CN115128163A - Bridge pile foundation integrity detection method based on small offset scattered wave imaging method - Google Patents
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Abstract
The invention belongs to the technical field of integrity detection of bridge pile foundations, and provides a method for detecting integrity of a bridge pile foundation based on a small offset scattered wave imaging method.
Description
Technical Field
The invention belongs to the technical field of bridge pile foundation integrity detection, and particularly relates to a bridge pile foundation integrity detection method based on a small offset scattered wave imaging method.
Background
Based on the rapid development of the capital construction project in China, the requirements of the pile foundation are developed towards a larger direction, a deeper direction, a more complex direction and the like. However, due to many factors such as uncertainty of geological conditions and complexity of construction process, integrity defects such as hole enlargement, necking, segregation, mud inclusion, pile breaking and the like often occur in the pile foundation forming process. If the defects are not detected, serious safety accidents can be caused, and great hidden dangers are brought to the property and life safety of the country and people. Therefore, the method has important safety significance for detecting the integrity of the pile foundation.
At present, the integrity detection methods for the concrete solid pile foundation with the diameter larger than 1m mainly comprise low (high) strain detection, a sound wave transmission method, a thermal integrity pile foundation detection method, a fiber grating method and the like. They each have their own limitations. The low (high) strain is easily influenced by the surrounding environment, the dynamic response signals are mainly analyzed from a time domain, the speed is easily interfered, the detection on the depth and the pile length of the defect position is inaccurate, the sensitivity on small defects is low, and the horizontal position information of the defect cannot be obtained; the sound wave transmission method has a detection blind area and can only detect the area between sound wave tubes; thermal integrity pile foundation detection needs to arrange a large amount of temperature sensors, and detection cost is higher and temperature sensors are susceptible to interference. The fiber grating method also requires a large number of sensors, which increases the detection cost and complicates the detection steps. Based on the situation, the accurate, efficient and nondestructive detection of the integrity of the pile foundation of the concrete solid pile with the diameter larger than 1m is a problem which needs to be solved urgently at present in the industry.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a method for detecting the integrity of a bridge pile foundation based on a small offset scattered wave imaging method, which can effectively solve the problems that the speed of the traditional detection method is easy to interfere and the detection has a blind area, does not need to carry out any treatment on the pile foundation and greatly improves the working efficiency.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for detecting integrity of a bridge pile foundation based on a small offset scattered wave imaging method comprises the following steps:
the method comprises the following steps: arranging a plurality of detectors at the top of the pile foundation;
step two: connecting the detector with an acquisition base station and an earthquake acquisition host through a large earthquake line, and forming a small offset scattered wave acquisition system by taking the position of a first earthquake source as a coordinate origin, the depth direction along the pile foundation as a Z direction and the line measuring direction as an X direction;
step three: a hammering device is arranged and connected with a signal trigger box, and parameters of the signal trigger box are set;
step four: hammering is carried out on the middle of the adjacent detectors through the hammering device, and hammering signals are recorded through the earthquake acquisition host;
step five: arranging and moving the detectors, and collecting hammering signals according to the fourth step;
step six: repeating the fifth step until the detector reaches the edge of the pile foundation, and completing hammering signal acquisition;
step seven: carrying out data processing on the collected hammering signal to obtain a longitudinal wave superposition velocity model;
step eight: performing acoustic forward numerical simulation by combining a longitudinal wave superposition velocity model, obtaining Green function values of each point in a model space at different corresponding moments, and obtaining a forward extrapolation field;
step nine: performing wave field extrapolation of longitudinal waves by taking the detector as an original point to obtain a wave equation numerical solution of a limited bandwidth Green function of a wave detection point;
step ten: and performing cross-correlation imaging by using the forward extrapolation field and the backward extrapolation field of the longitudinal wave to obtain a final scattered wave offset imaging result.
Preferably, in the first step: a plurality of installation positions with the same channel spacing are outwards arranged in the center of the top end face of the pile foundation, and the detector is arranged in the installation positions; in the five steps: the distance of the detectors moving in an arrangement mode is the size of the distance between the adjacent detectors.
