CN112711918A - Air bubble size distribution inversion method based on Gaussian function fitting - Google Patents

Air bubble size distribution inversion method based on Gaussian function fitting Download PDF

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CN112711918A
CN112711918A CN202011464262.5A CN202011464262A CN112711918A CN 112711918 A CN112711918 A CN 112711918A CN 202011464262 A CN202011464262 A CN 202011464262A CN 112711918 A CN112711918 A CN 112711918A
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size distribution
bubble
coefficient
gaussian function
inversion
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CN112711918B (en
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郑广赢
徐传秀
邵游
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715th Research Institute of CSIC
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Abstract

The invention provides a Gaussian function fitting-based bubble size distribution inversion method. And then establishing a cost function required by inversion by combining with the equivalent density fluid approximate model corrected by bubble vibration as a forward model, and optimizing by utilizing a mixed optimization algorithm DEPSO to obtain a corrected Gaussian function coefficient to be inverted so as to obtain the size distribution of bubbles in the gas-containing marine sediments. The method considers the existence form of the size distribution of the bubbles in the sediment, can reduce the number of parameters to be inverted to a certain degree, can realize inversion of the size distribution of the bubbles by only utilizing attenuation information, and has good coincidence between the attenuation data fitted by an inversion result and the measured attenuation data. The method is an innovative method applied in the field of submarine shallow gas exploration and identification.

