CN110703331A - Attenuation compensation reverse time migration implementation method based on constant Q viscous sound wave equation - Google Patents
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Abstract
The invention relates to an attenuation compensation reverse time migration implementation method based on a constant Q viscous sound wave equation, which comprises the following steps: adopting a decoupling constant Q viscous acoustic wave equation which takes Taylor series expansion as a strategy to process a variable fractional order problem as a forward model to carry out forward and backward continuation of a wave field; according to the absorption attenuation mechanism of sound waves in viscoelastic media and from the perspective of indirect compensation, a compensation operator is represented by the ratio of a pure frequency dispersion sound wave field to a viscous sound wave field, and is embedded into an excitation amplitude imaging condition to obtain an imaging condition of absolute stable compensation. Realizing stable attenuation compensation reverse time migration of the viscous sound wave by using new imaging conditions; the method is popularized to three-dimensional on the basis of a two-dimensional constant Q viscous acoustic wave equation, and reverse time migration of the three-dimensional constant Q viscous acoustic wave equation under the condition of stably compensated excitation amplitude imaging is achieved. The method can be widely applied to forward simulation, reverse time migration and attenuation compensation reverse time migration of the viscous sound wave in the two-dimensional/three-dimensional viscoelastic medium.
Description
Technical Field
The invention belongs to the technical field of geological exploration, and particularly relates to an attenuation compensation reverse time migration implementation method based on a normal Q viscous acoustic wave equation.
Background
The concept of reverse time migration was first proposed by three different groups (Baysal et al, 1983; McMechan, 1983; Whitmore, 1983). To date, reverse time migration has been considered to be the most accurate of the current seismic wave migration imaging methods, which can theoretically achieve energy homing for any type of wave group. Furthermore, the reverse time migration is based on two-way wave equation continuation, and thus there is no limitation of the imaging angle. With the rapid development of computer technology, reverse time migration has become an indispensable technical means in the field of migration imaging in recent years due to its unique imaging advantages in complex-structured areas. In actual seismic surveying, areas of strongly attenuating medium are often encountered, and since these areas are not fully elastic, seismic waves travel in the area with significant amplitude attenuation and phase changes reflected on the seismic record as amplitude attenuation and waveform distortion. If the data is used to directly perform reverse time migration, the migration result shows the characteristics of insufficient illumination in the attenuation region and below, low resolution, false in the in-phase axis, etc. To achieve good reverse time migration results in these regions, the viscosity of the medium must be compensated for.
Currently, absorption attenuation compensation methods can be basically classified into two main categories, the first category is seismic trace-based attenuation compensation which mainly includes unsteady inverse folding and inverse Q filtering. While this type of method is simple and efficient to operate, it essentially ignores the fact that attenuation of the seismic wave occurs in its propagation path. Li et al (2015) proposes a two-step inverse Q filter compensation strategy to perform attenuation compensation along both offset and propagation time directions, but this method assumes that seismic waves propagate at a small angle near the earth surface, and it is difficult to satisfy the complex practical situation. The second type of attenuation compensation method is pre-stack depth migration based on the viscous wave equation, which compensates for the effects of Q during seismic migration. This type of method implements Q-value compensation along the propagation path of the seismic wave, which has a higher compensation accuracy than the first type of method. The compensation method based on the fluctuation square equation further comprises a Q-compensated single-pass wave offset, a Q-compensated Gaussian beam offset and a Q-compensated reverse time offset, wherein the Q-compensated reverse time offset has the highest precision and is a current research hotspot.
One key technique for Q-compensating reverse time migration is to select an appropriate viscous wave equation to characterize the attenuation of the seismic wave. In the field of geophysical, a generalized standard linear body (SLS) model is widely used to describe the attenuation of seismic waves, but the factors controlling amplitude and phase in the viscous wave equation based on the SLS model are coupled and cannot correct for phase changes correctly while compensating for amplitude attenuation. Kjartansson (1979) proposes a constant Q model, namely, the attenuation model is well matched with an actual observation result on the assumption that a seismic quality factor Q does not change along with frequency, so that the attenuation model is widely used in the field of seismic exploration. Carcione et al (2002) and Carcione (2009) have derived viscous acoustic waves and viscoelastic wave equations describing the propagation of seismic waves in an attenuating medium based on an ordinary Q model, respectively. These equations all contain time-fractional derivatives, the history and the globality of which in the time direction increase the difficulty of numerical solution, and consume a large amount of memory. Zhu and Harris (2014) proposes a time domain ordinary Q viscous acoustic wave equation and a wave equation propagating in a viscoelastic medium in the same year, wherein the equation comprises a fractional Laplace operator instead of a time fractional derivative, and numerical calculation can be conveniently carried out by adopting fast Fourier transform. Meanwhile, the control amplitude term and the phase term in the fractional order Laplace operator viscous sound wave equation are decoupled, so that absorption attenuation compensation can be realized only by inverting the amplitude term and keeping the phase term unchanged. However, the fractional order in the fractional order laplacian viscous acoustic wave equation changes with the Q value, and the numerical solution is difficult. The solution is to simplify the method into a constant fractional order, and the most common method at present is to use an average value strategy, a Taylor expansion approximation strategy and the like. The former is simple in calculation, but a large simulation error is introduced under the condition that a Q model is relatively complex, and the propagation of seismic waves in a viscoelastic medium cannot be accurately described, so that the strategy is lower than a Taylor approximate expansion strategy in the aspect of migration imaging accuracy.