Preferably, in the step one: the number of the detectors is six.
Preferably, in the fourth step: hammering by the hammering device between the detector in the second pass and the detector in the second pass from the edge of the top end surface of the pile foundation to the center, wherein the hammering signal is recorded as x (t) 1 ) (ii) a Hammering the middle of the detector in the fourth pass and the detector in the fifth pass by the hammering device, wherein the hammering signal is recorded as x (t) 2 )；
In the fifth step: collecting hammering signals which are x (t) respectively according to the fourth step 3 )、x(t 4 )；
In the sixth step: repeating the fifth step, enabling the detector which is vertically positioned in the sixth step to reach the edge of the pile foundation, and completing the collection work of hammering signals, wherein the collected hammering signals are x (t) respectively 5 )…x(t m )。
Preferably, in the third step: the parameters of the signal trigger box comprise sampling time t and sampling interval t
The sampling frequency is AHz.
Preferably, in the seventh step:
A. and (3) performing channel processing, and inputting the observation system into a seismic record: x (t) 1 )…x(t m )；
B. Performing band-pass filtering processing on the seismic record to remove the noise signal collected in the seismic record;
C. separating longitudinal waves and transverse waves by polarization analysis to obtain seismic records of the longitudinal waves;
D. performing deconvolution processing on the longitudinal wave seismic record to improve the time resolution of seismic waves;
E. extracting a common midpoint gather (CMP);
F. performing dynamic correction to eliminate the influence of offset distance and form a two-way travel time with zero offset distance;
G. analyzing the velocity of each seismic record to obtain a velocity spectrum O of each seismic record 1 …O n ；
H. Stacking the seismic records, and combining the velocity spectrum to obtain a primary velocity model Q (v) p )。
Preferably, in the step eight: forward external field U Z (x, z, t), wherein x, z are the positions of the points and t is the time;
A. to obtain a formal solution of the Green function, first the Helmholtz equation:
wherein
Is Laplace operator, G Z (r-r s ) Is a green function, r s For the location of the seismic source, r is the other location of the wavefield, δ (r-r) s ) Is a pulse signal, rs is the position of a seismic source, r is other positions of a wave field, S (W) is the frequency spectrum of a seismic source wavelet, w is the circumferential rate, and v (r) is the velocity;
B. left end plus zero factor [ v (r)] -2 -[v 0 (r)] -2 Here, the source of scattering, and then the term shifting process is performed:
C. let O be 1 (r)＝[v(r)] -2 -[v 0 (r)] -2 To obtain the classic L-S equation:
G Z (r,r s )＝G 0 (r,r s )+ω 2 ∫ V G 0 (r,r′)O 1 (r′)G Z (r′,r s )dr′； (3-3)；
G 0 (r,r s ) As a green function of the background wave field, omega 2 ∫ V G 0 (r,r′)O 1 (r′)G Z (r′,r s ) dr 'is a perturbation term, and r' is a position in the scatterer;
D. using background Green's function G in scatterers 0 (r,r s ) Equivalent overall Green function G Z (r,r s ) Carry out Born approximation:
G Z (r,r s )≈G 0 (r,r s )+ω 2 ∫ V G 0 (r,r′)O 1 (r′)G 0 (r′,r s )dr′； (3-4)；
E. the scattered wavefield is then obtained:
wherein, the first and the second end of the pipe are connected with each other,
as the normal derivative, x (t) m ) Representing a complex conjugate for the seismic record; curved surface where S' observation point is located, n s Is the outer normal direction of S';
F. the background perturbation field is:
G. the total inverse extrapolation field is:
U Z (x,z,t)＝U 0 +U 1 ； (3-7)。
preferably, in the step nine:
A. to obtain a formal solution of the Green function, first the Helmholtz equation:
wherein
Is Laplacian, G F (r-r R ) Is the green function, delta (r-r) R ) For a pulse signal, r R Is the position of the detector, r is the other positions of the wavefield, w is the circumferential ratio, v (r) is the velocity;
B. the left end is added with zero factor [ v (r)] -2 -[v 0 (r)] -2 Here, the source of scattering, and then the term shifting process is performed:
C. let O be 1 (r)＝[v 0 (r)] -2 -[v 0 (r)] -2 To obtain the classic L-S equation:
G F (r,r s )＝G 0 (r,r R )+ω 2 ∫ V G 0 (r,r′)O 1 (r′)G F (r′,r R )dr′； (4-3)；
G 0 (r,r R ) As a green function of the background wave field, omega 2 ∫ V G 0 (r,r′)O 1 (r′)G F (r′,r R ) dr 'is a perturbation term, r' is a position within the scatterer;
D. using background Green's function G in scatterers 0 (r,r R ) Equivalent overall Green's function G F (r,r R ) Carry out Born approximation:
