosive cord called detonating cord.
• the detonating cord is also connected within the Perforating Gun to a detonator.
• the explosion is initiated by the detonator and travels along the detonating cord and past the series of shaped charges, detonating each of them in turn, to the last shaped charge in the Perforating Gun.
• the operator may get an indication of a probable firing of the gun from a transducer positioned on the well structure at or near the well head. Presumably, the absence of a signal indicates a total misfire. This method often fails to give correct indications of gun firing or misfiring, as the case may be. Moreover, this wellhead transducer method provides neither an indication of a partial misfire nor a quantitative estimate of the extent of detonation.
• TCP Guns Tubing-conveyed Perforating Guns
• TCP Tubing-conveyed Perforating Guns
• the operator thus may never leam from retrieval and direct inspection of the gun that a partial detonation has occurred. He may suffer direct economic loss in that the productive rock formation is only partially perforated and petroleum production from the perforated borehole is correspondingly reduced. A potentially far greater economic loss may stem from the operators resultant under-estimation of the production potential of the oil field, based on the lower production rate after a partial perforation that he believes to be a complete perforation of the formation.
• a preferred embodiment of the invention is a set of seismic receivers, a seismic recording and control system linked to the Perforating Gun detonation control system and containing a computer programmed to process and analyze the seismic wave amplitudes enabling the practitioner to determine the extent of detonation of a subsurface borehole-emplaced Perforating Gun.
• the seismic receivers consist of conventional geophones or other transducers deployed singly or in arrays or sub-arrays of multiple transducers. Emplacement of the seismic receivers may be at or near the earth's surface or in boreholes proximate the vicinity of the Perforating Gun positioned to allow advantage in sensing and processing the directly arriving seismic waves from the Perforating Gun.
• the Perforating Gun may be positioned as necessary to achieve its purpose at any depth within a borehole and may be of any practicable length or style of construction. It may be detonated by any of the available means. The detonation is assumed to be initiated by a detonator and to progress away from the position of the detonator as it travels along the gun.
• the axis of the borehole may be vertical, horizontal, linear, or curved, i.e. of any curvilinear shape.
• Seismic waves caused by the progressive explosion travel in all directions and arrive at the seismic receivers. Amplitudes of the seismic waves are detected, recorded and then processed to improve the signal-to-noise ratio and form a best signal estimate.
• a control and processing computer activates the recording prior to the instant of detonation, enabled to do so by a link to the detonation control system.
• the link may be an automated electronic link or may simply be voice communication between human operators of the seismic recorder and the detonation system.
• the best signal estimate is analyzed and a determination is made of the extent-of-detonation (EOD) of the Perforating Gun, i.e. whether the Perforating Gun fired successfully, partially misfired or totally misfired, and in the case of a partial misfire, the quantitative extent of detonation of the gun.
• EOD extent-of-detonation
• the determination may include comparison of the best signal estimate to predicted signal based on modeling and/or to signal estimates from other detonations.
• the determination may also include an application of novel inversion algorithms and further analysis to best quantify the extent of detonation. In all of these approaches the determination relies upon pre-determined potentials of the perforating gun. The process can be performed rapidly and results provided on site so as to make the result available to the operator soon after the detonation.
• Figure 1 is a cut-away view of a rock formation showing a well bore and system elements as well as a Composite Wavelet received at the surface from the detonation of a Perforating Gun.
• Figure 2 is a view of a portion of the preferred embodiment as positioned at or near the earth's surface.
• Figure 3 is a view of the portion of the preferred embodiment with seismic receivers deployed in a deep borehole.
• Figure 4 is a schematic view of the seismic receiver at the surface of the earth.
• Figure 5 is a schematic view of the seismic receiver positioned in a borehole.
• Figure 6 is a depiction of the signal processor showing its essential elements.
• Figure 7 is a schematic view of the process controller.
• Figure 8 is a schematic view of a section of the Perforating Gun.
• Figure 9 is a time-line of the detonation and recording process.
• Figure 10 depicts the successive stages of gun detonation and seismic energy propagation.
• Figure 11 illustrates modeled composite wave forms and autocorrelations for varying Gun Lengths.
• Figure 12 shows a basic wavelet and its composite for 6, 24 and 96 milliseconds (msec) Duration
• Figure 13 shows successive stages of the inversion of a Composite Wavelet for varying assumptions of extent of detonation.
• Figure 14 contains three graphs that show the input and output of the inversion process to determine the Duration in the 24 msec case
• Figure 15 contains three graphs that show the input and output of the inversion process to determine the Duration in the 6 msec case
• Figure 16 shows the effect of noise on the inversion process comparing to Figure 14.
• Figure 17 illustrates the autocorrelation method of estimating Duration.
• Figure 19 shows a table of successive steps in the first stage of inversion and the second stage of inversion of a modeled Composite Wavelet for a curvilinear borehole.
• Figure 20 graphically illustrates the results of the second stage of inversion of a Composite Wavelet modeled using the Pulse Density Method.
• Figure 21 illustrates the results comparable to Fig 20 but for a Composite Wavelet modeled using the Time Shift Method
• Figure 22 gives sample equations for successive stages of decomposition of a Composite Wavelet.
• Figure 23 shows a table of values of Duration and Travel Time versus Gun
• Figure 24 is a diagram of the Perforating Gun divided into Gun Segments and showing the point of misfire and effective Gun Length.
• Figure 25 shows the seismic recording of a successful detonation and of a total misfire of a Perforating Gun.
• a number of seismic sensors 100 are shown in position at or near the earth's surface 160 and connected to a signal processor and recorder 105.
• This unit 105 is further linked to the extent of detonation (EOD) controller 110.
• EOD detonation
• This controller 110 controls all of the equipment that is unique to this invention. Together these three subsystems make up the complete EOD system 115.
• the remainder of the equipment in Fig 1 comprises items that are normally used in the business of drilling, perforating, completing and producing petroleum from boreholes.
• the borehole and borehole equipment 170 are shown connected to wellhead apparatus 120.
• a Perforating Gun 140 is shown positioned in the borehole, ready for detonation.
• the perforation operator When the Perforating Gun is ready to be detonated, the perforation operator notifies the seismic observer, who activates the EOD system.
• the EOD system then begins to record seismic data, received by the seismic sensors 100 and then processed and digitized in the signal processor and recorder 105.