In the attenuation compensation process for implementing the viscous wave equation reverse time migration, the inverse of the wavefield attenuation is typically used to compensate for the absorbed energy and to correct for wavelet phase distortion due to velocity dispersion. Since the absorption takes the form of exponential decay, the direct compensation strategy amplifies the decayed wavefield exponentially, however, this will also amplify the high frequency noise in the seismic recording as well as the background noise, resulting in a numerically unstable compensation result. Therefore, solutions are continuously researched, such as the technical solutions disclosed in patent documents with application numbers CN110163830A and CN109977501A, the technical solution disclosed in patent documents with application numbers CN109977501A and CN109977501A, the technical solution disclosed in patent documents with application numbers CN109884394A and CN102230973A, the technical solution disclosed in patent documents with patent numbers CN102230973A and CN102230973A, the patent document with invention names "a three-dimensional step fourier viscous sound wave depth migration method", and the technical solution disclosed in patent documents with application numbers CN108919356A and CN108919356A, for another example, the geophysical prospecting computing technology is disclosed in non-patent documents including a "fractional order viscoelastic medium numerical simulation method based on a normal Q model" published in 2019, a "viscoelastic medium seismic forward modeling and reverse time migration based on Q decoupling" published in 2017 and 4, a "absorption compensation method based on a viscous acoustic wave equation" published in 2014, a "attenuation compensation method in viscoelastic acoustic wave equation reverse time migration imaging" published in 2018 and 6, and a "seismic wave attenuation and compensation method" published in 20156.
Summarizing the above solution, the main solution to the above technical problem is as follows: 1) a filter method. The method cannot avoid damage to high frequency, the selection of the cut-off frequency is uncertain, and the blind selection brings the problem of repeated calculation. 2) Stability factor method. Unlike low-pass filters which damage high-frequency information, the method only uses the ratio of the frequency dispersion wave field to the viscous wave field to represent the attenuation compensation operator, does not involve any energy increase, and therefore has good effect on inhibiting the numerical instability phenomenon of compensation. 3) And (4) an iterative method. In recent years, Least Squares Reverse Time Migration (LSRTM) and Full Waveform Inversion (FWI) techniques have been gaining increasing attention. The compensation can be realized by matching the observation records in the iterative process, the numerical instability is indirectly avoided, and the huge calculation amount of the numerical instability can not be borne by the hardware condition at the present stage.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method for realizing attenuation compensation reverse time migration based on a normal Q viscous sound wave equation, which solves the technical problems.
In order to achieve the above object, the present invention provides the following technical solutions:
an attenuation compensation reverse time migration implementation method based on a constant Q viscous sound wave equation comprises the following steps:
step 1) when a forward model of reverse time migration is selected, adopting a decoupling constant Q viscous acoustic wave equation for processing a variable fractional order problem by a Taylor series expansion strategy, using the decoupling constant Q viscous acoustic wave equation for continuation of a wave field, and recording wave field information in a viscous medium at a wave detection point;
step 2) recording the amplitude maximum value p of each space point of the viscous wave field in all sampling moments in the forward simulation process of the viscous sound wave equationvisAnd a moment t _ max corresponding to the maximum amplitude value, taking the sound wave field information in the viscous medium recorded by the wave detection point in the step 1) as a seismic source, performing wave field reverse continuation by adopting a constant Q viscous sound wave equation, and extracting the maximum amplitude value of the pure frequency dispersion sound wave field corresponding to the t _ max in the reverse transmission process
With amplitude maxima of the viscous acoustic wave field
The upper mark indicates that the reverse transmission seismic source is a viscous sound record;
step 3) attenuation compensation reverse time migration of the normal Q viscous sound wave is carried out by utilizing the excitation amplitude imaging condition of stable compensation;
and 4) popularizing the method to three dimensions on the basis of a two-dimensional constant Q viscous acoustic equation, obtaining a corresponding stable compensation method based on excitation amplitude imaging conditions, and realizing attenuation compensation reverse time migration of the three-dimensional constant Q viscous acoustic equation.
Preferably, in the step 1), the decoupling constant Q viscous acoustic wave equation that adopts the taylor series expansion strategy to process the variable fractional order problem includes the following steps:
step a), selecting a decoupling constant Q viscous acoustic wave equation which has higher simulation precision in a Q model complex region and processes a variable fractional order problem by a Taylor series expansion strategy as a forward equation;
and b) carrying out forward simulation on the given speed and Q model and selecting proper excitation parameters according to the forward modeling equation in the step a), and recording forward continuation viscous wave field information at a detection point.
Preferably, in the step a), the forward equation in the decoupling constant Q sticky acoustic wave equation for processing the fractional order problem by the taylor series expansion strategy is as follows:
wherein, p ═ p (x, t) represents a viscous acoustic wave field variable, x ═ x (z) is a two-dimensional cartesian rectangular coordinate system, and t is time(s);is the velocity (m/s), c0For the reference speed (m/s), gamma ≈ 1/(pi Q) is a fractional order coefficient; pi is the circumference ratio; q is a seismic quality factor; λ ═ ω (ω)d/ω0)2γ，ω0Is the angular frequency (rad/s), ω, corresponding to the reference frequencyd＝2πfd，ωdAngular frequency (rad/s) corresponding to the primary frequency, where fdThe dominant frequency (Hz) of the seismic source.
Wherein the content of the first and second substances,
is a two-dimensional Laplace operator, and epsilon is a smaller constant; in the equation
The two terms are mainly used for controlling the frequency dispersion,
the amplitude attenuation is mainly controlled. As Q approaches infinity, the equation will degenerate to the conventional second order acoustic wave equation.