G F (r,r R )≈G 0 (r,r R )+ω 2 ∫ V G 0 (r,r′)O 1 (r′)G 0 (r′,r R )dr′； (4-4)；
E. and then obtaining a scattered wave field:
wherein the content of the first and second substances,
is the normal derivative, x (t) m ) Representing a complex conjugate for the seismic record; curved surface where S' observation point is located, n R Is the outer normal direction of S';
F. the background perturbation field is:
G. the total inverse extrapolated field is:
U F (x,z,t)＝U 0 +U 1 ； (4-7)。
preferably, in the step ten:
A. the forward direction is pushed outwards to form a field U Z (x, z, t) and the inverse extrapolation field U F (x, z, t) is substituted into the following equation:
I(x,z)＝∫dωH Z (x,z,w)H F (x,z,w)； (5-1)；
wherein w is the fillet frequency;
B. and obtaining a zero-time shift cross-correlation offset image field.
Preferably, the hammering device is a manual hammer.
Compared with the prior art, the invention has the following beneficial effects:
this scheme is through carrying out little offset scattered wave imaging detection pile foundation integrality at the pile foundation, utilizes scattered wave imaging to detect pile foundation integrality, has characteristics such as accurate, high efficiency, harmless, provides a technical guidance for pile foundation integrality detects.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a scenario in which the scheme of the present invention is applied.
Wherein:
1-pile foundation, 2-detector and 3-hammering seismic source.
Detailed Description
So that the manner in which the above recited objects, features and advantages of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments thereof which are illustrated in the appended drawings. In addition, the embodiments and features of the embodiments of the present application may be combined with each other without conflict. In the following description, numerous specific details are set forth to provide a thorough understanding of the present invention, and the described embodiments are merely a subset of the embodiments of the present invention, rather than a complete embodiment. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments of the present invention, belong to the protection scope of the present invention.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.
Example (b):
as shown in fig. 1, in this embodiment, a method for detecting integrity of a bridge pile foundation based on a small offset scattered wave imaging method is provided, and the following tools are used: the signal triggers box, detector 2, gathers basic station, earthquake collection host computer, big line of earthquake, electric wire, hammering device, and in this embodiment, hammering device is manual hammer.
The method comprises the following steps:
the method comprises the following steps: arranging a plurality of detectors at the top of the pile foundation 1;
step two: connecting a detector with an acquisition base station and an earthquake acquisition host through an earthquake large line, and forming a small offset scattered wave acquisition system by taking the position of a first earthquake source as a coordinate origin, the depth direction along a pile foundation as a Z direction and the line measuring direction as an X direction;
step three: a hammering device is arranged and connected with a signal trigger box, and parameters of the signal trigger box are set;
step four: hammering is carried out on the middle of the adjacent detectors through a hammering device, a hammering focus 3 is arranged at a hammering position, and hammering signals are recorded through an earthquake acquisition host;
step five: arranging and moving the detectors, and collecting hammering signals according to the fourth step;
step six: repeating the fifth step until the detector reaches the edge of the pile foundation, and completing the collection work of the hammering signal;
step seven: carrying out data processing on the collected hammering signal to obtain a longitudinal wave superposition speed model;
step eight: performing acoustic forward numerical simulation by combining a longitudinal wave superposition velocity model, obtaining Green function values of each point in a model space at different corresponding moments, and obtaining a forward extrapolation field;
step nine: performing wave field extrapolation of longitudinal waves by taking the wave detector as an original point to obtain a wave equation numerical solution of a limited bandwidth Green function of the wave detection point;
step ten: and performing cross-correlation imaging by using the forward extrapolation field and the backward extrapolation field of the longitudinal wave to obtain a final scattered wave migration imaging result.
