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CN112163378A - Inversion method of multi-layer seabed geoacoustic parameters in shallow sea based on nonlinear Bayesian theory - Google Patents

Inversion method of multi-layer seabed geoacoustic parameters in shallow sea based on nonlinear Bayesian theory Download PDF

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CN112163378A
CN112163378A CN202011171008.6A CN202011171008A CN112163378A CN 112163378 A CN112163378 A CN 112163378A CN 202011171008 A CN202011171008 A CN 202011171008A CN 112163378 A CN112163378 A CN 112163378A
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祝捍皓
薛洋洋
崔志强
陈超
王其乐
肖瑞
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Zhejiang Ocean University ZJOU
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Abstract

The invention belongs to the technical field of geophone parameter inversion, and particularly relates to a shallow sea multilayer seabed geophone parameter inversion method based on nonlinear Bayes theory, which comprises the following steps: the submarine geophone parameters are inverted according to a nonlinear Bayes inversion method, so that the actual submarine structure can be accurately judged from the measured data; the accuracy and resolution of the inversion result can be improved by adopting a forward-pulling simulated annealing algorithm; compared with two types of sound velocity attenuation and density, the uncertainty of longitudinal wave sound velocity and transverse wave sound velocity is smaller; the uncertainty of each parameter in the deposited layer is smaller compared to a semi-infinite substrate.