Preferably, in the step b), forward modeling is performed on a given velocity and a Q model and selecting an appropriate excitation parameter, and forward extended viscous wave field information is recorded at a detection point, and the method includes the following steps:
step b1) setting a uniform speed and Q model according to the speed and Q value of the excitation point, performing forward modeling by using the model, and recording the wave field information of the direct wave at the wave detection point;
step b2) performing forward modeling according to the actual speed and the Q model, recording actual wave field information at the wave detection point, and subtracting the wave field information of the direct wave in the step b1) from the actual wave field information to obtain the wave field information without the direct wave.
Preferably, in the step 2), the viscous acoustic wave field information recorded by the wave detection point in the step 1) is used as a seismic source for reverse continuation, and the maximum amplitude value of the pure frequency dispersion acoustic wave field at the corresponding moment in the reverse transmission process is extracted according to t _ max
With amplitude maxima of the viscous acoustic wave field
The method specifically comprises the following steps:
step c) selecting proper smooth speed and a smooth Q model to carry out forward continuation of the wave field according to the normal Q viscous sound wave forward equation selected in the step a), and recording the maximum amplitude value p of each space point of the forward viscous sound wave field in all sampling momentsvisSimultaneously recording the corresponding time t _ max when the maximum amplitude value is obtained;
step d) taking the viscous sound wave field information recorded by the wave detection point in the step 1) as a seismic source, respectively performing reverse transmission according to a pure frequency dispersion sound wave equation and a viscous sound wave equation, and extracting the maximum amplitude value of the pure frequency dispersion sound wave field at the corresponding moment in the reverse transmission process according to t _ max in the step c)
With amplitude maxima of the viscous acoustic wave field
The superscript indicates that the source of retroactive seismic is a viscous acoustic recording.
Preferably, in step d), the wave field backward continuation is performed according to a pure dispersion equation, which is specifically in the form of:
preferably, in step 3), the excitation amplitude imaging condition for stable compensation is in the specific form:
wherein IC(x) The compensated imaging result is obtained; T-T _ max is the time corresponding to each spatial point when the maximum amplitude value is obtained, and the unit is second;
respectively representing the maximum amplitude value of each space point in the pure frequency dispersion wave field and the viscous sound wave field reversely transmitted by the wave detection point at all sampling moments, and the superscript of the maximum amplitude value indicates that the reverse seismic source is viscous sound wave record; p is a radical ofvisIs the maximum of the amplitude of each spatial point in the propagating viscous acoustic wavefield at all sampling instants,
expression finding
Maximum value of term, σ2Is a regularization factor used to avoid dividing the expression by 0, whose value can be empirically chosen by analyzing the degree of morbidity of the denominator.
Preferably, the performing attenuation compensation reverse time migration of the normal Q sticky acoustic wave by using the excitation amplitude imaging condition of the stable compensation in the step 3) specifically includes the following steps:
step e) according to waves in a viscoelastic mediumAttenuation mechanism, defining attenuation compensation operator
Sum-and-dispersion compensation operator
Step f) compensating the attenuation by an operatorSum frequency dispersion compensation operator
Embedding the image into an excitation amplitude imaging condition to obtain a stable compensated imaging condition;
step g) applying the corresponding wave field saved in the step 2) to the imaging condition in the step 3) to perform attenuation compensation reverse time migration of the normal Q viscous sound wave.
Preferably, in said step e), the attenuation compensation operator is defined according to the attenuation mechanism of the acoustic wave in the viscoelastic medium
Sum frequency dispersion compensation operatorThe method specifically comprises the following steps:
step e1) setting psid,uAnd phid,uFor the decoupled attenuation and dispersion operators on the wave propagation path, p (x, t) is the unattenuated acoustic record,
for recording viscous sound waves with attenuated detection points, Lu,dRepresenting the up and down travel paths, the compensation operator for the down wavefield is represented as:
wherein L isdIs shown belowLine propagation path, αdRepresenting the attenuation coefficient on the downstream propagation path. The compensation operator for the upgoing wavefield is:
wherein L isuFor the upstream propagation path, αuRepresenting the attenuation coefficient on the upstream propagation path.
As used herein
When the wave field of the detection point is propagated in a reverse time manner, the viscous sound wave record needs to be turned over along the time direction, and the wave field only containing dispersion continuation is physically equal to the phase correction process;
in said step f), compensating the amplitude attenuation by an operator
Sum frequency dispersion compensation operator
Embedding the image into the excitation amplitude imaging condition to obtain the stable compensated imaging condition. Wherein the excitation amplitude imaging conditions are:
where T-T _ max-argmax { a (x, T) }, the function argmax returns the time T at which each spatial point makes a maximum a, also called imaging time, in seconds, a being the amplitude of the wavefield variable; i (x) as a result of imaging, pSAnd pRRespectively representing the forward acoustic wavefield of the seismic source and the backward acoustic wavefield of the detector. The reflection coefficient for ideal attenuation compensation should be:
subjecting step e1)
And
substitution into IC(x) And adding a stabilizing factor to obtain a compensated offset result as follows:
whereinExpression finding
Maximum value of term, σ2Is a regularization factor used to avoid dividing the expression by 0, whose value can be empirically chosen by analyzing the degree of morbidity of the denominator.