In this embodiment, for the arrangement of the detectors, specifically, in step one: a plurality of installation positions with the same channel spacing are outwards arranged at the center of the top end surface of the pile foundation, and the detector is arranged at the installation positions; in the five steps: the distance of the detectors is the distance between adjacent detectors.
In the present embodiment, the number of detectors is six.
In the present embodiment, the recording operation of the hammer signal is specifically as follows:
in step four: hammering is carried out between the detector in the second path and the detector in the second path from the edge of the top end surface of the pile foundation to the center through a hammering device, and the hammering signal is recorded as x (t) here 1 ) (ii) a The detector in the fourth track and the detector in the fifth trackThe detector of (2) is hammered by a hammering device, and the hammering signal is recorded as x (t) 2 )；
In the fifth step: collecting hammering signals which are respectively x (t) according to the fourth step 3 )、x(t 4 )；
In the sixth step: repeating the fifth step, and finishing the collection work of the hammering signals when the detector which is vertically positioned in the sixth step reaches the edge of the pile foundation, wherein the collected hammering signals are x (t) respectively 5 )…x(t m )。
In step three: the parameters of the signal trigger box comprise a sampling time t and a sampling interval t
The sampling frequency is AHz.
In this embodiment, in step seven, the method of obtaining the velocity model of the superimposed longitudinal wave is as follows:
A. and (3) performing channel processing, and inputting the observation system into a seismic record: x (t) 1 )…x(t m )；
B. Performing band-pass filtering processing on the seismic record to remove the noise signal collected in the seismic record;
C. separating longitudinal waves and transverse waves by polarization analysis to obtain seismic records of the longitudinal waves;
D. performing deconvolution processing on the longitudinal wave seismic record to improve the time resolution of seismic waves;
E. extracting a common midpoint gather (CMP);
F. performing dynamic correction to eliminate the influence of offset distance and form a two-way travel time with zero offset distance;
G. performing velocity analysis on each seismic record to obtain a velocity spectrum O of each seismic record 1 …O n ；
H. Stacking the seismic records, and combining the velocity spectrum to obtain a primary velocity model Q (v) p )。
In this embodiment, in step eight, the method of obtaining the forward extrapolated field and the backward extrapolated field is as follows:
forward external field U Z (x, z, t) wherein xZ is the position of the point, and t is the time;
A. to obtain a formal solution of the Green function, first the Helmholtz equation:
wherein
Is Laplacian, G Z (r-r s ) Is a green function, r s For the location of the seismic source, r is the other location of the wavefield, δ (r-r) s ) Is a pulse signal, rs is the position of a seismic source, r is other positions of a wave field, S (W) is the frequency spectrum of a seismic source wavelet, w is the circumferential rate, and v (r) is the velocity;
B. the left end is added with zero factor [ v (r)] -2 -[v 0 (r)] -2 Here, the source of scattering, and then the term shifting process is performed:
C. let O be 1 (r)＝[v(r)] -2 -[v 0 (r)] -2 To obtain a classical L-S equation:
G Z (r,r s )＝G 0 (r,r s )+ω 2 ∫ V G 0 (r,r′)O 1 (r′)G Z (r′,r s )dr′； (3-3)；
G 0 (r,r s ) Green functions of background wave field, ω 2 ∫ V G 0 (r,r′)O 1 (r′)G Z (r′,r s ) dr 'is a perturbation term, and r' is a position in the scatterer;