• the EOD system continues to record and store data in memory and on media (such as tape) until the seismic energy caused by the explosion of the Perforating Gun has abated.
• Seismic ray paths 145 are shown on Fig 1 to indicate the approximate travel path of seismic waves from the Perforating Gun 140 to the seismic sensors 100. These ray paths are not perfectly straight lines as shown in Fig 1 but will be bent as they pass through layers of earth with differing seismic wave velocities and are refracted.
• the amplitude versus time graph 150 called the Composite Wavelet, represents the seismic amplitude received at the seismic sensors 100 and recorded and processed digitally.
• the amplitudes prior to reception of the energy from the detonation of the Perforating Gun 140 will be small if seismic noise level is low, the early amplitudes of the seismic waves emanating from the detonation will be relatively high and they will gradually subside after a few hundred milliseconds (msec) to lower levels, eventually dying out after some seconds and leaving only seismic noise again.
• the seismic noise is defined herein to be the combination of ambient noise, i.e. seismic waves from uncontrolled external sources, such as caused by wind and traffic, and seismic waves resulting from the perforating gun detonation (gun- generated noise), but other than signal waves, i.e. the direct arrivals through the earth from the perforating gun itself.
• signal is defined as these directly arriving seismic waves, the Composite Wavelet 150.
• any other seismic waves caused directly or indirectly by the perforating gun detonation process are considered to be a component of seismic noise.
• gun-generated noise components are seismic waves caused by movement of the equipment in the borehole and at the well head, when such movement is caused by the detonation, and seismic waves traveling from the perforating gun to the sensors by indirect paths that include reflection from impedance boundaries (but not reverberations).
• Reverberations defined as short-period multiple reflection energy following the direct arrival events, contribute energy to the source wavelet and are considered to be signal for the purpose of extent-of-detonation determination.
• Signal will ordinarily be compressional wave energy only, because it will generally be better separated from gun-generated seismic noise than other modes due to its early arrival. However, in principal, signal could also be shear wave or other modes of directly arriving seismic energy.
• Fig 2 provides further detail of the EOD system 115.
• the seismic sensors 100 are linked together and connected to the signal processor 105 by a surface seismic cable 200.
• the sensors may be commercially available geophones and/or hydrophones, hydrophones being suitable if the area is water covered.
• the sensors may be at the ground surface or may be buried to improve coupling and to reduce ambient noise.
• the sensors may also be emplaced in shallow boreholes.
• the geophones may be vertical and/or horizontal geophones, i.e. able to sense vertical or horizontal motion of the earth.
• the geophones may be 3-component geophones, that sense three orthogonal components of motion.
• a combination of all four sensors, one vertical sensor, two horizontal sensors and a pressure-sensitive sensor or hydrophone may also be used (called 4C sensor).
• hydrophones may be used as the sole type of sensor. Any type of transducer or sensing apparatus capable of sensing variations in pressure or ground motion is potentially suitable for the EOD purpose.
• Fig 4 shows surface seismic sensors 100 emplaced at the surface in a one- dimensional array with four geophones per sub-array and 7 sub-arrays comprising the total seismic array aperture 410.
• the geophones in the sub-arrays may be combined additively, to improve the signal-to-noise ratio, preferably with individual time shifts to align the signal prior to combination, or they may be combined using other array-processing algorithms.
• Multiple arrays of various sensor types, each consisting of multiple sub-arrays may be utilized. Diversity stacking, adaptive noise editing, adaptive filtering, coherency filtering, Weiner filtering, and other methods exploiting the multiple sensor sub-arrays and arrays, that sample the signal waves and noise waves, may be employed, to improve the signal estimate.
• more sub-arrays with suitable two-dimensional or three-dimensional geometric design may be utilized to provide greater redundancy of channels with desired signal and noise characteristics to facilitate the signal-to-noise ratio enhancement through array processing.
• the sub-arrays could be emplaced over a rectangular area in a two-dimensional array with 7 sub-arrays inline and 7 sub-arrays cross-line for a total of 49 sub-arrays. With appropriate processing a better signal estimate would result from this augmentation of the sampling effort.
• the employment of these multiple sub-arrays, arrays and processing techniques may be viewed as an effort to obtain the best possible representation of the true Composite Wavelet. However under ideal conditions a single sensor could be used rather than the more elaborate approach described above, and this would be preferred for cost reasons. With experience, the practitioner can decide what level of effort will provide the desired degree of result quality.
• the resultant signal estimate the best available representation of the ideal noise-free Composite Wavelet 150, is subjected to analysis and further mathematical processing to yield determinations of whether the gun fired or misfired, whether there was a partial misfire, and if there was a partial misfire, the quantitative extent of detonation of the perforating gun.
• the connecting cable 200 may be replaced by a radio linkage to the signal processor and recorder 105 to provide an equivalent method of transferring the seismic data. Another equivalent method is to record data at each sensor or group of sensors and later transmit or transfer it to the central signal processor and recorder 105.
• FIG 3. An alternative method of configuring the EOD system 115 is presented in Fig 3.
• This borehole may either be the same borehole 170 as contains the Perforating Gun 140 or it may be a different but adjacent borehole.
• the downhole seismic sensors 330 may be connected to each other and up the borehole to the surface and to the signal processor and recorder 105 by a downhole cable 320. Alternatively they may store their information for later retrieval. In this adaptation the seismic wave recordings may be retrieved from the downhole seismic sensors after they are returned to the surface, or information may be transmitted to the surface by other available methods such as EM or borehole pressure wave telemetry.
• multiple downhole sensors may be combined using a wide range of processing techniques, as described for surface sensors, to enhance the signal-to-noise ratio of the signal estimate.
• the downhole sensors may not be distributed areally but instead limited to emplacement along a borehole. However, downhole sensors may be deployed in multiple boreholes.
• the best combined signal estimate is subjected to further analysis and processing to determine the success, partial success, or failure of the detonation and to quantify the extent-of-detonation.
• Fig 5 shows details of the downhole seismic sensors 330 as they are deployed for use. Individual geophones are contained in cases that have locking arms that may be actuated.
• Downhole geophones in this configuration are in conventional use in the industry.
• other types of downhole seismic sensors may be employed such as hydrophones.
