CN106291673A - Crack based on shear-wave birefringence attribute factor extracting method and device - Google Patents
Crack based on shear-wave birefringence attribute factor extracting method and device Download PDFInfo
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Abstract
On the one hand a kind of crack based on shear-wave birefringence attribute factor extracting method is proposed, including: obtaining the horizontal component data volume received by multi-components cymoscope, described horizontal component data volume includes radial component data volume R (t) and tangential component data volume T (t);Obtain making the value σ (θ of standardization cross-correlation and function, δ) maximum θ and δ, as crack attribute factor, wherein θ is the angle between natural system of coordinates and observation coordinate system, it indicates fracture azimuth, δ is the quick shear wave after division and time delay between shear wave at a slow speed, and it indicates fracture development density.
Description
Technical field
The invention belongs to seismic data interpretation field, be specifically related to a kind of crack based on shear-wave birefringence attribute
Factor extraction method and device.
Background technology
The most widely distributed the crack of full fluid, there is good permeability in these cracks, they
The most still reservoir space of oil gas, and be the migration pathway of oil gas, say, that in stratum, crack sends out
Educate degree and connectedness determines oil-gas accumulation degree, thus, the research of fracture attribute is significant.
In the region having vertical (or near upright) crack of orientation, when shear wave is through fracture medium, i.e.
Separating phenomenon can occur.Thus producing quick shear wave and shear wave at a slow speed, the former parallel fracture moves towards polarization, with
The speed of rock medium is propagated;The latter's vertical fracture moves towards polarization, and spread speed is affected by frac-pack thing.
Therefore quickly shear wave and at a slow speed shear wave itself carry the information in crack, if to quick shear wave and shear wave at a slow speed
Study, it is possible to be effectively obtained the attribute character of subterranean fracture medium.
By the main stream approach of quick shear wave and the information retrieval crack attribute factor of shear wave at a slow speed it is at present
Alford circumgyration and polarization analysis.Alford proposed Alford and rotates in 1986, proposed first
By estimating the method that the delay profile of quick shear wave and shear wave at a slow speed estimates crack attribute factor.Crampin
Proposing polarization analysis in 1997, the method utilizes thing component and the north-south component of digital seismic recording
Particle motion diagram estimate crack attribute factor.Both approaches theoretical derivation is accurate, but in precision
Extremely limit to in range, largely constrain its application.
Crack attribute factor is important fracture medium characteristic parameter, the growth in crack in its reflection underground medium
Direction and growth density, this is to judging that reservoir property and Reservoir Scale are the most helpful.Traditional utilization is quick
The method of shear wave and at a slow speed shear wave feature extraction crack attribute factor often to use pure shear wave exploration, namely
Double source four componets data.Do so has bigger limitation, first, the shear wave source needed for pure shear wave exploration
Excite needs a series of special requirements, be extremely difficult to during work area data acquisition in the wild;Secondly, shear wave
Acquisition cost required for exploration is significantly larger than the acquisition mode that common p-wave source excites.This results in
In actual seismic prospecting, it is difficult to obtain double source four componets data.On the other hand, quick shear wave and at a slow speed
Shear wave is aliasing in together in elliptical polarization often, and traditional polarization analysis only has one in requiring analysis window
The requirement of individual lineups is just difficult to meet.
Summary of the invention
It is an object of the invention to solve a difficult problem present in above-mentioned prior art, it is provided that a kind of double based on shear wave
The crack attribute factor extracting method of refraction, makes the input data be reduced to two component datas, it is to avoid shear wave is surveyed
Visit the cost that causes and technical problem, and by quick shear wave and the waveform dependency relation of shear wave at a slow speed, around
Open the problem that analysis window lineups are difficult to select, improve the feasibility of method.
On the one hand a kind of crack based on shear-wave birefringence attribute factor extracting method is proposed, including: obtain
The horizontal component data volume received by multi-components cymoscope, described horizontal component data volume includes radial component
Data volume R (t) and tangential component data volume T (t);Obtain making standardization cross-correlation and function in below equation
θ and δ that value σ (θ, δ) is maximum, as crack attribute factor:
Wherein θ is the angle between natural system of coordinates and observation coordinate system, and it indicates fracture azimuth, and δ is
Time delay between quick shear wave after division and at a slow speed shear wave, it indicates fracture development density, and L is for analyzing
Time window length,
Wherein, the expression formula of X (t, φ) is as follows:
WhereinSymbol represents relevant, RφT () represents the rotation that radial component R (t) obtains after rotated counterclockwise by angle φ
Radial component, TφT () represents the rotation tangential component that tangential component T (t) obtains after rotated counterclockwise by angle φ,
Wherein, the expression formula of B (t, φ, θ, δ) is as follows:
A (t) is the sum of the auto-correlation function of horizontal component data volume, ε=θ-φ.