D. using background Green's function G in scatterers 0 (r,r s ) Equivalent overall Green function G Z (r,r s ) Carry out Born approximation:
G Z (r,r s )≈G 0 (r,r s )+ω 2 ∫ V G 0 (r,r′)O 1 (r′)G 0 (r′,r s )dr′； (3-4)；
E. the scattered wavefield is then obtained:
wherein, the first and the second end of the pipe are connected with each other,
as the normal derivative, x (t) m ) Representing a complex conjugate for the seismic record; curved surface where S' observation point is located, n s An outer normal direction of S'; it is to be noted here that: the reason for taking the complex conjugate of the Green function is that the purpose of reverse extrapolation is to solve the reflected field at the imaging point, and therefore, the propagation effect, mainly the time shift effect, needs to be eliminated;
F. the background perturbation field is:
G. the total inverse extrapolated field is:
U Z (x,z,t)＝U 0 +U 1 ； (3-7)。
in this embodiment, in step nine, the method for obtaining the wavefield extrapolation field for the longitudinal wave is as follows:
A. to obtain a formal solution of the Green function, first the Helmholtz equation:
wherein
Is Laplace operator, G F (r-r R ) Is the green function, delta (r-r) R ) For a pulse signal, r R Is the position of the detector, r is the other position of the wavefield, wIs the circumferential ratio, v (r) is the velocity;
B. the left end is added with zero factor [ v (r)] -2 -[v 0 (r)] -2 Here, the source of scattering, and then the term shifting process is performed:
C. let O be 1 (r)＝[v 0 (r)] -2 -[v 0 (r)] -2 To obtain a classical L-S equation:
G F (r,r s )＝G 0 (r,r R )+ω 2 ∫ V G 0 (r,r′)O 1 (r′)G F (r′,r R )dr′； (4-3)；
G 0 (r,r R ) As a green function of the background wave field, omega 2 ∫ V G 0 (r,r′)O 1 (r′)G F (r′,r R ) dr 'is a perturbation term, and r' is a position in the scatterer;
D. using background Green's function G in scatterers 0 (r,r R ) Equivalent overall Green's function G F (r,r R ) To make Born approximation:
G F (r,r R )≈G 0 (r,r R )+ω 2 ∫ V G 0 (r,r′)O 1 (r′)G 0 (r′,r R )dr′； (4-4)；
E. and then obtaining a scattered wave field:
wherein the content of the first and second substances,
as the normal derivative, x (t) m ) For seismic records, denotes the complex conjugate; curved surface where S' observation point is located, n R An outer normal direction of S'; the reason for taking the complex conjugate of the Green function is that it is backward extrapolatedThe aim is to find the reflected field at the imaging point r', for which purpose it is necessary to eliminate the reflected field from r R Point-to-r' propagation effects, primarily time-shifting effects;
F. the background perturbation field is:
G. the total inverse extrapolated field is:
U F (x,z,t)＝U 0 +U 1 ； (4-7)。
in this embodiment, in step ten:
A. the forward direction is pushed outwards to form a field U Z (x, z, t) and the inverse extrapolation field U F (x, z, t) is substituted into the following equation:
I(x,z)＝∫dωH Z (x,z,w)H F (x,z,w)； (5-1)；
wherein w is the fillet frequency;
B. and obtaining a zero-time shift cross-correlation offset image field.
The embodiment detects the integrity of the pile foundation by performing small offset scattered wave imaging on the pile foundation and detecting the integrity of the pile foundation by utilizing the scattered wave imaging, has the characteristics of accuracy, high efficiency, no damage and the like, has no detection blind area in a sound wave transmission method, does not need a fiber grating method to lay a large number of sensor tools, and reduces the detection cost and has fussy detection steps.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, so that any modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention will still fall within the scope of the technical solution of the present invention.