• Multi-component geophones may be combined with pressure- sensitive sensors, just as in the surface sensor method.
• the seismic sensors may be placed closer to the explosion if a borehole is used, a means of improving the signal-to-noise ratio of the seismic data is available via the downhole method, relative to the surface method. Closer emplacement provides higher seismic energy levels and more high frequency signal, but also simplifies the seismic ray path geometry of the seismic energy arriving at the sensors, which is beneficial to the methods of this invention.
• Another advantage of downhole emplacement is that the ambient noise level will generally be much lower than at the earth surface. Militating against the downhole sensor emplacement strategy however is the cost of deploying the sensors. This cost is generally significantly greater than the cost of surface deployment.
• a compromise solution is to place sensors at a shallow depth in boreholes or to simply bury the sensors just below the surface
• the practitioner should consider the effect that gun-generated noise may have on the directly arriving signal events. Positioning of the sensors at a distance such that gun-generated noise events do not arrive simultaneously with signal events may require in some cases that a minimum distance from the well head be maintained, or in the case of borehole sensors, that a minimum distance from the perforating gun to the sensors be maintained. This is because high velocity waves traveling up the borehole may interfere, or may excite secondary noise modes at or near the well-head, that can interfere with the directly arriving waves that travel through the earth. Experience will provide a guide as to when such conditions will exist. The solution is to place the sensors beyond this critical minimum distance.
• Fig 6 shows the elements of the signal processor and recorder 105 and Fig 7 shows the EOD controller. Both of these devices are essentially computers of commercially available types. All of the hardware components are of familiar type and commercially available. The software and method of use of the EOD controller provide the uniqueness of the system.
• seismic signals are input to the device 105 via cable 100 or 300. These may be analog, as assumed in the present figure, or may be digital having been digitized at or in proximity to the seismic sensors. In the later case commands may be sent from the CPU 640 to the online devices controlling the sensors. If the seismic signals are brought to the device 105 in analog form as electrical voltages in the cable, a pre-amplifier 610 amplifies and conditions the signal prior to analog-to-digital conversion in the A/D converter 620. Digitized seismic amplitudes are stored in memory and may be written to physical media such as tape by I/O devices 650. Other standard subsystems of the device 105 include power supply 680, monitor and keyboard 670 and clock 630. The system elements shown for the signal processor and recorder 105 are present in integrated form in commercially available PC-based seismic data acquisition systems such as the ARAM ARIES system manufactured by Gec-X Systems Ltd.
• a second computer system is shown in Fig 7 and is designated as the EOD controller 110. It is networked or otherwise connected to the signal processor and recorder 105 as indicated in the Fig 7 or it may be interfaced solely by the physical media recorded by the device 105 and control information provided to device 105 by the EOD controller 110 via physical media.
• the EOD controller 110 includes standard types devices as shown: a CPU 720, memory 740, clock 710, I/O devices 730, monitor and keyboard 750 and power supply 760. It is shown as linked to the detonation controller 130.
• the detonation controller may be any means for detonating or controlling the detonation of the Perforating Gun 140. It may be contained in a single device located in the proximity of the wellhead and in communication with the Perforating Gun assembly in borehole. Alternatively, the detonation controller 130 may be a cooperative assembly of numerous devices located at both, the well surface and downhole e.g. physically coupled to the Perforating Gun.
• the EOD controller may utilize any type of physical, electronic or electrical linkage, or it may include a communication linkage effected by radio, cell phone or other means.
• the purpose of the linkage is to alert the seismic observer so that he may activate the seismic recording at the correct time just prior to the detonation of the Perforating Gun and to allow general coordination of well activity and seismic activity.
• the signal processor and recorder 105 may be combined with the EOD controller 110 so that only one computer instead of two are required to carry out the required activities, as an alternative and equivalent implementation of the method.
• the Perforating Gun 140 is shown in Fig 8. Essential elements of this include the electrical wire connected at the top of the gun to the detonator 850; the detonating cord 860, and a series of shaped charges 855. Each shaped charge 855 is provided with a primer explosive charge 870, a case 875, a liner 880, and a main explosive charge 890. Although only four shaped charges are depicted in Fig 8, normally many more would be contained in a Perforating Gun of the lengths commonly utilized.
• the Perforating Gun sections are manufactured such that total gun assembly lengths varying from a few feet to many hundreds of feet may be achieved.
• the shaped charges will typically be uniformly spaced over the entire length of the active portion of the gun assembly with less than 1 ft separation between charges. In perforating guns designed to perforate multiple zones with intervening zones to be left un- perforated, there will be portions of the gun with no shaped charges.
• each successive shaped charge will be detonated in turn, until the last shaped charge, furthest from the detonator 850, explodes, completing the detonation process.
• a 'total misfire' of the Perforating Gun occurs. If the detonator detonates, but a misfire interrupts the progression of the detonation front along the detonating cord before the last shaped charge is detonated, a 'partial misfire' occurs. If all shaped charges detonate including the furthest shaped charge from the detonator, a 'complete firing' or 'successful firing' occurs.
• Fig 8 indicates three critical parameters of the Perforating Gun: these are the position deemed the "top of the gun” 800, the “bottom of the gun” 810" and the “Gun Length” 820.
• the "top of the gun” is defined as the position of the center of the uppermost shaped charge along the borehole axis.
• the “bottom of the gun” is the position of the center of the lowermost shaped charge within the borehole. Both of these positions are defined in terms of X, Y and Z coordinates of three-dimensional space with the Perforating Gun positioned ready for detonation.
• the “Gun Length” is the distance along the borehole axis between the "top of the gun” and “bottom of the gun”.
• the position of the seismic receiver is given by the coordinates in three dimensions of the geometric center of the seismic sensor array aperture 420.
• Fig 9 shows the sequence of steps that take place when the perforation operator notifies the seismic observer of his intent to commence detonation at a specified time.
• the seismic observer activates the EOD system 115 (Fig 1) at time to, having already deployed the seismic sensors and tested all of the subsystems.
• the signal processor and recorder 105 Prior to the earliest possible time of the detonation commencement t3 he causes the signal processor and recorder 105 to begin to record seismic data, and the recording continues from this time ti onward to t ⁇ .