On the other hand a kind of crack based on shear-wave birefringence attribute factor extraction element is proposed, including: use
In the parts of the horizontal component data volume that acquisition is received by multi-components cymoscope, described horizontal component data volume
Including radial component data volume R (t) and tangential component data volume T (t);For obtaining the standard made in below equation
Change θ and δ that value σ (θ, δ) of cross-correlation and function is maximum, as the parts of crack attribute factor:
Wherein θ is the angle between natural system of coordinates and observation coordinate system, and it indicates fracture azimuth, and δ is
Time delay between quick shear wave after division and at a slow speed shear wave, it indicates fracture development density, and L is for analyzing
Time window length,
Wherein, the expression formula of X (t, φ) is as follows:
WhereinSymbol represents relevant, RφT () represents the rotation that radial component R (t) obtains after rotated counterclockwise by angle φ
Radial component, TφT () represents the rotation tangential component that tangential component T (t) obtains after rotated counterclockwise by angle φ,
Wherein, the expression formula of B (t, φ, θ, δ) is as follows:
A (t) is the sum of the auto-correlation function of horizontal component data volume, ε=θ-φ.
Compared with prior art, the invention has the beneficial effects as follows: this method utilizes horizontal component data volume to carry out
The inverting of shear-wave birefringence crack, final acquisition crack attribute factor, belong to than traditional parallel-vertical shear wave crack
Property extracting method have easily realization, strong robustness, adapt to feature widely, such as, be suitable for crack elimination pre-
Survey.
Accompanying drawing explanation
By combining accompanying drawing, disclosure illustrative embodiments is described in more detail, the disclosure above-mentioned
And other purpose, feature and advantage will be apparent from, wherein, in disclosure illustrative embodiments
In, identical reference number typically represents same parts.
Fig. 1 is the attribute factor extraction side, crack based on shear-wave birefringence according to one embodiment of the present of invention
The flow chart of method.
Fig. 2 is that crack based on the shear-wave birefringence attribute factor according to an alternative embodiment of the invention extracts
The flow chart of method.
Fig. 3 is the model parameter containing fracture medium two dimensional model of the horizontal layer according to an example.
Fig. 4 is that Fig. 3 model is just being drilled the data radial component obtained.
Fig. 5 is that Fig. 3 model is just being drilled the data tangential component obtained.
Fig. 6 is that Fig. 4 and Fig. 5 data carry out the crack attribute factor that the inverting of shear-wave birefringence crack obtains.
Fig. 7 be Fig. 4 and Fig. 5 data are carried out lower floor's crack attribute that the inverting of shear-wave birefringence crack obtains because of
Son.
Detailed description of the invention
It is more fully described the preferred implementation of the disclosure below with reference to accompanying drawings.Although accompanying drawing shows
The preferred implementation of the disclosure, however, it is to be appreciated that may be realized in various forms the disclosure and should be by
Embodiments set forth herein is limited.On the contrary, it is provided that these embodiments are to make the disclosure more saturating
Thorough and complete, and the scope of the present disclosure intactly can be conveyed to those skilled in the art.
When the present invention propagates in fracture medium (the such as fracture medium containing vertical fracture system) according to shear wave
The division rule (i.e. shear wave splitting, Shear Wave Splitting) produced, after to containing division
The geological data of quick shear wave and at a slow speed shear wave is implemented shear-wave birefringence inverting and is extracted crack attribute factor.