Preferably, in the step 4), the method is popularized to three dimensions on the basis of a two-dimensional constant-Q viscous acoustic wave equation, and corresponding imaging conditions based on excitation amplitude are obtained,
wherein: the three-dimensional constant-Q viscous acoustic wave equation has the following form:
where p ═ p (x) denotes a three-dimensional viscous acoustic wave field, x ═ (x, y, z) is a three-dimensional cartesian coordinate system,
andis a three-dimensional laplacian operator. The excitation amplitude imaging conditions for three-dimensional improved stabilization compensation are of the form:
the invention has the beneficial effects that:
1) compared with the conventional linear body viscous wave equation, the absorption attenuation compensation reverse time offset expanded based on the decoupled normal Q viscous acoustic wave equation can realize the correction of a distortion phase while compensating energy, and has higher compensation precision;
2) when the fractional order Laplace viscous acoustic wave equation is solved based on the pseudo-ordinary method, the problem of a space wave number mixed domain operator is expanded through a Taylor series, a variable fractional order is converted into a constant fractional order for solving, numerical calculation is simple, simulation precision is high, and the method is more suitable for areas with severely changed Q values;
3) based on the idea of indirect compensation, the improved excitation amplitude imaging condition of stable compensation is adopted, and the method has better stability, noise resistance and energy fidelity compared with the traditional compensation method;
4) based on the two-dimensional constant Q viscous acoustic wave equation and the attenuation compensation imaging condition thereof, the method can be easily popularized to the three-dimensional situation, the actual three-dimensional seismic data is processed, and the migration imaging resolution is improved.
Drawings
FIG. 1 is a schematic diagram of forward modeling of a normal Q-viscoacoustic equation for a layered model in the present invention, wherein FIGS. 1(a), 1(b), and 1(c) are respectively a wave field snapshot of a mean value strategy, a Taylor expansion strategy, and a reference solution at 600 ms; fig. 1(d) is a comparison of single-pass observations at x ═ 1.5km, where the mean value strategy is represented by a black dashed line, the circles represent the taylor approximation expansion strategy, and the reference solution is a black solid line;
FIG. 2 is an observation record obtained by applying the constant Q viscous acoustic wave equation of the Taylor expansion strategy to Marmousi model forward modeling and using the Taylor series expansion strategy to process a variable fractional order problem;
FIG. 3 is a schematic diagram of the two-dimensional BP gas cloud model stable attenuation compensation of the present invention, and FIGS. 3(a) and 3(b) are velocity and Q models of the BP gas cloud model, respectively; FIG. 3(c) is a reference offset profile obtained using conventional acoustic wave reverse time offset with unattenuated acoustic recording; FIG. 3(d) is an uncompensated excursion profile obtained by a conventional acoustic reverse time excursion algorithm using attenuated viscous acoustic data; FIG. 3(e) is an imaging result using recording of attenuation and using a stable attenuation compensated reverse time migration algorithm;
FIG. 4 is a schematic diagram of horizontal position extraction of three offset traces for single-trace comparison and spectral analysis in the offset result of FIG. 3, wherein the solid black line is the reference trace, the dashed black line indicates the offset trace without Q compensation for the attenuation data, the circle corresponds to the result of stable absorption attenuation compensation reverse time offset, and FIG. 4(a) is the single-trace comparison at x ═ 1.0 km; fig. 4(b) is a single pass comparison at x-2.0 km; fig. 4(c) is a single pass comparison at x-3.0 km;
FIG. 5 is a test result for examining the noise immunity of the algorithm, wherein FIG. 5(a) is the result of the reverse time migration of sound wave of un-attenuated noisy data, and FIG. 5(b) is the result of the reverse time migration of the stability of attenuated data under noisy conditions;
FIGS. 6(a), (b), (c) are the results of three positions, 2.7km, 1.5km and 0.75km, respectively, along the inline, crossline and top view for three-dimensional phantom acoustic offset, viscous acoustic offset and attenuation compensation offset, respectively;
fig. 7(a) shows a single pass comparison of three offset profiles at x of 2.1km and y of 2.25km, and fig. 7(b) shows a single pass comparison of three offset profiles at x of 1.7km and y of 1.5 km.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the scope of protection of the present invention.
Embodiment 1, a method for implementing attenuation compensation reverse time offset based on a constant Q viscous acoustic wave equation in this embodiment includes: step 1) when a forward modeling of reverse time migration is selected, adopting a decoupling constant Q viscous acoustic wave equation which processes a variable fractional order problem by a Taylor series expansion strategy for extending a wave field, and recording acoustic wave field information in a viscous medium at a detection point, wherein the form of the wave field information is shown in a figure 1(d), and the viscous acoustic wave equation is a forward modeling equation; fig. 1 is a schematic diagram of forward modeling of a normal Q viscous acoustic wave equation for a layered model in the present invention, where the upper layer Q is 100, the lower layer Q is 20, and excitation points are located at 20 sampling points above a horizontal interface; FIGS. 1(a), 1(b), 1(c) are wavefield snapshots at 600ms for the mean strategy, Taylor expansion strategy, and reference solution, respectively; fig. 1(d) is a comparison of single-pass observation records at x ═ 1.5km, where the mean value strategy calculation result is a black dotted line, the taylor approximation expansion strategy calculation result is represented by a circle, the reference solution is a black solid line, and fig. 2 is an observation record obtained by forward modeling of the Marmousi model by using the taylor approximation expansion strategy. It can be observed from fig. 1(d) that the forward simulation precision of the taylor approximation expansion strategy is higher than that of the mean value strategy.
