CN106291673B - Crack attribute factor extracting method based on shear-wave birefringence and device - Google Patents
Crack attribute factor extracting method based on shear-wave birefringence and device Download PDFInfo
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Abstract
On the one hand a kind of crack attribute factor extracting method based on shear-wave birefringence is proposed, including：The horizontal component data volume received by multi -components wave detector is obtained, the horizontal component data volume includes radial component data volume R (t) and tangential component data volume T (t)；Obtain the value σ (θ for making standardization cross-correlation and function, δ) maximum θ and δ, as crack attribute factor, angles of the wherein θ between natural system of coordinates and observation coordinate system, it indicates fracture azimuth, δ is the quick shear wave and delay time between shear wave at a slow speed after division, indicates fracture development density.
Description
Technical field
The invention belongs to seismic data interpretation fields, and in particular to a kind of crack attribute factor based on shear-wave birefringence carries
Take method and apparatus.
Background technology
There is good permeability in widely distributed the crack for being full of fluid, these cracks in the earth formation, they are not still
The reservoir space of oil gas, and be the migration pathway of oil gas, that is to say, that the development degree in crack and connectivity determine in stratum
Oil-gas accumulation degree, thus, the research of fracture attribute is of great significance.
In the region for possessing vertical (or near upright) crack of orientation, when shear wave passes through fracture medium, i.e., it can occur point
Split phenomenon.Thus quick shear wave and at a slow speed shear wave are generated, the former parallel fracture moves towards polarization, is propagated with the speed of rock medium；
The latter's vertical fracture moves towards polarization, and spread speed is influenced by frac-pack object.Therefore quick shear wave and shear wave itself is taken at a slow speed
The band information in crack, if to quick shear wave and shear wave is studied at a slow speed, so that it may to be effectively obtained subterranean fracture medium
Attributive character.
It is at present Alford rotations by quick shear wave and the at a slow speed main stream approach of the information extraction crack attribute factor of shear wave
Robin and polarization analysis.Alford proposed Alford rotations in 1986, be put forward for the first time by estimate quick shear wave and
The delay profile of shear wave estimates the method for crack attribute factor at a slow speed.Crampin proposed polarization analysis, the party in 1997
Method estimates crack attribute factor using the thing component of digital seismic recording and the particle motion diagram of north-south component.Both sides
Law theory derives accurately, but limits in precision and extremely in use scope, largely restricts its application.
Crack attribute factor is important fracture medium characteristic parameter, it reflect underground medium in crack development direction and
Density is developed, this is very helpful to judging reservoir property and Reservoir Scale.The quick shear wave of traditional utilization and at a slow speed shear wave are special
The method of sign extraction crack attribute factor will often use pure shear wave exploration, that is, double source four componets data.Done so compared with
Big limitation, first, the excitation of the shear wave source needed for pure shear wave exploration need a series of special requirements, in the wild work area
Data are extremely difficult to when acquiring；Secondly, the required acquisition cost of shear wave exploration is significantly larger than common p-wave source excitation
Acquisition mode.This is resulted in actual seismic prospecting, it is difficult to obtain double source four componets data.On the other hand, quickly horizontal
Wave is in elliptical polarization together with shear wave being at a slow speed often aliasing, traditional polarization analysis require in analysis window only there are one
The requirement of lineups is just difficult to meet.
Invention content
It is an object of the invention to solving above-mentioned problem existing in the prior art, provide a kind of based on shear-wave birefringence
Crack attribute factor extracting method, makes input data be reduced to two component datas, cost and skill caused by avoiding shear wave exploration
Art problem, and by quick shear wave and the waveform correlativity of shear wave at a slow speed, get around analysis window lineups and be difficult to selection
Problem, the feasibility of improvement method.