Embodiment 1
Fig. 1 show a kind of crack based on shear-wave birefringence according to an embodiment of the invention attribute because of
Sub-extracting method, the method includes:
Step 101, it is thus achieved that the horizontal component data volume received by multi-components cymoscope, described horizontal component number
Radial component data volume R (t) and tangential component data volume T (t) is included according to body;
Step 102, value σ (θ, δ) obtaining making standardization cross-correlation and function in below equation (1) is maximum
θ and δ, wherein θ is the angle between natural system of coordinates and observation coordinate system, i.e. fracture azimuth orientation
Angle, it indicates fracture azimuth, and δ is the quick shear wave after division and time delay between shear wave at a slow speed,
It indicates fracture development density:
Wherein, L is analysis window length, and the expression formula of X (t, φ) is as follows, hereSymbol represents relevant:
RφT () represents the rotation radial component that radial component R (t) obtains after rotated counterclockwise by angle φ, TφT () expression is cut
The rotation tangential component obtained after rotated counterclockwise by angle φ to component T (t), an example of rotation is such as joined
See below equation (3):
In formula (1), the expression formula of B (t, φ, θ, δ) is as follows:
Wherein A (t) is the sum of auto-correlation function of horizontal component data volume.It can be to use multi-components cymoscope to receive
To horizontal component data volume carry out what autocorrelation calculation obtained, i.e. by R (t) and T (t) are asked respectively from
After Xiang Guan, summation obtains again, and it is unrelated with anglec of rotation φ;ε=θ-φ.
This embodiment offers a kind of crack based on shear-wave birefringence attribute factor extracting method, by more than
Step 101 and 102 has obtained crack attribute factor, i.e. fracture azimuth and fracture development density, makes defeated
Enter data and be reduced to two component datas, it is to avoid cost that shear wave exploration causes and technical problem, and pass through
The waveform dependency relation of quick shear wave and at a slow speed shear wave, gets around the problem that analysis window lineups are difficult to select,
The feasibility of raising method.
In one example, obtain making the crack of the value maximum of formula (1) Plays cross-correlation and function send out
Educate direction azimuth angle theta and δ time delay, can be by θ and δ be swept with given interval in given range
Retouch and obtain.Such as to θ can from 0 to 180 degree and with 10 degree for be spaced be scanned, to δ can from 0 to
10 are scanned with 1 for interval.It will be understood by those skilled in the art that range above and interval are merely illustrative,
It is not intended to limit the present invention.It is true that the sweep limits of θ and δ and interval can the most arbitrarily be chosen.
A large amount of tests show, are scanned θ, δ with given interval in given range, therefrom choose and make σ (θ, δ)
Big θ, δ, can calculate natural system of coordinates and the angle theta of observation coordinate system and quickly shear wave and at a slow speed horizontal stroke
Time delay δ between ripple, determines fracture azimuth and grows density, i.e. θ indicates fracture azimuth,
δ indicates fracture development density, and δ-value shows that the most greatly crack is the most intensive.
It will be understood by those skilled in the art that above scan method is merely illustrative.Those skilled in the art can basis
Need θ and δ maximum for σ (θ, δ) utilizing any known method in this area to obtain making maximum.
Embodiment 2
Fig. 2 show a kind of crack based on shear-wave birefringence according to an embodiment of the invention attribute because of
Sub-extracting method.This embodiment is on the basis of embodiment 1, further comprising the steps of:
Step 103, it may be judged whether in the presence of layer fracture layers, this judgement can observe from earthquake record and obtain,
If it does, enter step 104, if it does not exist, then the method terminates.
Step 104, is corrected according to below equation (5);
Rdown(t)=R (t) cos θ-T (t) sin θ (5)
Tdown(t)=R (t) sin θ+T (t) cos θ
Wherein Rdown(t) and TdownT () represents lower floor's radial component data volume and lower floor's tangential component data volume, here under
Layer refers to the lower floor relative to R (t) He the current layer at T (t) place, after then using step 104 correction
Rdown(t) and TdownT the R (t) in () alternative steps 102 and T (t), re-executes step 102 to obtain this lower floor
Fracture azimuth and fracture development density.
In one example, step 102 can be repeated to step 105, until having calculated splitting of all slits layer
Seam grows direction and fracture development density.
In the case of this embodiment considers that underground exists multilayer crack medium further, current layer crack is utilized to be situated between
Lower floor is modified by qualitative attribution factor information, eliminates anisotropic impact, and then asks accurately and effectively
Take off the attribute factor of layer fracture medium.
