CN112711918B - Bubble size distribution inversion method based on Gaussian function fitting - Google Patents
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Abstract
The invention provides a bubble size distribution inversion method based on Gaussian function fitting. And then, establishing a cost function required by inversion by combining an equivalent density fluid approximate model corrected by bubble vibration as a forward model, and optimizing by using a hybrid optimization algorithm DEPSO to obtain a corrected Gaussian function coefficient to be inverted, thereby obtaining the bubble size distribution in the gas-containing marine sediment. According to the method, the existence form of the bubble size distribution in the sediment is considered, the number of parameters to be inverted can be reduced to a certain extent, inversion of the bubble size distribution can be realized by using only attenuation information, and the attenuation data fitted by the inversion result are well matched with the measured attenuation data. The method is an innovative method applied to the field of submarine shallow gas exploration and identification.
Description
Technical Field
The invention belongs to the technical field of marine acoustics and submarine shallow gas exploration and identification, and particularly relates to a 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 neglecting the distribution of shallow air in submarine sediments. The sediments in the domestic long triangle and Hangzhou Bay areas have a large amount of shallow stratum gas distribution, and the dynamic balance of the internal sediments, fluid, pore water, an upper coating layer, gas, temperature, pressure and other factors is very fragile, so that accident disasters are more and more serious.
For engineering applications, in addition to knowing the geographical location of the gas-bearing deposit, more information is needed: the gas content and the size distribution of the bubbles. For example, a meteorological practitioner needs to estimate how much a marine source contributes to atmospheric methane by the content of gas in the sediment; sediment pore pressure and sediment strength are sensitive to 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. Furthermore, the acoustic properties of the gas-bearing deposits are very sensitive to the bubble content and bubble size distribution, making this information important for shallow sea acoustic fields. The acoustic inversion technique of the relevant bubbles in the marine sediments is to infer the content of the bubbles and the distribution of the bubble sizes from the measured acoustic characteristics of the compressional waves by the corresponding acoustic theory. Since the size of bubbles inside the marine sediment medium in nature often presents a complex distribution, it often presents gaussian distribution, rayleigh distribution, etc. In general, 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 shows a few obvious peaks, and the number of parameters of fitting can be reduced to a certain extent by considering the fitting of the size distribution of the bubbles by using a modified Gaussian function.
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, wherein the corrected Gaussian function is used for fitting the bubble size distribution to be inverted in marine sediments, and an optimization algorithm is used for optimizing to obtain corrected Gaussian function coefficients, so that the bubble size distribution to be inverted is obtained.
The invention aims at being completed by the following technical scheme: a bubble size distribution inversion method based on Gaussian function fitting comprises the following steps: firstly, aiming at an attenuation coefficient peak value of an air-bearing sediment observed through experiments, using a modified Gaussian function to represent a size distribution function of air bubbles, setting a cost function as a square sum of a simulated attenuation coefficient and a 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 Gaussian function coefficients obtained by inversion. According to the method, the existence form of the bubble size distribution in the sediment is considered, the number of parameters to be inverted can be reduced to a certain extent, inversion of the bubble size distribution can be realized by using only attenuation information, and the attenuation data fitted by the inversion result are well matched with the measured attenuation data. The method is an innovative method applied to the field of submarine shallow gas exploration and identification.
Further, the method specifically comprises the following steps:
(1) Constructing a model input bubble size distribution, wherein the first term represents the attenuation coefficient of a formant of the fitted bubble by using a plurality of modified Gaussian distributions, and the second term adjusts the attenuation coefficient of a non-formant by using a plurality of linear functions, and in the initial constructed bubble size distribution, the parameter a i3 The bubble radius corresponding to the attenuation peak value and other parameters are randomly generated;
f (a) bubble radius size distribution, a is a bubble radius variable, N i 、a i1 、a i2 、a i3 For the Gaussian function coefficients to be solved, k j 、b j The linear function coefficient is a primary linear function coefficient to be solved;
(2) Setting initial model input environmental parameters:
(3) Substituting the equivalent density fluid approximate model corrected by bubble vibration to calculate the attenuation coefficient of the gas-containing marine sediment;
ρ eff for sediment equivalent fluid density, K eff In order for the equivalent bulk modulus of the deposit,for the equivalent fluid density of bubble vibration correction, ω is the angular frequency, b (a) is the damping coefficient of the vibration corresponding to the bubble size, i is the imaginary unit, ω 0 Is the bubble resonance frequency, β is the sediment porosity;
(4) Calculating an inversion-set objective functionWherein->For acoustic wave attenuation coefficient measurements at different frequencies, and (2)>The forward model forecast value under the corresponding frequency is obtained;
(5) Repeating the steps (1) - (4) using a two-stage hybrid optimization algorithm (DEPSO: differential evolution algorithm and particle swarm algorithm).