Description

Air bubble size distribution inversion method based on Gaussian function fitting
Technical Field
The invention belongs to the technical field of marine acoustics and seabed shallow gas exploration and identification, and particularly relates to a gas bubble size distribution inversion method based on Gaussian function fitting.
Background
In modern engineering construction of submarine tunnels, cross-sea bridges and the like, unnecessary engineering accidents are often caused by negligence of distribution of shallow gas in submarine sediments. The sediments in the domestic long triangle and Hangzhou bay areas have a large amount of shallow formation gas distribution, and the dynamic balance of factors such as internal sediments, fluid, pore water, an upper coating, gas, temperature, pressure and the like is very weak, so that accident disasters are more and more serious.
For engineering applications, in addition to knowing the geographical location of the airborne deposits, more information needs to be known: the content of gas and the size distribution of the bubbles. For example, meteorologists need to estimate how much the ocean source contributes to atmospheric methane by the content of gas in the sediment; the sediment pore pressure and sediment strength are sensitive to the bubble content and size distribution, and knowledge of these parameters allows the oil exploration industry to more reliably locate offshore structures and avoid blowouts during drilling operations. In addition, the acoustic properties of gas bearing sediments are sensitive to bubble content and bubble size distribution, making this information important for shallow sea sound fields. The acoustic inversion technique for bubbles in marine sediments is to infer the content of bubbles and the distribution of bubble sizes from the measured compressional wave acoustic properties by corresponding acoustic theory. Since the bubble sizes in the natural marine sediment medium often show a complex distribution, a gaussian distribution, a rayleigh distribution, and the like. Generally, the attenuation coefficient of the gas-containing sediment is measured in a frequency band corresponding to the size distribution of the bubbles, the result of the attenuation coefficient often presents a plurality of obvious peak values, and the number of fitted parameters can be reduced to a certain extent by considering that the corrected Gaussian function is used for fitting the size distribution of the bubbles.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a bubble size distribution inversion method based on Gaussian function fitting.
The purpose of the invention is achieved by the following technical scheme: a bubble size distribution inversion method based on Gaussian function fitting comprises the following steps: firstly, aiming at the attenuation coefficient peak value of gas-containing sediments observed in experiments, representing the size distribution function of bubbles by using a modified Gaussian function, then setting a cost function as the square sum of the simulated attenuation coefficient and the measured attenuation coefficient error, and inverting the modified Gaussian function coefficient by using an optimization algorithm; and finally fitting the size distribution of the bubbles by using the Gaussian function coefficient obtained by inversion. The method considers the existence form of the size distribution of the bubbles in the sediment, can reduce the number of parameters to be inverted to a certain degree, can realize inversion of the size distribution of the bubbles by only utilizing attenuation information, and has good coincidence between the attenuation data fitted by an inversion result and the measured attenuation data. The method is an innovative method applied in the field of submarine shallow gas exploration and identification.
Further, the method specifically comprises the following steps:
(1) constructing the bubble size distribution of the model input, wherein the first term represents the attenuation coefficient of the resonance peak of the fitting bubble realized by using a plurality of modified Gaussian distributions, and the second term adjusts the attenuation coefficient of the non-resonance peak by using a plurality of linear functions, in the initially constructed bubble size distribution, the parameter ai3Other parameters are randomly generated corresponding to the bubble radius of the attenuation peak value;
Figure BDA0002833582410000021
(a) distribution of bubble radius size, a being the variation of bubble radius, Ni、ai1、ai2、ai3For the coefficient of the Gaussian function to be solved, kj、bjIs the linear function coefficient to be solved;
(2) setting initial model input environment parameters:
(3) substituting the equivalent density fluid approximate model corrected by bubble vibration to calculate the attenuation coefficient of the gas-containing marine sediment;
Figure BDA0002833582410000022
Figure BDA0002833582410000023
Figure BDA0002833582410000024
ρefffor deposit equivalent fluid density, KeffFor the equivalent bulk modulus of the deposit,
Figure BDA0002833582410000025
ω is the angular frequency, b (a) is the damping coefficient for the bubble size vibration, i is the imaginary unit, ω is the equivalent fluid density for bubble vibration correction0Is the bubble resonance frequency, beta is the sediment porosity;
(4) calculating an objective function of an inversion set
Figure BDA0002833582410000026
Wherein
Figure BDA0002833582410000027
As a measure of the attenuation coefficient of the sound wave at different frequencies,
Figure BDA0002833582410000028
predicting a value for the forward model at the corresponding frequency;
(5) repeating steps (1) - (4) using a two-stage hybrid optimization algorithm (DEPSO: differential evolution algorithm and particle swarm optimization).
Further, the model input environment parameters include: physical parameters of the sediment: particle size, particle density, particle bulk modulus, pore water density, pore water bulk modulus, pore water viscosity coefficient, porosity, permeability, tortuosity; gas physical parameters: gas density, static pressure, thermal diffusivity of the gas, surface tension, specific heat ratio.