• the perforation operator takes action at time t 2 to initiate the detonation process as required by the particular type of perforation system and according to the schedule that has been communicated to the seismic observer. Sometime later (at ) the detonation commences, i.e.
• the detonator 850 detonates.
• the amount of delay between initiation of the detonation process and the instant of detonation commencement is variable depending on the type of firing system and control system used. In any case the seismic recording process must be initiated prior to detonation and continue some time after the detonation of the Perforating Gun ceases at t 5 .
• a unique feature of the method of this invention is that it is not a requirement that the time of detonation be known in order for the determination of the extent of detonation to succeed. Therefore no provision need be made to measure, determine or otherwise know that particular instant of time, the moment of detonation.
• This aspect simplifies the field implementation of the recording process because there does not have to be an electronic or electrical linkup between the detonation controller 130 and the EOD system 115. However if there is a link between the gun firing system and the seismic recording system, or if both systems are equipped with or have access to accurate synchronized clocks or to external time signals such as from GPS satellites, so that the instant of detonation is known precisely, a secondary benefit may befall the practitioner.
• VSP Very Seismic Profile
• Seismic surveys in the area may be calibrated with and tied to the detonation recording and further, to well geology, using this information and methods familiar to those skilled in the art.
• the Detonation Controller 130 controls an electrical firing system from the surface, it can be readily linked to the Process Controller 110. This would facilitate the use of the recorded data for this secondary purpose.
• the amount of additional time that must be recorded depends on the distance between the seismic sensors and the Perforating Gun, the seismic velocity and other factors. Normally at least 20 seconds of data would be recorded after the latest expected time of detonation. Only the first few hundred msec of data including the first arrivals and their immediate aftermath are useful to the inversion process of this invention, however additional evidence of the detonation and even the extent of detonation of the Perforating Gun may be gleaned from data at times later than this.
• seismic energy caused by later movement of the gases in the borehole, the gases having been generated by the explosion.
• Such seismic energy may arrive by diverse non-direct paths to the seismic sensors and can be useful in ascertaining that the detonation did in fact occur.
• Fig 10 illustrates in a cross-sectional view of the Perforating Gun 140 in the surrounding earth in four successive stages of detonation and seismic emanation from the gun.
• detonation commences, at the top of the gun.
• the detonation front 1030 has progressed 50% of the way along the gun to a position midway along the borehole axis between the top and the bottom of the gun.
• the detonation front 1030 has just initiated the detonation of the bottom-most shaped charge in the Perforating Gun.
• the detonation front 1030 travels along the axis of the Perforating Gun and the nearly co-located axis of the borehole itself, at a constant velocity V d .
• This detonation velocity V d is a characteristic of the particular design of the type of Perforating Gun chosen by the operator. It will have been measured in the laboratory and is a known quantity. A typical value for Vd is 10 ft per msec. This is less than half of the velocity of detonation of the detonating cord 860 that carries the detonation front 1030. This reduction in velocity is due to the helical configuration of the detonating cord within the Perforating Gun as it descends from shaped charge to shaped charge, the shaped charges being located with orientations from 0 to 360 degrees around the Perforating Gun axis. Because the cord typically takes this indirect path along the gun axis the length of cord required may be more than twice the length of the Perforating Gun. This results in the significant lowering of the effective detonation velocity as measured along the gun axis, Vd , from the absolute detonation velocity along the cord itself, for typical Perforating Guns.
• Certain Perforating Guns do not have this type of helical detonating cord configuration and have instead a more or less straight detonating cord along the Perforating Gun axis, either for the whole length of the gun or just for certain portions of the gun.
• These Perforating Gun designs will of course exhibit an effective detonation velocity that approaches the value of the absolute detonation velocity of the detonating cord itself, e.g. greater than 20 ft per msec.
• Fig 10 also depicts the seismic wavelet associated with the seismic energy that propagates from the exploding gun toward the earth surface.
• the seismic waves propagate in all directions, but only the upward traveling waves are considered here.
• Wave A in Fig 10 is the leading edge of the leading wave 1000, i.e. the first seismic energy in the seismic wavelet that travels upward from the first shaped charge to explode. It progresses upward at a velocity Vr that is the compressional wave velocity (p wave velocity) of the rock through which it travels and will typically be the first energy from the detonation to be received by the seismic sensor array.
• Vr is the compressional wave velocity (p wave velocity) of the rock through which it travels and will typically be the first energy from the detonation to be received by the seismic sensor array.
• Wave A 1000 will have reached a position well above the top of the gun as shown.
• the detonation front 1030 has reached a position midway along the Perforating Gun.
• a quasi-continuous series of seismic wavelets, one from each shaped charge are intermingled as they progress upward.
• the figure shows the leading edge of the leading wave from the shaped charge midway along the gun beginning to form at time s
• Wave A and following waves have progressed further upward and the detonation front has progressed further downward and just caused the bottommost shaped charge to explode.
• Wave B begins to emanate upward at this instant, representing the leading edge of the trailing wavelet.
• a Gun Segment 2410 may be defined as an arbitrarily small length of the live portion of the Perforating Gun containing one or more, but an integral number, of shaped charges. Using this definition, any Perforating Gun may be divided into a series of equally-powered Gun Segments (with the possible exception of the last segment). Each of the Gun Segments would generate the same Basic Wavelet 1210 under identical conditions of detonation.
• Figure 24 shows the Perforating Gun divided into a set of Gun Segments 2410.
• the Gun Segments 2410 would generate a series of upward-traveling seismic wavelets of identical form. These wavelets in addition to being of identical form would be separated in time upon departure from the vicinity of the gun and upon arrival at the seismic receiver by equal increments of time. This suggests a method of modeling the Composite Wavelet 1100 which is used in Fig 11 and subsequent figures, to model Composite Wavelets given an arbitrary Basic Wavelet 1210, i.e. the wavelet from one segment of the Perforating Gun.
• Fig 11 shows Composite Wavelets from five different lengths of Perforating Gun varying from 13 ft to 320 ft.
• the autocorrelation of each Composite Wavelet appears on the right side of the figure.
• the length of the Perforating Gun increases the appearance gradually changes from that of a fairly simple wavelet to a two-part wavelet with a predominately positive first half and a predominately negative second half.
• the second half appears to be the same as the first half but with opposite polarity. This is the exact case.