Further, the model input environment parameters include: (1) physical parameters of deposit: particle size, particle density, particle bulk modulus of elasticity, pore water density, pore water bulk modulus of elasticity, pore water viscosity coefficient, porosity, permeability, tortuosity; (2) physical parameters of gas: gas density, static pressure, thermal diffusivity of gas, surface tension, specific heat ratio.
The beneficial effects of the invention are as follows: compared with the traditional bubble inversion method, the method considers possible existing distribution in the natural world, reduces the number of parameters to be inverted to a certain extent, and utilizes the attenuation coefficient of the inversion bubble size distribution fitting to be well matched with the measured attenuation coefficient.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
FIG. 2 is a schematic diagram of the observed attenuation coefficient versus the model fit attenuation coefficient.
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 attached drawings:
the invention discloses a bubble size distribution inversion method based on Gaussian function fitting, which comprises the following steps: and fitting an unknown bubble size distribution function in the marine sediment by using the modified Gaussian function, and solving the modified Gaussian function coefficient by using an optimization algorithm to invert the bubble size distribution in the marine sediment. The method comprises the following steps: the size distribution function of the bubbles was first expressed by a modified gaussian function for the experimentally observed peak of the attenuation coefficient of the gas-containing deposit. And setting the cost function as the square sum of the simulated attenuation coefficient and the error of the measured attenuation coefficient, and inverting the corrected Gaussian function coefficient by using an optimization algorithm. And finally fitting the size distribution of the bubbles by using Gaussian function coefficients obtained by inversion. The method can accurately invert the size distribution of the bubbles under the condition that the sound velocity and attenuation information of the gas-bearing sediment are not completely known, taking inversion by using attenuation coefficients only as an example, and the fitted attenuation coefficients are well matched with the attenuation coefficients measured by experiments.
(1) The model input bubble size distribution is constructed as shown in the following formula, wherein the first term represents the attenuation coefficient of the fitted bubble formants realized by using a plurality of modified Gaussian distributions, and the second term adjusts the attenuation coefficient of the non-formants by using a plurality of linear functions. In the initially structured bubble size distribution, parameter a i3 Other parameters are randomly generated corresponding to the bubble radius of the decay peak.
f (a) bubble radius size distribution, a is a bubble radius variable, N i 、a i1 、a i2 、a i3 For the Gaussian function coefficients to be solved, k j 、b j The linear function coefficient is a primary linear function coefficient to be solved;
(2) Setting initial model input environmental parameters: (1) physical parameters of deposit: particle size, particle density, particle bulk modulus of elasticity, pore water density, pore water bulk modulus of elasticity, pore water viscosity coefficient, porosity, permeability, tortuosity, and the like; (2) physical parameters of gas: gas density, static pressure, thermal diffusivity of gas, surface tension, specific heat ratio, etc.
(3) And substituting the equivalent density fluid approximate model corrected by the bubble vibration to calculate the attenuation coefficient of the gas-containing marine sediment.
ρ eff For sediment equivalent fluid density, K eff In order for the equivalent bulk modulus of the deposit,for the equivalent fluid density of bubble vibration correction, ω is the angular frequency, b (a) is the damping coefficient of the vibration corresponding to the bubble size, i is the imaginary unit, ω 0 Is the bubble resonance frequency, β is the sediment porosity;
(4) Calculating an inversion-set objective functionWherein->For acoustic wave attenuation coefficient measurements at different frequencies, and (2)>Is a forward model forecast value at the corresponding frequency.