Embodiment 3
According to another embodiment of the present invention, it is proposed that a kind of crack based on shear-wave birefringence attribute factor carries
Fetching is put, including:
For obtaining the parts of the horizontal component data volume received by multi-components cymoscope, described horizontal component
Data volume includes radial component data volume R (t) and tangential component data volume T (t);
For obtaining making θ and δ of value σ (θ, the δ) maximum of standardization cross-correlation and function in below equation, make
Parts for crack attribute factor:
Wherein θ is the angle between natural system of coordinates and observation coordinate system, and it indicates fracture azimuth, and δ is
Time delay between quick shear wave after division and at a slow speed shear wave, it indicates fracture development density, and L is for analyzing
Time window length,
Wherein, the expression formula of X (t, φ) is as follows:
WhereinSymbol represents relevant, RφT () represents the rotation that radial component R (t) obtains after rotated counterclockwise by angle φ
Radial component, TφT () represents the rotation tangential component that tangential component T (t) obtains after rotated counterclockwise by angle φ,
Wherein, the expression formula of B (t, φ, θ, δ) is as follows:
A (t) is the sum of the auto-correlation function of horizontal component data volume, ε=θ-φ.
In one example, R (t), T (t) and Rφ(t)、TφT () can meet relationship below:
In one example, can be by being scanned being made with given interval in given range to θ and δ
The angle theta of σ (θ, δ) maximum and δ time delay.
In one example, described device may also include that
For judging whether lower floor's fracture layers, if it is present the portion being corrected according to below equation
Part;
Rdown(t)=R (t) cos θ-T (t) sin θ
Tdown(t)=R (t) sin θ+T (t) cos θ
Wherein Rdown(t) and TdownT () represents lower floor's radial component data volume and lower floor's tangential component data volume,
R after using correctiondown(t) and TdownT () substitutes R (t) and T (t), re-execute and obtain making standardization
θ and δ that value σ (θ, δ) of cross-correlation and function is maximum, as the parts of crack attribute factor.
Fig. 3 shows the horizontal layer model parameter containing fracture medium two dimensional model.Using this model as
A Ge Zhengyan road collection, the effect of the embodiment of the present invention is described by following experimental data.
(1) just drilling Fig. 3 institute representation model, design ground p-wave source excites, p-wave source well constraint inversion
For 700m.In well, multi-components cymoscope receives, and cymoscope starts to dispose from well head, assigns one every 7m,
Place 380 cymoscopes altogether.Sampling interval is 2ms, and record length is 800ms.The VSP model note obtained
As shown in Figure 4, tangential component is as shown in Figure 5 for record data radial component.
(2) data shown in Fig. 4 and Fig. 5 are carried out the inverting of shear-wave birefringence crack, obtain crack, upper strata attribute
As shown in Figure 6, abscissa represents that fracture azimuth, vertical coordinate represent fracture development density, in figure to the factor
The central point instruction fracture azimuth of Voice segment group and fracture development density.By with the splitting of model specification
Seam attribute factor contrast, it is positive 70 ° that inverting obtains upper strata fracture azimuth, and fracture development density is 5,
Fit like a glove with model parameter.
(3) crack, the upper strata attribute factor obtaining data separate shown in Fig. 4 and Fig. 5 (2) carries out layer stripping
From correction, revised data are carried out the inverting of shear-wave birefringence crack, obtain lower floor's crack attribute factor such as
Shown in Fig. 7, abscissa represents that fracture azimuth, vertical coordinate represent fracture development density, and in figure, energy gathers
The central point instruction fracture azimuth of burnt group and fracture development density.By the crack attribute with model specification
Factor pair ratio, it is negative 55 ° that inverting obtains lower floor's fracture azimuth, and fracture development density is 9, with model
Parameter fits like a glove.
The disclosure can be system, method and/or computer program.Computer program can include
Computer-readable recording medium, containing for making processor realize the computer of various aspects of the disclosure
Readable program instructions.
Computer-readable recording medium can be to keep and to store the instruction used by instruction execution equipment
Tangible device.Computer-readable recording medium such as may be-but not limited to-storage device electric,
Magnetic storage apparatus, light storage device, electromagnetism storage device, semiconductor memory apparatus or above-mentioned any conjunction
Suitable combination.The more specifically example (non exhaustive list) of computer-readable recording medium includes: portable
Formula computer disks, hard disk, random access memory (RAM), read only memory (ROM), erasable type can be compiled
Journey read only memory (EPROM or flash memory), static RAM (SRAM), Portable compressed dish are only
Read memorizer (CD-ROM), digital versatile disc (DVD), memory stick, floppy disk, mechanical coding equipment, example
As stored the punch card or groove internal projection structure and the combination of above-mentioned any appropriate having instruction on it.