The invention has the beneficial effects that: according to the invention, the corrected Gaussian function fitted bubble size distribution is used, compared with the traditional bubble inversion method, the possible distribution in nature is considered, the number of the parameters to be inverted is reduced to a certain extent, and the attenuation coefficient fitted by utilizing the inverted bubble size distribution is well matched with the measured attenuation coefficient.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
FIG. 2 is a graph showing the comparison of observed attenuation coefficients to model fitted attenuation coefficients.
FIG. 3 is a schematic diagram of the optimal bubble size distribution obtained by model fitting.
Detailed Description
The invention will be described in detail below with reference to the following drawings:
the invention discloses a Gaussian function fitting-based bubble size distribution inversion method, which comprises the following steps of: and fitting the unknown bubble size distribution function in the marine sediments by using the corrected Gaussian function, and solving the coefficient of the corrected Gaussian function by using an optimization algorithm to invert the bubble size distribution in the marine sediments. The method specifically comprises the following steps: firstly, aiming at the attenuation coefficient peak value of the gas-containing sediment observed in the experiment, the size distribution function of the bubbles is expressed by a modified Gaussian function. And then setting the cost function as the square sum of the simulated attenuation coefficient and the measured attenuation coefficient error, and inverting the corrected Gaussian function coefficient by using an optimization algorithm. And finally fitting the size distribution of the bubbles by using the Gaussian function coefficient obtained by inversion. The method can accurately invert the size distribution of the bubbles under the condition that the acoustic velocity and the attenuation information of the gas-containing sediments are not completely known, and the fitted attenuation coefficient is well matched with the experimentally measured attenuation coefficient by taking the inversion only using the attenuation coefficient as an example.
(1) Constructing the bubble size distribution of the model input, wherein the first term represents the attenuation coefficient of fitting the bubble formant with a plurality of modified Gaussian distributions, and the second term adjusts the non-formant with a plurality of linear functionsThe attenuation coefficient of (2). In the initially constructed bubble size distribution, the parameter ai3Other parameters were randomly generated corresponding to the bubble radius of the decay peak.
Figure BDA0002833582410000031
(a) distribution of bubble radius size, a being the variation of bubble radius, Ni、ai1、ai2、ai3For the coefficient of the Gaussian function to be solved, kj、bjIs the linear function coefficient to be solved;
(2) setting initial model input environment parameters: physical parameters of the sediment: particle size, particle density, particle bulk modulus, pore water density, pore water bulk modulus, pore water viscosity coefficient, porosity, permeability, tortuosity, and the like; gas physical parameters: gas density, static pressure, thermal diffusivity of the gas, surface tension, specific heat ratio, and the like.
(3) Substituting the equivalent density fluid approximate model corrected by bubble vibration to calculate the attenuation coefficient of the aerated marine sediment.
Figure BDA0002833582410000032
Figure BDA0002833582410000041
Figure BDA0002833582410000042
ρeffFor deposit equivalent fluid density, KeffFor the equivalent bulk modulus of the deposit,
Figure BDA0002833582410000043
for the equivalent fluid density of bubble vibration correction, ω is the angular frequency, b (a) is the corresponding bubble sizeDamping coefficient of vibration, i being imaginary unit, ω0Is the bubble resonance frequency, beta is the sediment porosity;
(4) calculating an objective function of an inversion set
Figure BDA0002833582410000044
Wherein
Figure BDA0002833582410000045
As a measure of the attenuation coefficient of the sound wave at different frequencies,
Figure BDA0002833582410000046
and predicting values for the forward model at the corresponding frequency.
(5) Repeating steps (1) - (4) using a two-stage hybrid optimization algorithm (DEPSO: differential evolution algorithm and particle swarm optimization).
Fig. 1 is a diagram illustrating inversion of bubble size distribution by an inversion method for fitting bubble size distribution based on a modified gaussian function, and comparison of an attenuation coefficient obtained by fitting with an attenuation coefficient predicted by a model. In the figure, the solid line represents the measured attenuation coefficient, and the dotted line represents the attenuation coefficient predicted by the model. 4 attenuation peaks caused by bubble resonance can be obviously observed from the attenuation data of 500-3000Hz, the inversion method can accurately fit the four peaks A-D in the attenuation curve, and the attenuation of 500-3000Hz frequency is consistent with the measured attenuation data.
Fig. 2 is the optimal bubble size distribution obtained by model fitting, and it can be clearly seen that the bubble size distribution has 3 peaks of 1.236mm, 1.614mm and 2.025mm, and the peak of 3.62mm is not obvious, which corresponds to the smaller amplitude of the attenuation coefficient peak a.
Fig. 3 is a bubble size distribution inversion flow chart, and the whole inversion processing process is described in detail in the "implementation method".
The frequencies of the four formants A-D and their corresponding attenuation coefficients are given in Table 1. The attenuation of the formant A reaches 109dB/m at 900Hz, the attenuation of the formant B reaches 296dB/m at 1600Hz, the attenuation of the formant C reaches 365dB/m at 2000Hz, and the attenuation of the formant D reaches 476dB/m at 2600 Hz. The bubble radii predicted by the corresponding decay peak model were 3.62mm, 2.025mm, 1.614mm, and 1.236mm, respectively.
TABLE 1 model prediction of observed formants
Figure BDA0002833582410000047
It should be understood that equivalent substitutions and changes to the technical solution and the inventive concept of the present invention should be made by those skilled in the art to the protection scope of the appended claims.