Claims (10)
1. A method for detecting integrity of a bridge pile foundation based on a small offset scattered wave imaging method is characterized by comprising the following steps:
the method comprises the following steps: arranging a plurality of detectors at the top of the pile foundation;
step two: connecting the detector with an acquisition base station and an earthquake acquisition host through a large earthquake line, and forming a small offset scattered wave acquisition system by taking the position of a first earthquake source as a coordinate origin, the depth direction along the pile foundation as a Z direction and the line measuring direction as an X direction;
step three: setting a hammering device, connecting the hammering device with a signal trigger box, and setting parameters of the signal trigger box;
step four: hammering is carried out on the middle of the adjacent detectors through the hammering device, and hammering signals are recorded through the earthquake acquisition host;
step five: arranging and moving the detectors, and collecting hammering signals according to the fourth step;
step six: repeating the fifth step until the detector reaches the edge of the pile foundation, and completing hammering signal acquisition;
step seven: carrying out data processing on the collected hammering signal to obtain a longitudinal wave superposition speed model;
step eight: performing acoustic forward numerical simulation by combining a longitudinal wave superposition velocity model, obtaining Green function values of each point in a model space at different corresponding moments, and obtaining a forward extrapolation field;
step nine: performing wave field extrapolation of longitudinal waves by taking the detector as an original point to obtain a wave equation numerical solution of a limited bandwidth Green function of a wave detection point;
step ten: and performing cross-correlation imaging by using the forward extrapolation field and the backward extrapolation field of the longitudinal wave to obtain a final scattered wave offset imaging result.
2. The method for detecting the integrity of a bridge pile foundation based on the small offset scattered wave imaging method as claimed in claim 1, wherein in the first step: a plurality of installation positions with the same road spacing are outwards arranged in the center of the top end face of the pile foundation, and the detector is arranged in the installation positions; in the five steps: the distance of the detectors moving in an arrangement mode is the size of the distance between the adjacent detectors.
3. The method for detecting the integrity of the bridge pile foundation based on the small offset distance scattered wave imaging method as claimed in claim 2, wherein in the step one: the number of the detectors is six.
4. The method for detecting the integrity of the bridge pile foundation based on the small offset scattered wave imaging method of claim 3, wherein in the fourth step: hammering by the hammering device between the detector in the second pass and the detector in the second pass from the edge of the top end surface of the pile foundation to the center, wherein the hammering signal is recorded as x (t) 1 ) (ii) a Hammering the middle of the detector in the fourth pass and the detector in the fifth pass by the hammering device, wherein the hammering signal is recorded as x (t) 2 )；
In the fifth step: collecting hammering signals which are respectively x (t) according to the fourth step 3 )、x(t 4 )；
In the sixth step: repeating the fifth step, enabling the detector which is vertically positioned in the sixth step to reach the edge of the pile foundation, and completing the collection work of hammering signals, wherein the collected hammering signals are x (t) respectively 5 )…x(t m )。
5. The method for detecting the integrity of the bridge pile foundation based on the small offset scattered wave imaging method of claim 1, wherein in the third step: the parameters of the signal trigger box comprise sampling time t and sampling interval t
The sampling frequency is AHz.
6. The method for detecting the integrity of the bridge pile foundation based on the small offset scattered wave imaging method as claimed in claim 4, wherein in the seventh step:
A. and (3) performing channel processing, and inputting the observation system into a seismic record: x (t) 1 )…x(t m )；
B. Performing band-pass filtering processing on the seismic record to remove the noise signal collected in the seismic record;
C. separating longitudinal waves and transverse waves by polarization analysis to obtain seismic records of the longitudinal waves;