• the first half of the Composite Wavelet of a long perforating gun may be either negative or positive, depending on the initial polarity of the Basic Wavelet, but will always be of opposite polarity to the second half.
• the 320 ft gun is also found to have a time delay between the first half and the second half exactly equal to the modeled time between the "leading edge of the leading wave” and the "leading edge of the trailing wave” (see Fig. 10).
• the autocorrelation also exhibits a strong negative side lobe peaking at this time relative to the zero-lag peak.
• Fig 12 provides three examples of Composite Wavelets 1210 of varying Duration: 6, 24 and 96 msec. Also shown is the Basic Wavelet 1210, which was summed to yield the Composite Wavelet.
• the Basic Wavelet is the wavelet from one segment of the Perforating Gun. Duration is defined as the time interval between the
• leading edge of the leading wave and the “leading edge of the trailing wave” may be computed — in the case of simple vertical geometry — by adding the time interval between the detonation of the first Gun Segment and the detonation of the last Gun Segment to the seismic travel time between the position of the last detonating Gun Segment and the position of the first Gun Segment.
• the Duration for a given detonation of a given Perforating Gun is a function of the position of the seismic sensor array. For a vertical borehole and uniform geology the maximum Duration value would be observed at the wellhead. In this case if the sensor array is positioned away from the well head the Duration is reduced — eventually to zero at very great distances away from the well head. For non-vertical boreholes, the Duration will be maximized at some set of positions away from the well-head. Because the determination of EOD is benefited if the Duration can be observed at maximum value, the practitioner should consider this when deciding the location of the sensor array. Ray-path modeling can guide this decision. A compromise between maximizing Duration and achieving best signal-to-noise ratio may be required in some cases. Again referring to Fig 12, the 6 msec and 24 msec Duration Composite
• Wavelets do not show separation into a first half on one polarity and a second half of opposite polarity. This is due to the fact that the Basic Wavelet is too long relative to the Duration to allow this appearance, causing the two parts to overlap. However the 96 msec Duration Composite Wavelet does show this clear separation into two opposite polarity halves. The time interval between the leading peak 1220 and its negative counterpart, the following trough 1230, is precisely 96 msec, the exact value of the Duration.
• Composite Wavelet may be measured directly or preferably with aid of the autocorrelation. This time is equated to the sum of detonation propagation time and the differential seismic travel time to the receiver for the first Gun Segment and the last Gun Segment. The position of the last Gun Segment that is assumed to actually have detonated is varied in the calculations to achieve the best equivalence. If this best equivalence is not obtained when calculating for the last physical Gun Segment in the Perforating Gun, a partial misfire is thereby determined to have occurred.
• a total misfire can also be conveniently determined using an autocorrelation method or by direct observation of the seismic recording. If the autocorrelation of the seismic data received after the gun is expected to have fired does not indicate a significantly higher level then during a period of known quiescence, total misfire is likely to have occurred. Further evidence of a total misfire is the absence of first energy on the seismic recording with its predictable delay time from one seismic sub- array to the next and its typical waveform and energy pattern as can be determined by one experienced in seismic methods.
• FIG 25a depicts a seismic recording made with the EOD system 115 with a typical Surface Seismic Receiver 210 as detailed in Figure 4.
• the Perforating Gun has detonated and fired successfully.
• a characteristic seismic energy pattern appears with successive arrival times as predictable from ray trace modeling from nearest to furthest seismic sensor sub-array from the Perforating Gun.
• the seismic energy stands above the level of the seismic noise energy. Measurement of like wavelet peak and trough times can be used together with the ray-path-modeling predicted travel times from the top of the gun to each seismic sub- array to determine whether the origination of the seismic energy was at the location of the Perforating Gun.
• Figure 25b shows the seismic recording made during a time period in which a
• the amplitude of the Composite Wavelet that is observed from the detonation of a perforating gun can also give an indication of the length of gun that actually detonated.
• Various measures of amplitude including, for example, maximum peak amplitude, rms amplitude, average absolute amplitude and average power may be used to compare a particular observed Composite Wavelet to other Composite Wavelets. Referring to Fig.
• the Composite Wavelets for the various gun lengths exhibit a progressive increase from shortest perforating gun to longest perforating gun (left side of figure labeled Gun Signatures.) These wavelets were modeled to simulate the wavelets that would be observed under identical physical conditions including geology, type of perforating gun, position of top of gun, and type and position of seismic receiver. If another perforating gun Composite Wavelet for these same conditions, but a different gun length were modeled, it could be readily compared to the six wavelets and its effective perforating gun length computed, interpolating between shorter and longer guns. A quantitative estimate of the length of gun that detonated to produce the new Composite Wavelet could be thus obtained. Of course, wavelet shape as well as amplitude could be used together to improve the estimate.
• comparison wavelets In the case of real observed Composite Wavelets the same procedure could be applied if comparison wavelets were available.
• the comparison wavelets would preferably have been obtained from identical gun type, at similar depth, under similar geologic conditions — it would not be possible to have identical conditions as in the model study above.
• perforating gun detonations were routinely recorded in a given geologic environment, such as within a geologic basin or within an oil field, a set of wavelets could be made available for comparison and computation of effective gun length and extent-of-detonation as described above for the models.
• Simple correction factors for varying depths, type of perforating gun and other variables can be applied to improve the accuracy of the determination.
• both wavelet shape and amplitude can be used separately and in combination to improve the accuracy of the extent-of-detonation computation.
• Another method of determining the extent-of-detonation of a perforating gun is next disclosed.
• This method relies on inversion of the Composite Wavelet instead of the previously described observations, comparisons and computations.
• the inversion method also relies upon predetermined potentials of the Perforating Gun, based on physical conditions, computations, theoretical predictions and/or actual observations of Composite Wavelets. It can be used independently or together with the other methods to give independent quantitative determinations of the extent-of-detonation.
• This inversion method of determining extent of detonation can work effectively when the Perforating Gun is detonated in a portion of a borehole that is neither perfectly linear nor perfectly vertical. In many cases the borehole will not be vertical — Perforating Guns are often used in horizontal boreholes or boreholes that represent less extreme cases of non-verticality but are none the less non-vertical.
• the borehole axis is not necessarily a straight line; it may be curved in two or three dimensions. A borehole that is curved in three dimensions is called herein a curvilinear borehole or a 3D borehole.