(5) Repeating the steps (1) - (4) using a two-stage hybrid optimization algorithm (DEPSO: differential evolution algorithm and particle swarm algorithm).
FIG. 1 is an inversion method for fitting bubble size distribution based on a modified Gaussian function, wherein the inversion method is used for inverting the bubble size distribution, and the attenuation coefficient obtained by fitting is compared with the attenuation coefficient predicted by a model. In the figure, the solid line is the measured attenuation coefficient, and the dotted line is the model predicted attenuation coefficient. The method can be used for accurately fitting four peaks A-D in the attenuation curve, and the attenuation of the frequency of 500-3000Hz is consistent with the measured attenuation data.
Fig. 2 is an optimal bubble size distribution obtained by model fitting, and it is apparent that the bubble size distribution has 1.236mm, 1.614mm and 2.025mm3 peaks, but the 3.62mm peaks are not apparent, which corresponds to the smaller amplitude of the attenuation coefficient peak a.
FIG. 3 is a bubble size distribution inversion flow chart detailing the overall inversion process in the detailed implementation.
The frequencies of the four formants A-D and their corresponding attenuation coefficient magnitudes are given in Table 1. Formant A decays to 109dB/m at 900Hz, formant B decays to 296dB/m at 1600Hz, formant C decays to 365dB/m at 2000Hz, and formant D decays to 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
It should be understood that equivalents and modifications to the technical scheme and the inventive concept of the present invention should fall within the scope of the claims appended hereto.
Claims (2)
1. A bubble size distribution inversion method based on Gaussian function fitting is characterized by comprising the following steps of: the method comprises the following steps: firstly, aiming at an attenuation coefficient peak value of an air-bearing sediment observed through experiments, using a modified Gaussian function to represent a size distribution function of air bubbles, setting a cost function as a square sum of a simulated attenuation coefficient and a measured attenuation coefficient error, and inverting the modified Gaussian function coefficient by using an optimization algorithm; finally, fitting the size distribution of the bubbles by using Gaussian function coefficients obtained by inversion;
the method specifically comprises the following steps:
(1) Constructing a model input bubble size distribution, wherein the first term represents the attenuation coefficient of a formant of the fitted bubble by using a plurality of modified Gaussian distributions, and the second term adjusts the attenuation coefficient of a non-formant by using a plurality of linear functions, and in the initial constructed bubble size distribution, the parameter a i3 The bubble radius corresponding to the attenuation peak value and other parameters are randomly generated;
f (a) bubble radius size distribution, a is a bubble radius variable, N i 、a i1 、a i2 、a i3 For the Gaussian function coefficients to be solved, k j 、b j The linear function coefficient is a primary linear function coefficient to be solved;
(2) Setting initial model input environmental parameters:
(3) Substituting the equivalent density fluid approximate model corrected by bubble vibration to calculate the attenuation coefficient of the gas-containing marine sediment;
ρ eff for sediment equivalent fluid density, K eff In order for the equivalent bulk modulus of the deposit,for the equivalent fluid density of bubble vibration correction, ω is the angular frequency, b (a) is the damping coefficient of the vibration corresponding to the bubble size, i is the imaginary unit, ω 0 Is the bubble resonance frequency, β is the sediment porosity;
(4) Calculating an inversion-set objective functionWherein->For acoustic wave attenuation coefficient measurements at different frequencies, and (2)>The forward model forecast value under the corresponding frequency is obtained;
(5) Repeating the steps (1) - (4) by using a two-stage hybrid optimization algorithm.
2. The bubble size distribution inversion method based on gaussian fitting according to claim 1, wherein: the model input environment parameters comprise: (1) physical parameters of deposit: particle size, particle density, particle bulk modulus of elasticity, pore water density, pore water bulk modulus of elasticity, pore water viscosity coefficient, porosity, permeability, tortuosity; (2) physical parameters of gas: gas density, static pressure, thermal diffusivity of gas, surface tension, specific heat ratio.
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Citations (4)
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|---|---|---|---|---|
| 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 |
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Patent Citations (4)
| 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)
| Title |
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| 水中气泡分布的共振估计法的误差分析及修正;黎章龙;屈科;张薇;何树斌;;海洋技术学报(06);全文 * |
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