Step 2) recording the maximum amplitude value p of each point in the forward propagating viscous sound wave field in the forward simulating process by using the viscous sound wave equationvisAnd a time t _ max corresponding to the maximum amplitude value, performing wave field reverse continuation by adopting a normal Q viscous sound wave equation by taking the sound wave field information in the viscous medium recorded by the wave detection point in the step 1) as a seismic source, and extracting the maximum amplitude value of the pure frequency dispersion sound wave field at the corresponding time in the reverse transmission process according to the t _ max
With amplitude maxima of the viscous acoustic wave field
The upper mark indicates that the reverse seismic source is viscous sound wave recording;
step 3) deducing excitation amplitude imaging conditions of stable compensation, and performing attenuation compensation reverse time migration on the normal Q viscous sound waves;
and 4) popularizing the method to three dimensions on the basis of a two-dimensional constant Q viscous acoustic equation, obtaining a corresponding stable compensation method based on excitation amplitude imaging conditions, and realizing attenuation compensation reverse time migration of the three-dimensional constant Q viscous acoustic equation.
step a), selecting a decoupling constant Q viscous acoustic wave equation which has higher simulation precision in a Q model complex region and processes a variable fractional order problem by a Taylor series expansion strategy as a forward equation;
and b) carrying out forward simulation on the given speed and Q model and selecting proper excitation parameters according to the forward modeling equation in the step a), and recording forward continuation viscous sound wave field information at a detection point.
In the step a), the forward equation in the decoupling constant Q viscous acoustic wave equation for processing the variable fractional order problem by using a Taylor series expansion strategy is as follows:
wherein, p ═ p (x, t) represents a viscous acoustic wave field variable, x ═ x (z) is a two-dimensional cartesian rectangular coordinate system, and t is time(s);
is the velocity (m/s), c0For the reference speed (m/s), gamma ≈ 1/(pi Q) is a fractional order coefficient; pi is the circumference ratio; q is a seismic quality factor; λ ═ ω (ω)d/ω0)2γ，ω0Is the angular frequency (rad/s), ω, corresponding to the reference frequencyd＝2πfd，ωdAngular frequency (rad/s) corresponding to the primary frequency, where fdThe dominant frequency (Hz) of the seismic source.
Wherein the content of the first and second substances,
is two-dimensional LaplaceThe operator, ε, is a small constant, here taken as 1/16. In the equationThe two terms are mainly used for controlling the frequency dispersion,
the amplitude attenuation is mainly controlled. As Q approaches infinity, the equation will degenerate to the conventional second order acoustic wave equation.
In the step b), forward simulation is carried out on the given speed and Q model and the proper excitation parameters are selected, and forward extended viscous acoustic wave field information is recorded at a wave detection point, and the method comprises the following steps:
step b1) setting a uniform speed and Q model according to the speed and Q value of the excitation point, performing forward modeling by using the model, and recording the wave field information of the direct wave at the wave detection point;
step b2) performing forward modeling according to the actual speed and the Q model, recording actual wave field information at the wave detection point, and subtracting the wave field information of the direct wave in the step b1) from the actual wave field information to obtain the wave field information without the direct wave.
Fig. 3(a) shows a velocity model and fig. 3(b) shows a corresponding Q model, which includes a strongly attenuated gas reservoir region with a quality factor Q of 20. The model mesh size is 398 × 161 and the spatial sampling interval is 10 m. The total of 80 cannons, the interval of the shot points is 50m, 398 demodulator probes are distributed at intervals of 10m, and the depths of the shot points and the demodulator probes are 10 m. A raoke wavelet with a main frequency of 25Hz is used as a seismic source. The total recording time was 2.5s and the time sampling interval was 1.0 ms. A Perfectly Matched Layer (PML) with a thickness of 20 layers was used as an absorbing boundary condition. Fig. 3(c) is a reference offset profile obtained by conventional acoustic wave reverse time offset using unattenuated acoustic recording, fig. 3(d) is an uncompensated offset profile obtained by conventional acoustic wave reverse time offset algorithm using attenuated viscous acoustic recording, and fig. 3(e) is an imaging result obtained by stable attenuation compensation of reverse time offset using attenuated viscous acoustic recording. Comparing the three sub-graphs shows that: the amplitude of the offset profile 3(d) without absorption attenuation compensation is relatively weak, the imaging result of the lower part of the gas reservoir is quite poor due to the existence of the strong attenuation gas reservoir, the energy of the same phase axis and the resolution ratio of the same phase axis are obviously damaged, and most reflecting interfaces are blurred. The section diagram 3(e) after attenuation compensation well shows due amplitude information, faults under the gas layer present more effective information, and illumination is more balanced.
where p ═ p (x) denotes a three-dimensional viscous acoustic wave field, x ═ (x, y, z) is a three-dimensional cartesian coordinate system,
and
is a three-dimensional laplacian operator. The excitation amplitude imaging conditions for three-dimensional improved stabilization compensation are of the form:
embodiment 4, based on embodiment 1, in step 2), the information of the viscous acoustic wave field recorded at the wave point in step 1) is used as the seismic source to perform backward continuation, and the maximum amplitude value of the pure frequency dispersion acoustic wave field at the corresponding moment in the backward transmission process is extracted according to t _ max
And amplitude maxima of the viscous acoustic wavefield
Upper standard watchThe method for showing the reverse transmission seismic source as the viscous sound wave record specifically comprises the following steps:
step c) selecting proper smooth speed and a smooth Q model to carry out forward continuation of the wave field according to the normal Q viscous sound wave forward equation selected in the step a), and recording the maximum amplitude value p of each point in the viscous sound wave field in all sampling momentsvisSimultaneously recording the corresponding time t _ max when the maximum amplitude value is obtained;
step d) taking the viscous sound wave field information recorded by the wave detection point in the step 1) as a seismic source, respectively performing reverse transmission according to a pure frequency dispersion sound wave equation and a viscous sound wave equation, and extracting the maximum amplitude value of the pure frequency dispersion sound wave field at the corresponding moment in the reverse transmission process according to t _ max in the step a)
With amplitude maxima of the viscous acoustic wave field
In the step d), wave field backward continuation is performed according to a pure frequency dispersion acoustic wave equation, wherein the equation has the form:
the formula removes the influence of an amplitude term on the basis of decoupling a constant Q viscous sound wave equation, so that a pure frequency dispersion sound wave field and a viscous sound wave field obtained in wave field reverse continuation have only difference in amplitude, and can be used for describing an attenuation operator.