Computer-readable recording medium used herein above is not construed as instantaneous signal itself, such as radio wave or
The electromagnetic wave of other Free propagations of person, the electromagnetic wave propagated by waveguide or other transmission mediums are (such as, logical
Cross the light pulse of fiber optic cables) or by the signal of telecommunication of wire transfer.
Computer-readable program instructions as described herein can download to each from computer-readable recording medium
Calculating/processing equipment, or by under network, such as the Internet, LAN, wide area network and/or wireless network
It is downloaded to outer computer or External memory equipment.Network can include copper transmission cable, fiber-optic transfer, wireless
Transmission, router, fire wall, switch, gateway computer and/or Edge Server.Each calculating/place
Adapter or network interface in reason equipment receive computer-readable program instructions from network, and forward
This computer-readable program instructions, for the computer-readable storage medium being stored in each calculating/processing equipment
In matter.
Can be assembly instruction, instruction set architecture for performing the computer program instructions of disclosure operation
(ISA) instruction, machine instruction, machine-dependent instructions, microcode, firmware instructions, condition setup data,
Or the source code write with the combination in any of one or more programming languages or object code, described programming language
Speech includes OO programming language such as Smalltalk, C++ etc., and the process type programming of routine
Language such as " C " language or similar programming language.Computer-readable program instructions can fully with
Perform on the computer of family, perform the most on the user computer, perform as independent software kit,
Part part on the user computer performs or on the remote computer completely in remote computer or service
Perform on device.In the situation relating to remote computer, remote computer can be by the network of any kind
It is connected to subscriber computer including LAN (LAN) or wide area network (WAN), or, it may be connected to outer
Portion's computer (such as utilizes ISP to pass through Internet connection).In certain embodiments,
Personalized customization electronic circuit is carried out by the status information utilizing computer-readable program instructions, the most able to programme
Logic circuit, field programmable gate array (FPGA) or programmable logic array (PLA), this electronic circuit
Computer-readable program instructions can be performed, thus realize various aspects of the disclosure.
Referring herein to the method according to disclosure embodiment, device (system) and the stream of computer program
Journey figure and/or block diagram describe various aspects of the disclosure.Should be appreciated that each of flow chart and/or block diagram
The combination of each square frame in square frame and flow chart and/or block diagram, can be real by computer-readable program instructions
Existing.
These computer-readable program instructions can be supplied to general purpose computer, special-purpose computer or other can compile
The processor of journey data processing equipment, thus produce a kind of machine so that computer is being passed through in these instructions
Or other programmable data processing means processor perform time, create in flowchart and/or block diagram
The device of the function/action of regulation in one or more square frames.Can also be these computer-readable program instructions
Storage in a computer-readable storage medium, these instruction make computer, programmable data processing means and/
Or other equipment work in a specific way, thus, storage has the computer-readable medium of instruction then to include one
Manufacture, it includes the function/action of regulation in the one or more square frames in flowchart and/or block diagram
The instruction of various aspects.
Can also computer-readable program instructions be loaded into computer, other programmable data processing means,
Or on miscellaneous equipment so that on computer, other programmable data processing means or miscellaneous equipment, perform one
Series of operative steps, to produce computer implemented process, so that at computer, other number able to programme
According to the one or more sides in the instruction flowchart performed in processing means or miscellaneous equipment and/or block diagram
Function/the action of regulation in frame.
Flow chart and block diagram in accompanying drawing show the system of multiple embodiments, method and meter according to the disclosure
Architectural framework in the cards, function and the operation of calculation machine program product.In this, flow chart or block diagram
In each square frame can represent a module, program segment or a part for instruction, described module, program segment
Or a part for instruction comprises the executable instruction of one or more logic function for realizing regulation.Having
In a little realizations as replacement, the function marked in square frame can also be to be different from marked in accompanying drawing suitable
Sequence occurs.Such as, two continuous print square frames can essentially perform substantially in parallel, and they sometimes can also
Performing in the opposite order, this is depending on involved function.It is also noted that block diagram and/or flow chart
In each square frame and the combination of square frame in block diagram and/or flow chart, can be by the function performing regulation
Or the special hardware based system of action realizes, or can be with specialized hardware and computer instruction
Combination realizes.