Claims (3)

1. A bubble size distribution inversion method based on Gaussian function fitting is characterized by comprising the following steps: the method comprises the following steps: firstly, aiming at the attenuation coefficient peak value of gas-containing sediments observed in experiments, representing the size distribution function of bubbles by using a modified Gaussian function, then setting a cost function as the square sum of the simulated attenuation coefficient and the measured attenuation coefficient error, and inverting the modified Gaussian function coefficient by using an optimization algorithm; and finally fitting the size distribution of the bubbles by using the Gaussian function coefficient obtained by inversion.
2. The bubble size distribution inversion method based on gaussian function fitting according to claim 1, wherein: the method specifically comprises the following steps:
(1) constructing the bubble size distribution of the model input, wherein the first term represents the attenuation coefficient of the resonance peak of the fitting bubble realized by using a plurality of modified Gaussian distributions, and the second term adjusts the attenuation coefficient of the non-resonance peak by using a plurality of linear functions, in the initially constructed bubble size distribution, the parameter ai3Other parameters are randomly generated corresponding to the bubble radius of the attenuation peak value;
Figure FDA0002833582400000011
(a) distribution of bubble radius size, a being the variation of bubble radius, Ni、ai1、ai2、ai3For the coefficient of the Gaussian function to be solved, kj、bjIs the linear function coefficient to be solved;
(2) setting initial model input environment parameters:
(3) substituting the equivalent density fluid approximate model corrected by bubble vibration to calculate the attenuation coefficient of the gas-containing marine sediment;
Figure FDA0002833582400000012
Figure FDA0002833582400000013
Figure FDA0002833582400000014
ρefffor deposit equivalent fluid density, KeffFor the equivalent bulk modulus of the deposit,
Figure FDA0002833582400000015
ω is the angular frequency, b (a) is the damping coefficient for the bubble size vibration, i is the imaginary unit, ω is the equivalent fluid density for bubble vibration correction0Is the bubble resonance frequency, beta is the sediment porosity;
(4) calculating an objective function of an inversion set
Figure FDA0002833582400000016
Wherein
Figure FDA0002833582400000017
As a measure of the attenuation coefficient of the sound wave at different frequencies,
Figure FDA0002833582400000018
predicting a value for the forward model at the corresponding frequency;
(5) repeating steps (1) - (4) using a two-stage hybrid optimization algorithm.
3. The bubble size distribution inversion method based on gaussian function fitting according to claim 2, wherein: the model input environment parameters comprise: physical parameters of the sediment: particle size, particle density, particle bulk modulus, pore water density, pore water bulk modulus, pore water viscosity coefficient, porosity, permeability, tortuosity; gas physical parameters: gas density, static pressure, thermal diffusivity of the gas, surface tension, specific heat ratio.
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Citations (4)

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Publication number Priority date Publication date Assignee Title
US5784160A (en) * 1995-10-10 1998-07-21 Tsi Corporation Non-contact interferometric sizing of stochastic particles
WO2015094307A1 (en) * 2013-12-19 2015-06-25 Halliburton Energy Services, Inc. Pore size classification in subterranean formations based on nuclear magnetic resonance (nmr) relaxation distributions
CN110530765A (en) * 2019-09-26 2019-12-03 哈尔滨工程大学 Underwater bubble group's size distribution parameter inversion method based on measuring non-linear parameters
CN110648342A (en) * 2019-09-30 2020-01-03 福州大学 Foam infrared image segmentation method based on NSST significance detection and image segmentation

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5784160A (en) * 1995-10-10 1998-07-21 Tsi Corporation Non-contact interferometric sizing of stochastic particles
WO2015094307A1 (en) * 2013-12-19 2015-06-25 Halliburton Energy Services, Inc. Pore size classification in subterranean formations based on nuclear magnetic resonance (nmr) relaxation distributions
CN110530765A (en) * 2019-09-26 2019-12-03 哈尔滨工程大学 Underwater bubble group's size distribution parameter inversion method based on measuring non-linear parameters
CN110648342A (en) * 2019-09-30 2020-01-03 福州大学 Foam infrared image segmentation method based on NSST significance detection and image segmentation

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
黎章龙;屈科;张薇;何树斌;: "水中气泡分布的共振估计法的误差分析及修正", 海洋技术学报, no. 06 *

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