Example 5, based on example 1, in step 3), the excitation amplitude imaging conditions for stable compensation are specifically as follows:
wherein IC(x) The compensated imaging result is obtained; T-T _ max is the time corresponding to each spatial point when the maximum amplitude value is obtained, and the unit is second;
respectively representing the maximum amplitude value of each space point in the pure frequency dispersion acoustic wave field and the viscous sound wave field reversely transmitted by the wave detection point at all sampling moments, and the superscript of the maximum amplitude value indicates that a seismic source reversely transmitted is viscous sound wave record; p is a radical ofvisIs the maximum of the amplitude of each spatial point in the propagating viscous acoustic wavefield at all sampling instants,
expression finding
Maximum value of term, σ2The regularization factor used to avoid dividing 0 in the formula is empirically chosen by analyzing the degree of morbidity of the denominator, and is typically 5 × 10-6。
Deriving the excitation amplitude imaging condition of the stable compensation in the step 3), and specifically performing the attenuation compensation reverse time migration of the normal Q viscous sound wave comprises the following steps:
step e) defining an attenuation compensation operator according to the attenuation mechanism of the wave in the viscoelastic medium
Sum-and-dispersion compensation operator
Step f) compensating the attenuation by an operator
Sum frequency dispersion compensation operatorEmbedding the image into an excitation amplitude imaging condition to obtain a stable compensated imaging condition;
step g) applying the corresponding wave field saved in the step 2) to the imaging condition in the step 3) to perform attenuation compensation reverse time migration of the normal Q viscous sound wave.
In said step e), defining an attenuation compensation operator according to the attenuation mechanism of the acoustic wave in the viscoelastic medium
Sum frequency dispersion compensation operator
The method specifically comprises the following steps:
step e1) setting psid,uAnd phid,uFor the decoupled attenuation and dispersion operators on the wave propagation path, p (x, t) is the unattenuated acoustic record,
for recording viscous sound waves with attenuated detection points, Lu,dRepresenting the up and down travel paths, the compensation operator for the down wavefield is represented as:
wherein L isdDenotes the downstream propagation path, αdRepresenting the attenuation coefficient on the downstream propagation path. The compensation operator for the upgoing wavefield is:
wherein L isuFor the upstream propagation path, αuRepresenting the attenuation coefficient on the upstream propagation path.
As used herein
When the wave field of the detection point is propagated in a reverse time, the viscous sound wave record needs to be turned over along the time direction, and at the moment, only the wave field of frequency dispersion continuation is physically equal to the phase correction process;
in said step f), compensating the amplitude attenuation by an operator
Sum frequency dispersion compensation operator
Embedding the image into the excitation amplitude imaging condition to obtain the stable compensated imaging condition. Wherein the excitation amplitude imaging conditions are:
where T-T _ max-argmax { a (x, T) }, the function argmax returns the time T at which each spatial point makes a maximum a, also called imaging time, in seconds, a being the amplitude of the wavefield variable; i (x) as a result of imaging, pSAnd pRRepresenting the source forward wavefield and the receiver backward wavefield, respectively. The reflection coefficient for ideal attenuation compensation should be:
subjecting step e1)
And
substitution into IC(x) And adding a stabilizing factor to obtain a compensated offset result as follows:
wherein
Expression finding
Maximum value of term, σ2Is a regularization factor used to avoid dividing by 0 in the formula, the value of which can be analyzedThe degree of morbidity of the denominator is empirically selected and is typically 5X 10-6。
The single track information is further known. Three offset tracks are respectively extracted at the horizontal position x of 1.0km, x of 2.0km and x of 3.0km in the offset result of fig. 3 for single-track comparison, and the respective results are shown in fig. 4. Wherein the black solid line is the black dashed line of the reference trace, which represents the offset trace without Q compensation for the attenuation data, and the circle represents the result of the corresponding stable absorption attenuation compensation reverse time offset. It can be seen by comparison that the uncompensated single channel has weak energy compared with the reference channel, the waveform is widened, and the resolution is obviously reduced, especially the single channel passing through the air cloud region as shown in fig. 4(b), which will seriously reduce the reliability of the offset imaging result. In contrast, in the compensated single track, the attenuated amplitude and the distorted phase are better recovered, the coincidence degree with the reference track is higher, and the correct correction is carried out on the position of the underground reflecting layer.
The noise resistance of the algorithm is examined, and the test result is shown in fig. 5. Where fig. 5(a) is the result of the reverse time migration of sound waves without attenuating noisy data, and fig. 5(b) is the result of the reverse time migration of the stability of attenuated data in noisy conditions. Compared with the figure 5, the deviation results of the noise-containing and noise-free are highly consistent, and the algorithm also has stronger noise immunity, and can more accurately compensate the absorbed energy and correct the distorted phase under the noise-containing condition.
FIGS. 6(a), (b), (c) are results showing three positions along the inline, crossline and top views of acoustic wave excursion, viscous acoustic wave excursion and attenuation compensation excursion of the three-dimensional phantom at 2.7km, 1.5km and 0.75km, respectively. Through comparison, the stable algorithm is suitable for three-dimensional conditions, and energy attenuation of a deviation result caused by incomplete elasticity of a stratum is well compensated; meanwhile, through attenuation compensation, the imaging details at the depth of 0.75km are more finely depicted than the uncompensated result.