• a two-stage inversion process has been invented that is applied to the Composite Wavelet that is recorded when the Perforating Gun is detonated.
• the first stage (Stage 1) of the inversion ideally yields an output wavelet (Stage 1 Wavelet) that is equivalent to the convolution of the Basic Wavelet with a positive unity spike at time zero (+1) followed by a negative unity spike (-1) at a time equal to the Duration of the Composite Wavelet.
• This ideal output occurs in the Stage 1 inversion process only under one crucial condition. That condition is that the process is given the correct value of Duration to use. But the practitioner does not know this value, because this is the whole objective of the exercise, to team the actual value of Duration. Therefore a series of Stage 1 inversions must be performed, assuming every possible value of Duration.
• the maximum possible Duration corresponds to the detonation of the entire Perforating Gun.
• the minimum Duration corresponds to the firing of only the very first Gun Segment.
• the Duration range from maximum to minimum Duration is sampled at a suitably small interval, for example an interval equivalent to the
• Duration increment caused by adding a single Gun Segment .to the Perforating Gun.
• the ideal output results.
• the Stage 1 output will be similar in appearance to a Composite Wavelet from a longer gun.
• the second half will be a polarity-reversed repetition of the first half; however, unlike the Composite Wavelet, the first half will not be predominately of one polarity (the first polarity) and neither will the second half be predominately of one polarity (opposite to the first polarity).
• Each half will have a zero mean, i.e. will be oscillatory around zero amplitude.
• the first half will be overlapped with the second half, making it difficult to observe the positive and negative Basic Wavelet components of the Stage 1 Wavelet.
• the probable correct value of Duration is not possible.
• the second stage of the inversion process (Stage 2) is applied to the Stage 1
• the Stage 2 inversion assumes the same value of Duration that was assumed in the Stage 1 inversion and thus the two stages are consistent in this regard.
• the output wavelets from the two stages may be displayed on a one-for-one basis, as in Fig 13.
• On the left are shown five Stage 1 wavelets, each for a different assumed value of Duration, from 11 msec to 15 msec at 1 msec intervals.
• On the right are the corresponding Stage 2 wavelets.
• the value of Duration used to model the Composite Wavelet that was input to the inversion process is 13 msec.
• the Stage 1 wavelet for the 13 msec inversion 1310 is the most perfect repetition of positive front half followed by a polarity-reversed second half.
• each of the five gives a reasonably good representation of this appearance, and it would be somewhat challenging to determine the correct Duration from this evidence alone.
• the Stage 2 inversion wavelets are displayed.
• the Stage 2 wavelet for a Duration assumption of 13 msec 1320 clearly shows the minimum energy of the five. Its initial wavelet is followed by a quiescent tail whereas for other values of Duration, the tail continues to oscillate, even increasing in amplitude for Durations of 11 and 15 msec.
• the Stage 2 wavelets are compared mathematically and visually by the user to determine the correct value of Duration for the detonation that occurred.
• the correct value, Duration 13 msec, is chosen.
• This chosen value of Duration must then be converted to the value of the length of Perforating Gun that actually detonated. This is done using the known values of detonation velocity, seismic velocity and locations of the receiver and Perforating Gun, and modeling the seismic ray paths to determine the seismic travel times.
• the first step in this process is to build a Duration Table as illustrated in Fig 23, containing values of travel time from the center of each Gun Segment to seismic receiver and the corresponding values of Duration. These values of Duration are as would be observed if the gun misfired after that Gun Segment 2410. The point of the misfire 2440 and the Effective Gun Length 2430 are shown on Fig 24.
• VSP Vertical Seismic Profiling
• L is the Effective Gun Length 2430 i.e. the length of the gun that detonates down to the point of the misfire, or bottom of the gun if there is no misfire
• V d is the effective detonation velocity
• DT is the difference in seismic travel time (to the receiver) for the first Gun Segment and the last Gun Segment to fire.
• L is the primary measure of the extent of detonation of the Perforating Gun, and the objective of all of the preceding and following described processes of this invention.
• a related measure of the extent of detonation is the percentage of the total gun that actually detonated, found by dividing L by the total Gun Length and multiplying by 100.
• the length of the Perforating Gun that actually detonated is equal to the determined value of Duration less the differential seismic travel time between the first Gun Segment and the last Gun Segment that detonated and that quantity multiplied by the effective detonation velocity V d of the Perforating Gun.
• the result is dependent on differential travel time rather than total travel time the result is not dependent on highly accurate modeling of the intervening geology between the top of the gun and the receiver. Only the modeling of ray paths in the vicinity of the gun itself must be done accurately. This modeling is easily and accurately performed if the seismic velocity field in the vicinity of the Perforating Gun has been measured using conventional well logging techniques, as are well known in the industry, and has been extrapolated using structural geologic maps as are typically available for an oil field. If a VSP seismic survey has previously been performed for the well undergoing perforation the total seismic travel times will have been accurately measured for multiple positions along the borehole, for travel between the borehole and selected surface locations.
• Fig 14 shows results for a different example, a case where the gun is relatively short so that the two halves of the Composite Wavelet and of the Stage 1 Wavelet are heavily overlapped.
• the middle graph shows the Stage 2 wavelets 1320 for three differing assumed Durations, 23, 24, and 25 msec.
• the bottom graph is a plot of the RMS amplitude of the tail energy of the Stage 2 wavelets.
• the value of Duration to build the model was 24 msec.
• the Stage 2 wavelets have nearly identical first cycles but are highly divergent for later times.
• Fig 15 shows a similar modeled example, in which a much smaller value of Duration was assumed, 6 msec. This case is more challenging to the method, because of the extreme overlap in the Composite Wavelet and Stage 1 wavelet, i.e. the gun is very short.
• the three graphs of Fig 14 correspond to the three graphs of Fig 13. Less difference is observed among the three Stage 2 wavelets in the middle graph.
• the RMS Amplitude graph shows a minimum 1410 at 6 msec but it is not as well resolved as previously. Thus the method works, but not as powerfully and with not as much resolution for the very short Duration Perforating Gun.
• Fig 16 the effect of seismic noise on the inversion process is studied. In practical cases there will be some amount of seismic noise remaining in the final estimate of the true Composite Wavelet.