D. deconvolution processing is carried out on the longitudinal wave seismic record, and the time resolution of seismic waves is improved;
E. extracting a common midpoint gather (CMP);
F. performing dynamic correction to eliminate the influence of offset distance and form a two-way travel time with zero offset distance;
G. analyzing the velocity of each seismic record to obtain a velocity spectrum O of each seismic record 1 …O n ；
H. Stacking the seismic records, and combining the velocity spectrum to obtain a primary velocity model Q (v) p )。
7. The method for detecting the integrity of the bridge pile foundation based on the small offset distance scattered wave imaging method of claim 1, wherein in the step eight: forward external field U Z (x, z, t), wherein x, z are the positions of the points and t is the time;
A. to obtain a formal solution of the Green function, first the Helmholtz equation:
wherein
Is Laplace operator, G Z (r-r s ) Is a green function, r s For the location of the seismic source, r is the other location of the wavefield, δ (r-r) s ) Is a pulse signal, rs is the position of a seismic source, r is other positions of a wave field, S (W) is the frequency spectrum of a seismic source wavelet, w is the circumferential rate, and v (r) is the velocity;
B. left end plus zero factor [ v (r)] -2 -[v 0 (r)] -2 Here, the source of scattering, and then the term shifting process is performed:
C. let O be 1 (r)＝[v(r)] -2 -[v 0 (r)] -2 To obtain a classical L-S equation:
G Z (r,r s )＝G 0 (r,r s )+ω 2 ∫ V G 0 (r,r′)O 1 (r′)G Z (r′,r s )dr′；(3-3)；
G 0 (r,r s ) As a green function of the background wave field, omega 2 ∫ V G 0 (r,r′)O 1 (r′)G Z (r′,r s ) dr 'is a perturbation term, and r' is a position in the scatterer;
D. using background Green's function G in scatterers 0 (r,r s ) Equivalent overall Green's function G Z (r,r s ) Carry out Born approximation:
G Z (r,r s )≈G 0 (r,r s )+ω 2 ∫ V G 0 (r,r′)O 1 (r′)G 0 (r′,r s )dr′；(3-4)；
E. the scattered wavefield is then obtained:
wherein the content of the first and second substances,
as the normal derivative, x (t) m ) Representing a complex conjugate for the seismic record; curved surface where S' observation point is located, n s Is the outer normal direction of S';
F. the background perturbation field is:
G. the total inverse extrapolated field is:
U Z (x,z,t)＝U 0 +U 1 ；(3-7)。
8. the method for detecting the integrity of the bridge pile foundation based on the small offset scattered wave imaging method as claimed in claim 7, wherein in the ninth step:
A. to obtain a formal solution of the Green function, first the Helmholtz equation:
wherein
Is Laplace operator, G F (r-r R ) Is the green function, delta (r-r) R ) For a pulse signal, r R Is the position of the detector, r is the other positions of the wavefield, w is the circumferential ratio, v (r) is the velocity;
B. the left end is added with zero factor [ v (r)] -2 -[v 0 (r)] -2 Here, the source of scattering, and then the term shifting process is performed:
C. let O be 1 (r)＝[v 0 (r)] -2 -[v 0 (r)] -2 To obtain the classic L-S equation:
G F (r,r s )＝G 0 (r,r R )+ω 2 ∫ V G 0 (r,r′)O 1 (r′)G F (r′,r R )dr′；(4-3)；
G 0 (r,r R ) As a green function of the background wave field, omega 2 ∫ V G 0 (r,r′)O 1 (r′)G F (r′,r R ) dr' as perturbationThe term, r', is the location within the scatterer;
D. using background Green's function G in scatterers 0 (r,r R ) Equivalent overall Green function G F (r,r R ) Carry out Born approximation:
G F (r,r R )≈G 0 (r,r R )+ω 2 ∫ V G 0 (r,r′)O 1 (r′)G 0 (r′,r R )dr′；(4-4)；
E. the scattered wavefield is then obtained:
wherein the content of the first and second substances,
as the normal derivative, x (t) m ) Representing a complex conjugate for the seismic record; curved surface where S' observation point is located, n R Is the outer normal direction of S';
F. the background perturbation field is:
G. the total inverse extrapolated field is:
U F (x,z,t)＝U 0 +U 1 ；(4-7)。
9. the method for detecting integrity of bridge pile foundation based on small offset scattered wave imaging method according to claim 8, wherein in the step ten:
A. the forward direction is pushed outwards to form a field U Z (x, z, t) and the inverse extrapolation field U F (x, z, t) is substituted into the following equation:
I(x,z)＝∫dωH Z (x,z,w)H F (x,z,w)；(5-1)；
wherein w is the fillet frequency;
B. and obtaining a zero-time shift cross-correlation offset image field.
10. The method for detecting integrity of bridge pile foundation based on small offset scattered wave imaging method according to claim 1, wherein the hammering device is a manual hammer.
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