On the one hand a kind of crack attribute factor extracting method based on shear-wave birefringence is proposed, including：It obtains by more points
The horizontal component data volume that receives of amount wave detector, the horizontal component data volume include radial component data volume R (t) and tangential
Component data body T (t)；The maximum θ and δ of value σ (θ, δ) for obtaining making the standardization cross-correlation and function in following formula, as
Crack attribute factor：
Angles of the wherein θ between natural system of coordinates and observation coordinate system indicates that fracture azimuth, δ are after dividing
Quick shear wave and delay time between shear wave at a slow speed, indicate that fracture development density, L are analysis window length,
Wherein, the expression formula of X (t, φ) is as follows：
WhereinSymbolic indication is related, Rφ(t) rotation that radial component R (t) is obtained after rotated counterclockwise by angle φ is indicated
Turn radial component, Tφ(t) the rotation tangential component that tangential component T (t) is obtained after rotated counterclockwise by angle φ is indicated,
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 attribute factor extraction element based on shear-wave birefringence is proposed, including：For obtaining
By the component for the horizontal component data volume that multi -components wave detector receives, the horizontal component data volume includes radial component data
Body R (t) and tangential component data volume T (t)；Value σ (θ, δ) for obtaining making standardization cross-correlation and function in following formula
Maximum θ and δ, the component as crack attribute factor：
Angles of the wherein θ between natural system of coordinates and observation coordinate system indicates that fracture azimuth, δ are after dividing
Quick shear wave and delay time between shear wave at a slow speed, indicate that fracture development density, L are analysis window length,
Wherein, the expression formula of X (t, φ) is as follows：
WhereinSymbolic indication is related, Rφ(t) rotation that radial component R (t) is obtained after rotated counterclockwise by angle φ is indicated
Turn radial component, Tφ(t) the rotation tangential component that tangential component T (t) is obtained after rotated counterclockwise by angle φ is indicated,
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 beneficial effects of the invention are as follows：This method carries out shear wave pair using horizontal component data volume
Crack inverting is reflected, it is final to obtain crack attribute factor, there is easy reality compared with traditional parallel-vertical shear wave crack attributes extraction method
Existing, strong robustness adapts to extensive feature, such as is suitable for crack elimination prediction.
Description of the drawings
Disclosure illustrative embodiments are described in more detail in conjunction with the accompanying drawings, the disclosure above-mentioned and its
Its purpose, feature and advantage will be apparent, wherein in disclosure illustrative embodiments, identical reference label
Typically represent same parts.
Fig. 1 is the stream according to the crack attribute factor extracting method based on shear-wave birefringence of one embodiment of the present of invention
Cheng Tu.
Fig. 2 is the crack attribute factor extracting method based on shear-wave birefringence according to an alternative embodiment of the invention
Flow chart.
Fig. 3 is the model parameter according to exemplary horizontal layer two dimensional model containing fracture medium.
Fig. 4 is to carry out the data radial component that forward modeling obtains to Fig. 3 models.
Fig. 5 is to carry out the data tangential component that forward modeling obtains to Fig. 3 models.
Fig. 6 is to carry out the crack attribute factor that shear-wave birefringence crack inverting obtains to Fig. 4 and Fig. 5 data.
Fig. 7 is to carry out lower layer's crack attribute factor that shear-wave birefringence crack inverting obtains to Fig. 4 and Fig. 5 data.
Specific implementation mode
The preferred embodiment of the disclosure is more fully described below with reference to accompanying drawings.Although showing the disclosure in attached drawing
Preferred embodiment, however, it is to be appreciated that may be realized in various forms the disclosure without the embodiment party that should be illustrated here
Formula is limited.On the contrary, these embodiments are provided so that the disclosure is more thorough and complete, and can be by the disclosure
Range is completely communicated to those skilled in the art.
What the present invention generated when being propagated in fracture medium (such as fracture medium of the system containing vertical fracture) according to shear wave
Rule (i.e. shear wave splitting, Shear Wave Splitting) is divided, by containing the quick shear wave and at a slow speed after division
The seismic data of shear wave implements shear-wave birefringence inverting to extract crack attribute factor.