FIG. 7 is a diagram of two offset traces extracted from the offset result of FIG. 6 for single-trace comparison, in which the solid black line is the reference trace, the dashed black line represents the offset trace without Q compensation for the attenuation data, and the circle represents the result of the corresponding stable absorption-attenuation-compensated reverse time offset. Fig. 7(a) shows a single pass comparison of three offset profiles at x of 2.1km and y of 2.25km, and fig. 7(b) shows a single pass comparison of three offset profiles at x of 1.7km and y of 1.5 km. It can be observed that in the three-dimensional case, the effect of compensation is equally significant.
The invention has the beneficial effects that:
1) compared with the conventional linear body equation, the absorption attenuation compensation reverse time offset expanded based on the decoupled constant Q viscous sound wave equation can realize the correction of a distortion phase while compensating energy, and has higher compensation precision;
2) when the fractional order viscous sound wave equation is solved based on the pseudo-ordinary method, the problem of the spatial wave number mixed domain operator is expanded through Taylor series, the variable fractional order equation is converted into the constant fractional order equation to be solved, the numerical calculation is simple, the simulation precision is high, and the method is more suitable for the area with the change of the Q value;
3) based on the idea of indirect compensation, the improved excitation amplitude imaging condition of stable compensation is adopted, and the method has better stability, noise resistance and energy fidelity compared with the traditional compensation method;
4) based on the two-dimensional constant Q viscous acoustic wave equation and the attenuation compensation imaging condition thereof, the method can be easily popularized to the three-dimensional situation, the actual three-dimensional seismic data is processed, and the migration imaging resolution is improved.
The above-mentioned embodiments only express the embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. An attenuation compensation reverse time migration implementation method based on a constant Q viscous sound wave equation is characterized by comprising the following steps:
step 1) when a forward model of reverse time migration is selected, adopting a decoupling constant Q viscous acoustic wave equation for processing a variable fractional order problem by a Taylor series expansion strategy, using the decoupling constant Q viscous acoustic wave equation for wave field continuation, and recording acoustic wave field information in a viscous medium at a wave detection point;
step 2) recording the maximum amplitude value p of each space point of the viscous acoustic wave field in all sampling moments in the forward simulation process of the viscous acoustic wave equationvisAnd a moment t _ max corresponding to the maximum amplitude value, taking wave field information in the viscous medium recorded by the wave detection point in the step 1) as a seismic source, performing wave field reverse continuation by adopting a constant Q viscous sound wave equation, and extracting the maximum amplitude value of the pure frequency dispersion sound wave field corresponding to the t _ max in the backward transmission process
With amplitude maxima of the viscous acoustic wave field
Wherein the superscript indicates that the seismic source used for the reverse transmission is a viscous sound wave record;
step 3) attenuation compensation reverse time migration of the normal Q viscous sound wave is carried out by utilizing the excitation amplitude imaging condition of stable compensation;
and 4) popularizing the method to three dimensions on the basis of a two-dimensional constant Q viscous acoustic equation, obtaining a corresponding stable compensation method based on excitation amplitude imaging conditions, and realizing attenuation compensation reverse time migration of the three-dimensional constant Q viscous acoustic equation.
2. The method for realizing attenuation compensation reverse time migration based on the constant Q viscous sound wave equation is characterized in that,
in the step 1), the decoupling constant-Q viscous acoustic wave equation for processing the variable fractional order problem by using the Taylor series expansion strategy comprises the following steps:
step a), selecting a decoupling constant Q viscous acoustic wave equation which has higher simulation precision in a Q model complex region and processes a variable fractional order problem by a Taylor series expansion strategy as a forward equation;
and b) carrying out forward simulation on the given speed and Q model and selecting proper excitation parameters according to the forward modeling equation in the step a), and recording forward continuation viscous sound wave field information at a detection point.
3. The method for realizing attenuation compensation reverse time migration based on the ordinary Q viscous acoustic wave equation in the step a), wherein the forward equation in the decoupled ordinary Q viscous acoustic wave equation for processing the variable fractional order problem by the Taylor series expansion strategy is as follows:
wherein, p ═ p (x, t) represents a viscous acoustic wave field variable, x ═ x (z) is a two-dimensional cartesian rectangular coordinate system, and t is time(s);
is the velocity (m/s), c0For the reference speed (m/s), gamma ≈ 1/(pi Q) is a fractional order coefficient; pi is the circumference ratio; q is a seismic quality factor; λ ═ ω (ω)d/ω0)2γ，ω0Is the angular frequency (rad/s), ω, corresponding to the reference frequencyd＝2πfd，ωdAngular frequency (rad/s) corresponding to the primary frequency, where fdIs the dominant frequency (Hz) of the seismic source,
wherein the content of the first and second substances,
is a two-dimensional Laplace operator, and epsilon is a constant; in the equation
The two terms are mainly used for controlling the frequency dispersion,
mainly controlling amplitude attenuation; as Q approaches infinity, the equation will degenerate to the conventional second order acoustic wave equation.
4. The method for realizing attenuation compensation reverse time migration based on the constant-Q viscous sound wave equation in the step b), wherein forward modeling is performed on the given velocity, Q model and the selection of the proper excitation parameters, and forward continuation viscous sound wave field information is recorded at the detection point, and the method comprises the following steps:
step b1) setting a uniform speed and Q model according to the speed and Q value of the excitation point, performing forward modeling by using the model, and recording the wave field information of the direct wave at the wave detection point;
step b2) carrying out forward modeling according to the actual speed model and the Q model, recording actual wave field information at the wave detection point, and subtracting the wave field information of the direct wave in the step b1) from the actual wave field information to obtain the wave field information without the direct wave.