• the model used for Fig 14 was modified by the addition of random noise and again processed through the two stages of inversion. Noise appears together with signal in the Stage 1 wavelet 1310 and Stage 2 wavelets 1320.
• the RMS Amplitude graph shows a minimum at 23 msec instead of 24 msec, the correct value of Duration. Thus the noise has caused a small error in the Duration calculated by the process. Curve-fitting to the RMS Amplitude values can reduce the effect of the noise and allow the correct value, 24 msec, to be calculated in this case.
• Seismic noise may be reduced using well-designed arrays and sub-arrays of seismic receivers, positioning receivers in closer proximity to the Perforating Gun, positioning receivers at sufficiently great distance to avoid gun-generated noise interfering with signal and by using signal processing methods as previously described to reduce the effects of seismic noise and enhance the signal estimate.
• the inversion method may be performed in the manner next described.
• the inversion method is applied to the final estimate of the true Composite Wavelet defined previously.
• the basis of the method is the assumption that the Composite Wavelet is the sum of Basic Wavelets from a series of Gun Segments, the Perforating Gun being arbitrarily divided into a series of these uniform segments, each containing an identical or at least substantially similar set of explosive components, with the possible exception of the last gun segment.
• the Composite Wavelet is a sum of Basic Wavelets with each Basic Wavelet delayed slightly relative to the one from the previous Gun Segment.
• the first sample of the Composite Wavelet is simply equal to the first sample of the Basic Wavelet. Knowing this, the second sample of the Basic Wavelet can be computed by subtracting the first value of the Basic Wavelet from the second value of the Composite Wavelet. Now the first two samples in the Basic Wavelet are known. The process can be continued for the whole Composite Wavelet until an assumed value of Duration is reached and then discontinued. The result will be a pure Basic Wavelet followed by a negative copy of the Basic Wavelet starting at the time of the Duration of the Composite Wavelet if the assumed value of Duration was correct.
• Stage 1 Wavelets The outputs of the first stage of the inversion are called Stage 1 Wavelets. These Stage 1 Wavelets will also become the inputs to the Stage 2 inversion; the Stage 2 inversion will use the same assumed value of Duration as was used to obtain that particular Stage 1 result.
• the foregoing process is the Stage 1 of the inversion method as appropriate for the simple case of straight vertical borehole and constant seismic velocity. It works by virtue of the fact that the first sample of the first Basic Wavelet is un- obscured. This allows a successive stripping away of overlying information to eventually reveal the Basic Wavelet summed with a delayed polarity-reversed version of itself, if the Duration assumption was correct. If this assumption was incorrect, the output will have a larger RMS amplitude and asymmetry compared to the result obtained when the correct assumption was made.
• the Stage 2 inversion process is applied to the Stage 1 result, and if the Duration assumption is correct will yield the simple and pure Basic Wavelet. Otherwise the symptoms of incorrect Duration assumption including higher RMS Amplitude and unstable or high frequency tail amplitudes will be observed.
• the Stage 2 inversion is very simple and is accomplished by subtracting sample by sample the early amplitudes of the Stage 1 inversion from the later Stage 1 amplitudes with a delay equal to the assumed Duration. The process continues from the first modified amplitude, at a time equal to the Duration, to a time substantially greater than the predicted total time of the Basic Wavelet.
• Stage 2 inversion after time equals twice the Duration the already-corrected Stage 2 value (rather than the corresponding Stage 1 amplitude) is used to subtract from the next Stage 1 value; thus the Stage 2 inversion iterates once for times greater than twice the Duration.
• the definition of the portion of the Perforating Gun that constitutes one Gun Segment 2410 is conveniently done by choosing the portion of gun that will have its Basic Wavelet separated from those of adjacent Gun Segments by one unit time sample.
• the size of the Gun Segment chosen should be suitably small relative to the bandwidth of the seismic signal received and recorded. For example if 1 msec recording sample period is suitable for the seismic signal, then the Gun Segment size should be chosen such that adjacent Basic Wavelets 1320 within the Composite Wavelet 1100 are separated by 1 msec or less. For a detonation velocity of 10,000 fps and a seismic velocity of 8000 fps, the Gun Segment would be 4.44 ft to conform to 1 msec sampling.
• the Gun Segment Length may be set at a shorter interval to make it contain an integral and invariant number of shaped charges for every Gun Segment in the Perforating Gun to avoid issues of variable number of shaped charges in various Gun Segments.
• the ray paths and the corresponding seismic travel times from the center of each of the Gun Segments to the receiver are first calculated. This may be done using various modeling methods in use within the industry. Preferably three- dimensional earth models, derived from all available sources of subsurface information, e.g. from drilling, well logging and prior seismic surveys, will be used, together with the coordinates of the Gun Segments and the receiver.
• the detonation velocity for the Perforating Gun is also used, as obtained from prior testing of an identical Perforating Gun.
• Pulse Density is simply the number of pulses arriving at the receiver per unit of time relative to the number of pulses arriving in the first sample of the Composite Wavelet. If, for example, the first sample in the Composite Wavelet results from the Basic Wavelet first arrival of the first Gun Segment only, and a later sample of the Composite Wavelet is the sum of first arrivals from two Gun Segments (due to hole curvature, ray path geometry, etc.) that later sample is said to have a Pulse Density of two (2). This convention is arbitrary but it makes possible a convenient adaptation of the previously described inversion method to account for the general case.
• the Composite Wavelet can be represented by one sample per unit time by accounting for multiple coincident Basic Wavelets originating within one time sample- by modifying amplitude with the Pulse Density.
• a series of Pulse Density values are derived, one per unit time increment, which is equal to the number of Basic Wavelets having the same Arrival Time at the receiver for that time increment of sampled Arrival Time.
• the Arrival Times fully account for borehole curvature in 3 dimensions and the space-time variant seismic velocity field between the Perforating Gun and the receiver, being based on ray path calculations or VSP observations, as well as the time delay incurred for propagation of the detonation front along the Perforating Gun.
• the Arrival Times can be calculated accordingly and thereby allow the Pulse Density to account for these factors.
• Perforating guns of this type are commonly used when multiple zones are to be perforated with intervening zones to be left un- perforated. Such guns may be constructed such that they exhibit variable detonation velocity along the gun axis.