Embodiment 1
Fig. 1 shows a kind of crack attribute factor extraction based on shear-wave birefringence according to an embodiment of the invention
Method, this method include：
Step 101, the horizontal component data volume received by multi -components wave detector, the horizontal component data volume packet are obtained
Include radial component data volume R (t) and tangential component data volume T (t)；
Step 102, obtain making the maximum θ and δ of value σ (θ, δ) of the standardization cross-correlation and function in following formula (1),
Angles of the wherein θ between natural system of coordinates and observation coordinate system, i.e. fracture azimuth azimuth indicate fracture development side
It is quick shear wave after division and delay time between shear wave at a slow speed to, δ, indicates fracture development density：
Wherein, L is analysis window length, and the expression formula of X (t, φ) is as follows, hereSymbolic indication is related：
Rφ(t) the rotation radial component that radial component R (t) is obtained after rotated counterclockwise by angle φ, T are indicatedφ(t) it indicates
The rotation tangential component that tangential component T (t) is obtained after rotated counterclockwise by angle φ, an example of rotation is for example, see following
Formula (3)：
The expression formula of B (t, φ, θ, δ) is as follows in formula (1)：
Wherein A (t) is the sum of the auto-correlation function of horizontal component data volume.It can be received using multi -components wave detector
To horizontal component data volume carry out autocorrelation calculation and obtain, i.e., by summing again after R (t) and T (t) are sought auto-correlation respectively
It obtains, and it is unrelated with rotation angle φ；ε=θ-φ.
The crack attribute factor extracting method based on shear-wave birefringence that this embodiment offers a kind of, passes through above step
101 and 102 have obtained crack attribute factor, i.e. fracture azimuth and fracture development density, and input data is made to be reduced to two points
Data, cost and technical problem caused by avoiding shear wave exploration are measured, and passes through quick shear wave and the waveform phase of shear wave at a slow speed
Pass relationship gets around the problem of analysis window lineups are difficult to select, the feasibility of improvement method.
In one example, the maximum fracture azimuth of value for making formula (1) Plays cross-correlation and function is obtained
Azimuth angle theta and delay time δ can be obtained by being scanned with given interval in given range to θ and δ.Such as it can to θ
It is scanned for interval from 0 to 180 degree and with 10 degree, δ can be scanned with 1 for interval from 0 to 10.Those skilled in the art
It should be understood that range above and interval are merely illustrative, it is not intended to limit the present invention.In fact, scanning range and the interval of θ and δ
It can arbitrarily choose as needed.A large amount of tests show to be scanned θ, δ with given interval in given range, Cong Zhongxuan
Taking makes σ (θ, δ) maximum θ, δ, you can calculate natural system of coordinates and observation coordinate system angle theta and quick shear wave at a slow speed
Time delay δ between shear wave determines that fracture azimuth and development density, i.e. θ indicate that fracture azimuth, δ instructions are split
Seam development density, δ values show that more greatly crack is more intensive.
It will be understood by those skilled in the art that the above scan method is merely illustrative.Those skilled in the art can be sharp as needed
Obtain making the maximum θ and δ of maximum σ (θ, δ) with any known method in this field.
Embodiment 2
Fig. 2 shows a kind of crack attribute factor extractions based on shear-wave birefringence according to an embodiment of the invention
Method.The embodiment is further comprising the steps of on the basis of embodiment 1：
Step 103, lower layer's fracture layers are judged whether, which can obtain from earthquake record, if deposited
104 are being entered step, if it does not exist, then this method terminates.
Step 104, it is corrected according to following formula (5)；
Rdown(t)=R (t) cos θ-T (t) sin θs (5)
Tdown(t)=R (t) sin θ+T (t) cos θ
Wherein Rdown(t) and Tdown(t) lower layer's radial component data volume and lower layer's tangential component data volume are indicated, here
Lower layer refers to the lower layer relative to the current layer where R (t) and T (t), then uses the R after step 104 correctiondown(t) and
Tdown(t) R (t) in alternative steps 102 and T (t), re-execute step 102 with obtain the lower layer fracture azimuth and
Fracture development density.
In one example, step 102 can be repeated to step 105, until the fracture development of all slits layer has been calculated
Direction and fracture development density.
In the case that the embodiment further considers underground there are multilayer crack medium, the category of current layer fracture medium is utilized
Sex factor information is modified lower layer, eliminates anisotropic influence, and then accurately and effectively seeks lower layer's fracture medium
Attribute factor.