5. The method for realizing attenuation compensation reverse time migration based on the constant Q viscous sound wave equation according to claim 2,
in the step 2), wave field information in the viscous medium recorded by the wave detection point in the step 1) is used as a seismic source, a constant Q viscous sound wave equation is adopted to perform wave field backward continuation, and the maximum amplitude value of the pure frequency dispersion sound wave field corresponding to t _ max in the backward transmission process is extracted
With amplitude maxima of the viscous acoustic wave field
Wherein the superscript indicates that the seismic source used for the back transmission is a viscous sound wave record, and the method specifically comprises the following steps:
step c) selecting proper smooth speed and smooth Q model to carry out forward continuation of the wave field according to the normal Q viscous sound wave forward equation selected in the step a), and recording the forward viscous sound waveAmplitude maximum p of each spatial point of the wave field in all sampling instantsvisSimultaneously recording the corresponding time t _ max when the maximum amplitude value is obtained;
step d) taking the viscous sound wave field information recorded by the wave detection point in the step 1) as a seismic source, respectively performing reverse transmission according to a pure frequency dispersion sound wave equation and a viscous sound wave equation, and extracting the maximum amplitude value of the corresponding pure frequency dispersion sound wave field according to t _ max in the step c) in the reverse transmission process
With amplitude maxima of the viscous acoustic wave field
6. The method for realizing attenuation compensation reverse time migration based on the constant Q viscous sound wave equation according to claim 5,
in the step d), wave field backward continuation is performed according to a pure frequency dispersion acoustic wave equation, wherein the equation is specifically formed as follows:
7. the method for realizing attenuation compensation reverse time migration based on the constant Q viscous sound wave equation is characterized in that,
in the step 3), the excitation amplitude imaging condition of the stable compensation is in a specific form:
wherein IC(x) The compensated imaging result is obtained; T-T _ max is the time corresponding to each spatial point when the maximum amplitude value is obtained, and the unit is second;respectively representing the maximum amplitude value of each space point in the pure frequency dispersion acoustic wave field and the viscous acoustic wave field reversely transmitted by the wave detection point at all sampling moments, wherein the upper mark represents that the reversely transmitted seismic source is the viscous acoustic wave record; p is a radical ofvisIs the maximum of the amplitude of each spatial point in the propagating viscous acoustic wavefield at all sampling instants,
expression finding
Maximum value of term, σ2Is a regularization factor used to avoid dividing 0 in the formula, the value of which is empirically chosen by analyzing the degree of morbidity of the denominator.
8. The method for realizing attenuation compensation reverse time migration based on the constant Q viscous sound wave equation according to claim 7,
the step 3) of performing attenuation compensation reverse time migration of the normal Q viscous sound wave by using the stable compensation excitation amplitude imaging condition specifically comprises the following steps:
step e) defining an attenuation compensation operator according to the attenuation mechanism of the wave in the viscoelastic medium
Sum frequency dispersion compensation operator
Step f) compensating the attenuation by an operator
Sum frequency dispersion compensation operator
Embedding the image into an excitation amplitude imaging condition to obtain a stable compensated imaging condition;
step g) applying the corresponding wave field extracted in the step 2) to the imaging condition in the step 3) to perform attenuation compensation reverse time migration of the normal Q viscous sound wave.
9. The method for realizing attenuation compensation reverse time migration based on the constant Q viscous sound wave equation according to claim 8,
in said step e), defining an attenuation compensation operator according to the attenuation mechanism of the acoustic wave in the viscoelastic medium
Sum frequency dispersion compensation operator
The method specifically comprises the following steps:
step e1) setting psid,uAnd phid,uFor the decoupled attenuation and dispersion operators on the acoustic propagation path, p (x, t) is the unattenuated acoustic record,
recording for a viscous acoustic wave having an attenuated detection point, wherein Lu,dRepresenting the up and down travel paths, the compensation operator for the down wavefield is represented as:
wherein L isdDenotes the downstream propagation path, αdRepresenting the attenuation coefficient on the downstream propagation path. The compensation operator for the upgoing wavefield is:
wherein L isuFor the upstream propagation path, αuRepresenting the attenuation coefficient on the upstream propagation path;
in said step f), compensating the amplitude attenuation by an operator
Sum frequency dispersion compensation operator
Embedding the image into the excitation amplitude imaging condition to obtain the stable compensated imaging condition. Wherein the excitation amplitude imaging conditions are:
where T-T _ max-argmax { a (x, T) }, the function argmax returns the time T at which each spatial point makes a maximum a, also called imaging time, in seconds, a being the amplitude of the wavefield variable; i (x) as a result of imaging, pSAnd pRRespectively representing the forward acoustic wavefield of the seismic source and the backward acoustic wavefield of the detector. The reflection coefficient for ideal attenuation compensation should be:
subjecting step e1)
And
substitution into IC(x) And adding a stabilizing factor to obtain a compensated offset result as follows:
wherein
Expression finding
Maximum value of term, σ2Is a regularization factor used to avoid dividing the expression by 0, whose value can be empirically chosen by analyzing the degree of morbidity of the denominator.
10. The method for realizing attenuation compensation reverse time migration based on the constant Q viscous sound wave equation is characterized in that,
in the step 4), the method is popularized to three dimensions on the basis of a two-dimensional constant Q viscous sound wave equation, and corresponding imaging conditions based on excitation amplitude are obtained,
wherein: the three-dimensional constant-Q viscous acoustic wave equation has the following form:
where p ═ p (x) denotes a three-dimensional viscous acoustic wave field, x ═ (x, y, z) is a three-dimensional cartesian coordinate system,
and
is a three-dimensional laplacian operator. The excitation amplitude imaging conditions for three-dimensional improved stabilization compensation are of the form:
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