• Amplitudes of the Basic Wavelets are affected by spherical divergence loss, absorption and transmission losses during their travel from the originating Gun Segments to the receiver. These losses are different for each Gun Segment due to varying distance of travel and differing absorption and transmission losses due to passage through differing rock. These loss mechanisms may not cause significant variation among the Basic Wavelets for relatively short Perforating Guns that are far from the receiver, however for longer guns and shorter travel paths, the differences are significant and must be accounted for in the inversion process.
• the spherical divergence, absorption and transmission losses expected to be incurred may be calculated through a seismic modeling process using techniques familiar to those skilled in seismic processing and modeling. Alternatively they may be measured directly from seismic recordings made in a VSP survey. These losses, one value per Gun Segment, may conveniently be multiplied by the Pulse Density values to compute Modified Pulse Density values. These values are then normalized by dividing each Gun Segment's Modified Pulse Density value by the value for the first Gun Segment. This normalizing method ensures that the complete inversion process, including Stage 1 and Stage 2, is a true amplitude process. The normalization is effected by dividing the initial Modified Pulse Density, for the first
• Modified Pulse Density Values are termed 'Weights'.
• Adjustment Factors the Normalized Modified Pulse Density Values as is next described, the effects of amplitude losses due to the listed causes, will be fully accommodated and therefore cause no errors in the calculation of the Stage 1 Wavelet.
• Adjustment Factors the normalized Modified Pulse Density values are converted to what is termed Adjustment Factors as follows:
• ⁇ i is the i th Adjustment Factor
• (MPD)i is the i ,h Normalized Modified Pulse Density.
• a n is the value in the solution matrix in column A, row n.
• ⁇ oi ⁇ i, ⁇ 2 1... , ⁇ n-i are the Adjustment Factors;
• Y ⁇ m is the n* 1 amplitude of the Stage 1 Wavelet for an assumed Duration of m time units.
• Equation 4 is used to calculate amplitude values of the Stage 1 Wavelet progressively, starting with the second value and continuing to the final value.
• the position of the final value is set arbitrarily but so as to include the entire significant portion of the Stage 1 Wavelet.
• the first amplitude value of the Stage 1 Wavelet is always set exactly equal to the first amplitude value of the Basic Wavelet, A1.
• the solution diagonal 1900 is computed progressively from first point (upper left) to last point (lower right). Values in the matrix at times later than the solution point are calculated by subtracting from the prior value, the prior solution value at the solution diagonal.
• Figure 22b shows examples of the equations that apply for points in the matrix away from the solution diagonal. Of particular importance are the calculations in the cells below the solution diagonal 1900. Note that as each successive value of the
• Stage 1 Wavelet is completed it is next subtracted from all values in the previous partial solution. This in effect gradually strips away overlying information to reveal the sought Stage 1 Wavelet, point by point.
• the right hand column contains the same values as have emerged along the solution diagonal, which comprise the Stage 1 Wavelet.
• any curvilinear borehole in a variable seismic velocity medium may be inverted to reveal the Stage 1 wavelet as previously described for the simpler cases.
• Fig 18 shows two Composite Wavelets for a curvilinear borehole, calculated using two different methods.
• the Pulse Density Method yields Composite Wavelet 1800 and a simple time-shift method yields Composite Wavelet 1810. Small differences are observed in the two wavelets and these are due to small errors in the interpolation method used (linear) rather than to any flaw in the Pulse Density general method.
• These Composite Wavelets were processed through the generalized inversion process based on Equation 4.
• the results of Stage 1 of the generalized inversion are shown in Fig 19a 19b and 19c.
• the solution emerges along the solution diagonal 1900.
• Fig 19c the final Stage 1 result appears 1910.
• the Stage 2 result 1920 appears to the right.
• the Stage 2 result 1920 perfectly reproduces the model wavelet used to build the Composite Wavelet that was input to the inversion process.
• the correct value of Duration, 13 msec yields the lowest RMS Amplitude value 1410 as observed on the graph, confirming the choice one would make from comparing the Basic Wavelets calculated for assumed Duration values of 12, 13 and 14 msec.
• Fig 19 The calculations of Fig 19 and the results shown in Fig 20 are obtained from the input Composite Wavelet 1800 formed using the Pulse Density method to simulate the wavelet that would be recorded in the real case.
• Fig 21 shows the inversion results from the time-shift Composite Wavelet 1810 and using the same generalized inversion method as illustrated in Fig 19 and Fig 20.
• the resultant Basic Wavelet 2120 shows nearly identical form to Basic Wavelet 1920, but with small tail amplitudes instead of zeroes. A sharp minimum in
• An alternate method of performing the inversion processing is to bypass the Stage 1 inversion step and perform the Stage 2 inversion on the best estimate of the true Composite Wavelet.
• the Stage 2 result by itself yields a stable decaying wavelet at the correct Duration, with the difference that the output is not a single Basic Wavelet but the summation of a series of Basic Wavelets over the Duration.
• the output of the Stage 2 inversion can be subjected to visual and mathematical analysis as previously described to find the best estimate of Duration and extent-of- detonation of the perforating gun.
• An advantage of this approach is that the Stage 2 inversion may be more robust in the presence of seismic noise than is the Stage 1 inversion. Both approaches may be tried and compared in practice.
• Stage 1 inversion may be applied to the Stage 2 output.
• the order of the stages may be reversed.
• the interpreted results would be identical.
• Yet another viable model-based method of determining the extent-of- detonation is to compute synthetic Composite Wavelets such as illustrated in Fig.11 and to compute best fit to the real Composite Wavelet estimate.
• An assumed Basic Wavelet can be summed repetitively with appropriate time delays for the physical environment and position of the perforating gun.
• the assumed Basic Wavelet may be judiciously chosen from actual recorded prior detonations under similar conditions, obtained from inversion according to the present invention from prior detonations, or otherwise provided.
• Various assumptions of extent-of-detonation can be used to compute corresponding synthetic Composite Wavelets.
• the synthetic Composite Wavelets are then compared to the real Composite Wavelet (best estimate of true Composite Wavelet).
• the method of comparison can be variously chosen ranging from visual comparison, differencing, power calculations, Least- Mean-Square Error (LSME) fit measurement, spectral fit and other methods.
• LSME Least- Mean-Square Error

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