Embodiment 3
According to another embodiment of the present invention, it is proposed that a kind of crack attribute factor extraction dress based on shear-wave birefringence
It sets, including：
Component for obtaining the horizontal component data volume received by multi -components wave detector, the horizontal component data volume
Including radial component data volume R (t) and tangential component data volume T (t)；
The maximum θ and δ of value σ (θ, δ) for obtaining making standardization cross-correlation and function in following formula, as crack
The component of attribute factor：
Angles of the wherein θ between natural system of coordinates and observation coordinate system indicates that fracture azimuth, δ are after dividing
Quick shear wave and delay time between shear wave at a slow speed, indicate that fracture development density, L are analysis window length,
Wherein, the expression formula of X (t, φ) is as follows：
WhereinSymbolic indication is related, Rφ(t) rotation that radial component R (t) is obtained after rotated counterclockwise by angle φ is indicated
Turn radial component, Tφ(t) the rotation tangential component that tangential component T (t) is obtained after rotated counterclockwise by angle φ is indicated,
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)、Tφ(t) following relationship can be met：
In one example, it can obtain making σ (θ, δ) by being scanned with given interval in given range to θ and δ
Maximum angle theta and delay time δ.
In one example, described device may also include：
For judging whether lower layer's fracture layers, if it is present according to the corrected component of following formula；
Rdown(t)=R (t) cos θ-T (t) sin θs
Tdown(t)=R (t) sin θ+T (t) cos θ
Wherein Rdown(t) and Tdown(t) lower layer's radial component data volume and lower layer's tangential component data volume are indicated,
For using the R after correctingdown(t) and Tdown(t) R (t) and T (t) is substituted, re-executing to obtain keeps standardization mutual
Related and function the maximum θ and δ of value σ (θ, δ), the component as crack attribute factor.
Fig. 3 shows the model parameter of horizontal layer two dimensional model containing fracture medium.Using the model as one
Forward modeling trace gather illustrates the effect of the embodiment of the present invention by following experimental data.
(1) forward modeling is carried out to Fig. 3 institutes representation model, design ground p-wave source excitation, p-wave source well constraint inversion is 700m.Well
Middle multi -components wave detector receives, and wave detector is disposed since well head, and one is assigned every 7m, places 380 wave detectors altogether.Sampling
Between be divided into 2ms, record length 800ms.Obtained VSP models record data radial component is as shown in figure 4, tangential component such as figure
Shown in 5.
(2) shear-wave birefringence crack inverting is carried out to data shown in Fig. 4 and Fig. 5, obtains upper layer crack attribute factor such as Fig. 6
Shown, abscissa indicates that fracture azimuth, ordinate indicate fracture development density, the central point instruction that Voice segment is rolled into a ball in figure
Fracture azimuth and fracture development density.It is compared by the crack attribute factor with model specification, inverting obtains upper layer crack
It is positive 70 ° to develop direction, and fracture development density is 5, is fitted like a glove with model parameter.
(3) it carries out layer stripping using the upper layer crack attribute factor that (2) obtain to data shown in Fig. 4 and Fig. 5 to correct, to repairing
Data after just carry out shear-wave birefringence crack inverting, obtain lower layer's crack attribute factor as shown in fig. 7, abscissa indicates crack
Direction is developed, ordinate indicates fracture development density, the central point instruction fracture azimuth and crack that Voice segment is rolled into a ball in figure
Develop density.It is compared by the crack attribute factor with model specification, it is minus 55 ° that inverting, which obtains lower layer's fracture azimuth, is split
Seam development density is 9, is fitted like a glove with model parameter.
The disclosure can be system, method and/or computer program product.Computer program product may include computer
Readable storage medium storing program for executing, containing for making processor realize the computer-readable program instructions of various aspects of the disclosure.
Computer readable storage medium can be can keep and store the instruction used by instruction execution equipment tangible
Equipment.Computer readable storage medium for example can be-- but be not limited to-- storage device electric, magnetic storage apparatus, optical storage
Equipment, electromagnetism storage device, semiconductor memory apparatus or above-mentioned any appropriate combination.Computer readable storage medium
More specific example (non exhaustive list) includes：Portable computer diskette, random access memory (RAM), read-only is deposited hard disk
It is reservoir (ROM), erasable programmable read only memory (EPROM or flash memory), static RAM (SRAM), portable
Compact disk read-only memory (CD-ROM), digital versatile disc (DVD), memory stick, floppy disk, mechanical coding equipment, for example thereon
It is stored with punch card or groove internal projection structure and the above-mentioned any appropriate combination of instruction.Calculating used herein above
Machine readable storage medium storing program for executing is not interpreted that instantaneous signal itself, the electromagnetic wave of such as radio wave or other Free propagations lead to
It crosses the electromagnetic wave (for example, the light pulse for passing through fiber optic cables) of waveguide or the propagation of other transmission mediums or is transmitted by electric wire
Electric signal.