Being described above the presently disclosed embodiments, described above is exemplary, and non-exclusive,
And it is also not necessarily limited to disclosed each embodiment.In the scope and spirit without departing from illustrated each embodiment
In the case of, many modifications and changes will be apparent from for those skilled in the art.
The selection of term used herein, it is intended to explain that the principle of each embodiment, reality are applied or to market best
In the technological improvement of technology, or make other those of ordinary skill of the art be understood that to disclose herein
Each embodiment.
Claims (8)
1. crack based on a shear-wave birefringence attribute factor extracting method, including:
Obtaining the horizontal component data volume received by multi-components cymoscope, described horizontal component data volume includes
Radial component data volume R (t) and tangential component data volume T (t);
Obtain making θ and δ of value σ (θ, the δ) maximum of standardization cross-correlation and function in below equation, as splitting
Seam attribute factor:
Wherein θ is the angle between natural system of coordinates and observation coordinate system, and it indicates fracture azimuth, and δ is
Time delay between quick shear wave after division and at a slow speed shear wave, it indicates fracture development density, and L is for analyzing
Time window length,
Wherein, the expression formula of X (t, φ) is as follows:
WhereinSymbol represents relevant, RφT () represents the rotation that radial component R (t) obtains after rotated counterclockwise by angle φ
Radial component, TφT () represents the rotation tangential component that tangential component T (t) obtains after rotated counterclockwise by angle φ,
Wherein, the expression formula of B (t, φ, θ, δ) is as follows:
A (t) is the sum of the auto-correlation function of horizontal component data volume, ε=θ-φ.
Method the most according to claim 1, wherein, R (t), T (t) and Rφ(t)、TφT () meets below
Relational expression:
Method the most according to claim 1, wherein, by θ and δ in given range with given
Interval is scanned obtaining making angle theta maximum for σ (θ, δ) and δ time delay.
Method the most according to claim 1, wherein, described method also includes:
Judge whether lower floor's fracture layers, if it is present be corrected according to below equation;
Rdown(t)=R (t) cos θ-T (t) sin θ
Tdown(t)=R (t) sin θ+T (t) cos θ
Wherein Rdown(t) and TdownT () represents lower floor's radial component data volume and lower floor's tangential component data volume,
Use the R after correctiondown(t) and TdownT () substitutes R (t) and T (t), re-execute and obtain making standardization mutual
Close θ and δ that value σ (θ, δ) with function is maximum, as the step of crack attribute factor.
5. crack based on a shear-wave birefringence attribute factor extraction element, including:
For obtaining the parts of the horizontal component data volume received by multi-components cymoscope, described horizontal component
Data volume includes radial component data volume R (t) and tangential component data volume T (t);
For obtaining making θ and δ of value σ (θ, the δ) maximum of standardization cross-correlation and function in below equation, make
Parts for crack attribute factor:
Wherein θ is the angle between natural system of coordinates and observation coordinate system, and it indicates fracture azimuth, and δ is
Time delay between quick shear wave after division and at a slow speed shear wave, it indicates fracture development density, and L is for analyzing
Time window length,
Wherein, the expression formula of X (t, φ) is as follows:
WhereinSymbol represents relevant, RφT () represents the rotation that radial component R (t) obtains after rotated counterclockwise by angle φ
Radial component, TφT () represents the rotation tangential component that tangential component T (t) obtains after rotated counterclockwise by angle φ,
Wherein, the expression formula of B (t, φ, θ, δ) is as follows:
A (t) is the sum of the auto-correlation function of horizontal component data volume, ε=θ-φ.
Device the most according to claim 5, wherein, R (t), T (t) and Rφ(t)、TφT () meets below
Relational expression:
Device the most according to claim 5, wherein, by θ and δ in given range with given
Interval is scanned obtaining making angle theta maximum for σ (θ, δ) and δ time delay.
Device the most according to claim 5, wherein, described device also includes:
For judging whether lower floor's fracture layers, if it is present the portion being corrected according to below equation
Part;
Rdown(t)=R (t) cos θ-T (t) sin θ
Tdown(t)=R (t) sin θ+T (t) cos θ
Wherein Rdown(t) and TdownT () represents lower floor's radial component data volume and lower floor's tangential component data volume,
R after using correctiondown(t) and TdownT () substitutes R (t) and T (t), re-execute and obtain making standardization
θ and δ that value σ (θ, δ) of cross-correlation and function is maximum, as the parts of crack attribute factor.
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