Computer-readable program instructions as described herein can be downloaded to from computer readable storage medium it is each calculate/
Processing equipment, or outer computer or outer is downloaded to by network, such as internet, LAN, wide area network and/or wireless network
Portion's storage device.Network may include copper transmission cable, optical fiber transmission, wireless transmission, router, fire wall, interchanger, gateway
Computer and/or Edge Server.Adapter or network interface in each calculating/processing equipment are received from network to be counted
Calculation machine readable program instructions, and the computer-readable program instructions are forwarded, for the meter being stored in each calculating/processing equipment
In calculation machine readable storage medium storing program for executing.
For execute the disclosure operation computer program instructions can be assembly instruction, instruction set architecture (ISA) instruction,
Machine instruction, machine-dependent instructions, microcode, firmware instructions, condition setup data or with one or more programming languages
Arbitrarily combine the source code or object code write, the programming language include the programming language-of object-oriented such as
Smalltalk, C++ etc., and conventional procedural programming languages-such as " C " language or similar programming language.Computer
Readable program instructions can be executed fully, partly execute on the user computer, is only as one on the user computer
Vertical software package executes, part executes or on the remote computer completely in remote computer on the user computer for part
Or it is executed on server.In situations involving remote computers, remote computer can pass through network-packet of any kind
It includes LAN (LAN) or wide area network (WAN)-is connected to subscriber computer, or, it may be connected to outer computer (such as profit
It is connected by internet with ISP).In some embodiments, by using computer-readable program instructions
Status information carry out personalized customization electronic circuit, such as programmable logic circuit, field programmable gate array (FPGA) or can
Programmed logic array (PLA) (PLA), the electronic circuit can execute computer-readable program instructions, to realize each side of the disclosure
Face.
Referring herein to according to the flow chart of the method, apparatus (system) of the embodiment of the present disclosure and computer program product and/
Or block diagram describes various aspects of the disclosure.It should be appreciated that flowchart and or block diagram each box and flow chart and/
Or in block diagram each box combination, can be realized by computer-readable program instructions.
These computer-readable program instructions can be supplied to all-purpose computer, special purpose computer or other programmable datas
The processor of processing unit, to produce a kind of machine so that these instructions are passing through computer or other programmable datas
When the processor of processing unit executes, work(specified in one or more of implementation flow chart and/or block diagram box is produced
The device of energy/action.These computer-readable program instructions can also be stored in a computer-readable storage medium, these refer to
It enables so that computer, programmable data processing unit and/or other equipment work in a specific way, to be stored with instruction
Computer-readable medium includes then a manufacture comprising in one or more of implementation flow chart and/or block diagram box
The instruction of the various aspects of defined function action.
Computer-readable program instructions can also be loaded into computer, other programmable data processing units or other
In equipment so that series of operation steps are executed on computer, other programmable data processing units or miscellaneous equipment, with production
Raw computer implemented process, so that executed on computer, other programmable data processing units or miscellaneous equipment
Instruct function action specified in one or more of implementation flow chart and/or block diagram box.
Flow chart and block diagram in attached drawing show the system, method and computer journey of multiple embodiments according to the disclosure
The architecture, function and operation in the cards of sequence product.In this regard, each box in flowchart or block diagram can generation
One module of table, program segment or a part for instruction, the module, program segment or a part for instruction include one or more use
The executable instruction of the logic function as defined in realization.In some implementations as replacements, the function of being marked in box
It can occur in a different order than that indicated in the drawings.For example, two continuous boxes can essentially be held substantially in parallel
Row, they can also be executed in the opposite order sometimes, this is depended on the functions involved.It is also noted that block diagram and/or
The combination of each box in flow chart and the box in block diagram and or flow chart can use function or dynamic as defined in executing
The dedicated hardware based system made is realized, or can be realized using a combination of dedicated hardware and computer instructions.
The presently disclosed embodiments is described above, above description is exemplary, and non-exclusive, and
It is not limited to disclosed each embodiment.Without departing from the scope and spirit of illustrated each embodiment, for this skill
Many modifications and changes will be apparent from for the those of ordinary skill in art field.The selection of term used herein, purport
In the principle, practical application or technological improvement to the technology in market for best explaining each embodiment, or this technology is made to lead
Other those of ordinary skill in domain can understand each embodiment disclosed herein.
Claims (6)
1. a kind of crack attribute factor extracting method based on shear-wave birefringence, including：
The horizontal component data volume received by multi -components wave detector is obtained, the horizontal component data volume includes radial component number
According to body R (t) and tangential component data volume T (t)；
The maximum θ and δ of value σ (θ, δ) for obtaining making the standardization cross-correlation and function in following formula, as crack attribute because
Son：
Angles of the wherein θ between natural system of coordinates and observation coordinate system indicates that fracture azimuth, δ are fast after dividing
Delay time between fast shear wave and at a slow speed shear wave indicates that fracture development density, L are analysis window length,
Wherein, the expression formula of X (t, φ) is as follows：
WhereinSymbolic indication is related, Rφ(t) indicate that the rotation that radial component R (t) is obtained after rotated counterclockwise by angle φ is radial
Component, Tφ(t) the rotation tangential component that tangential component T (t) is obtained after rotated counterclockwise by angle φ is indicated,
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；
Wherein, lower layer's fracture layers are judged whether, if it is present being corrected according to following formula；
Rdown(t)=R (t) cos θ-T (t) sin θs
Tdown(t)=R (t) sin θ+T (t) cos θ
Wherein Rdown(t) and Tdown(t) lower layer's radial component data volume and lower layer's tangential component data volume are indicated,
Use the R after correctiondown(t) and Tdown(t) R (t) and T (t) is substituted, re-executing to obtain makes standardization cross-correlation and letter
Several maximum θ and δ of value σ (θ, δ), the step of as crack attribute factor.
2. according to the method described in claim 1, wherein, R (t), T (t) and Rφ(t)、Tφ(t) meet following relationship：
3. according to the method described in claim 1, wherein, by θ and δ in given range with given interval be scanned come
It obtains making the maximum angle thetas of σ (θ, δ) and delay time δ.
4. a kind of crack attribute factor extraction element based on shear-wave birefringence, including：
Component for obtaining the horizontal component data volume received by multi -components wave detector, the horizontal component data volume include
Radial component data volume R (t) and tangential component data volume T (t)；
The maximum θ and δ of value σ (θ, δ) for obtaining making standardization cross-correlation and function in following formula, as crack attribute
The component of the factor：
Angles of the wherein θ between natural system of coordinates and observation coordinate system indicates that fracture azimuth, δ are fast after dividing
Delay time between fast shear wave and at a slow speed shear wave indicates that fracture development density, L are analysis window length,
Wherein, the expression formula of X (t, φ) is as follows：
WhereinSymbolic indication is related, Rφ(t) indicate that the rotation that radial component R (t) is obtained after rotated counterclockwise by angle φ is radial
Component, Tφ(t) the rotation tangential component that tangential component T (t) is obtained after rotated counterclockwise by angle φ is indicated,
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；
Wherein, for judging whether lower layer's fracture layers, if it is present according to the corrected component of following formula；
Rdown(t)=R (t) cos θ-T (t) sin θs
Tdown(t)=R (t) sin θ+T (t) cos θ
Wherein Rdown(t) and Tdown(t) lower layer's radial component data volume and lower layer's tangential component data volume are indicated,
For using the R after correctingdown(t) and Tdown(t) R (t) and T (t) is substituted, re-executing to obtain makes standardization cross-correlation
With the maximum θ and δ of value σ (θ, δ) of function, the component as crack attribute factor.
5. device according to claim 4, wherein R (t), T (t) and Rφ(t)、Tφ(t) meet following relationship：
6. device according to claim 4, wherein by θ and δ in given range with given interval be scanned come
It obtains making the maximum angle thetas of σ (θ, δ) and delay time δ.
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