Description

Shallow sea multilayer seabed ground sound parameter inversion method based on nonlinear Bayesian theory
Technical Field
The invention belongs to the technical field of earth sound parameter inversion, and particularly relates to a shallow sea multilayer seabed earth sound parameter inversion method based on a nonlinear Bayesian theory.
Background
The submarine earth sound parameter is one of important parameters forming a marine underwater sound environment, and acoustic parameters such as sound velocity, density and sound velocity attenuation of the seabed have important influence on sound propagation in the marine environment, particularly in a shallow sea environment. The mastering degree of the submarine earth sound parameters directly influences the prediction and evaluation of the performance of underwater sound equipment, the numerical prediction of an ocean sound field, the utilization of the characteristics of the ocean sound field and the like. How to efficiently and accurately acquire submarine earth sound parameter information is a research hotspot in the field of underwater sound.
Methods for acquiring submarine earth sound parameters are currently classified into direct measurement and indirect measurement. Compared with a direct measurement method for obtaining a seabed sediment sample for identification by drilling sampling and other modes, the indirect measurement method of the earth-sound parameters represented by the acoustic inversion technology is widely applied to obtaining the seabed earth-sound parameters because of the technical advantages of real time, rapidness and high efficiency. Because conventional sonars are developed by relying on medium/high frequency band sound waves, seabed surface layer acoustic characteristics are mostly concerned in the inversion research of seabed ground sound parameters, and the seabed is assumed to be a liquid medium. With the development of sonar equipment towards low frequency/very low frequency in recent years, the conventional understanding and mastering of the acoustic characteristics of the seabed surface layer cannot meet the analysis and verification of the current sound propagation problem, and the research on the deep seabed ground sound parameter inversion technology including seabed structures is more urgent. In addition, research results prove that the influence of the submarine transverse wave sound velocity cannot be ignored when the problem of low-frequency/very-low-frequency underwater sound propagation is researched, so that in the research of the current submarine geoacoustic parameter inversion problem, the submarine is regarded as a layered elastic medium, and accurate inversion of deep geoacoustic parameters including a layered structure, the transverse wave sound velocity and attenuation of the transverse wave sound velocity is a development target of the current submarine geoacoustic parameters, and related research work needs to be carried out urgently.
In addition, the seabed ground sound parameter inversion core is considered to be the solution of a nonlinear and multi-parameter complex function with correlation among parameters, and the global optimization methods such as a multi-purpose genetic algorithm, a simulated annealing algorithm and the like are used for solving in the past research [6 ]. However, the optimization result of the algorithm is only a set of parameters which can reflect the optimal sound field data information. Because various errors inevitably exist in the marine measured data, certain uncertainty exists in the inversion result due to the factors.
The nonlinear Bayesian inversion method is a global optimization algorithm based on the interdiscipline of probability theory, applied mathematics, optimization theory and the like, can effectively estimate parameters of a maximum posterior probability (MAP) model, can explain uncertainty of a parameter inversion result from a statistical angle, and better meets the research requirement of the current ground sound parameter inversion.
Therefore, a new shallow sea multilayer seabed ground sound parameter inversion method based on the nonlinear Bayesian theory needs to be designed based on the technical problems.
Disclosure of Invention
The invention aims to provide a shallow sea multilayer seabed ground sound parameter inversion method based on a nonlinear Bayesian theory.
In order to solve the technical problem, the invention provides a shallow sea multilayer seabed ground sound parameter inversion method, which comprises the following steps:
and (4) carrying out inversion on the submarine geoacoustic parameters according to a nonlinear Bayesian inversion method.
Further, the method for inverting the submarine geoacoustic parameters according to the nonlinear Bayesian inversion method comprises the following steps:
constructing a seabed model, and acquiring seabed ground sound parameters of the seabed model;
acquiring experimental data in a scaling experiment;
the vector d corresponding to the experimental data in the scaling experiment and the vector m corresponding to the seabed model parameters satisfy the Bayesian theorem:
P(m|d)＝P(d|m)P(m)/P(d)；
wherein P (m | d) is the posterior probability density; the conditional probability P (d | m) of d is represented by a likelihood function L (m); p (m) is the prior probability density function of the vector m; p (d) is the probability density function of vector d;
p (d) is independent of m, then
P(m|d)∝P(d|m)P(m)；
The likelihood function L (m) is:
L(m)＝P(d|m)∝exp[-E(m)]；
wherein E (m) is an error function;
normalizing E (m):
Figure BDA0002747291420000031
wherein, the integral domain spans M dimension parameter space, M is the number of the parameter to be inverted; m' is an unknown representing an arbitrary model parameter vector m.
Further, the method for inverting the submarine geoacoustic parameters according to the nonlinear bayesian inversion method further comprises the following steps:
obtaining the MAP value of the parameter to be inverted:
Figure BDA0002747291420000032
obtaining the mean value of the parameters to be inverted:
Figure BDA0002747291420000033
acquiring one-dimensional probability density distribution of a parameter to be inverted: p (m)i|d)＝∫(mi-mi′)P(m′|d)dm′；
Wherein, a Dirac Delta function;
obtaining the correlation of the parameters to be inverted:
Figure BDA0002747291420000034
wherein the correlation value RijBetween +1 and-1 whenWhen the correlation value is equal to +1, the two parameters to be inverted are completely correlated; when the value is equal to-1, the two parameters to be inverted are completely inversely correlated; when the value is equal to 0, the two parameters to be inverted are completely uncorrelated;
Figure BDA0002747291420000041
respectively, representing the correlation matrix generated by normalizing the covariance between the parameters in the model parameter vector m.
Further, the method for inverting the submarine geoacoustic parameters according to the nonlinear bayesian inversion method further comprises the following steps:
the likelihood function when the data errors are independent identically distributed random variables is:
Figure BDA0002747291420000042
wherein p isf meaFor the measured sound pressure received by a single sensor at position k at frequency f, in the same case, pf preIt is indicated that the predicted sound pressure,
Figure BDA0002747291420000043
represents the covariance matrix at frequency f;
predicted sound pressure pf preComprises the following steps:
Figure BDA0002747291420000044
wherein p isf FFMIs the sound pressure calculated by the fast field method; a. thefAnd thetafAmplitude and phase at each frequency for an unknown sound source;
when in use
Figure BDA0002747291420000045
Obtaining a maximum likelihood estimation value of a sound source:
Figure BDA0002747291420000046
wherein, is a conjugate transpose;
processing the corner-line covariance to Cf m＝vfI, then the likelihood function is:
Figure BDA0002747291420000047
wherein the variance vfIs frequency dependent; i is a unit array; b isf(m) is normalized Bartlett dispenser:
Figure BDA0002747291420000048
when in use
Figure BDA0002747291420000049
Obtaining the variance vfMaximum likelihood estimation of (2):
Figure BDA0002747291420000051
according to the variance vfThe maximum likelihood estimation value of (1) acquires an error function e (m) corresponding to the maximum likelihood function estimation value:
Figure BDA0002747291420000052
further, the method for inverting the submarine geoacoustic parameters according to the nonlinear bayesian inversion method further comprises the following steps:
when measuring data d, the likelihood function for the corresponding model is:
Figure BDA0002747291420000053
wherein M is the number of parameters in the corresponding model, and N is the number of data parameters;
replacing the likelihood function with an error function to obtain:
Figure BDA0002747291420000054
wherein, BIC is Bayesian information criterion, and the model with the smallest BIC value is the optimal model.
Further, the method for inverting the submarine geoacoustic parameters according to the nonlinear bayesian inversion method further comprises the following steps:
searching MAP value in prior interval based on error function, and carrying out micro-positive disturbance based on physical law of acoustic impedance, i.e.
Initialization parameter m1，m2；
Calculating an error function;
when m is satisfied2>m1Carrying out random disturbance calculation when in use, or else carrying out micro forward interference to make m2>m1Then random disturbance calculation is carried out;
judging whether the result of the random disturbance calculation meets Metropolis criterion or not, and reserving a parameter m when the result meets the Metropolis criterion1，m2Otherwise, judging m again2>m1；
Judging the reserved parameter m1，m2If the end condition is met, outputting the parameters if the end condition is met, otherwise, judging m again2>m1；
m1，m2Is two adjacent layers of sea floor, m1The sound velocity, density, sound velocity attenuation and sediment layer depth of a layer of seabed close to the sea level; m is2The sound velocity, density, sound velocity attenuation and sediment layer depth of a layer of seabed far away from the sea level;
the physical law of the acoustic impedance is as follows: c. Cm+1ρm+1≥cmρm m＝1,…,n；
Where c represents the sound velocity and ρ represents the density.
The method has the advantages that the method realizes the accurate judgment of the actual seabed structure from the measured data by inverting the seabed ground sound parameters according to the nonlinear Bayesian inversion method; the accuracy and resolution of the inversion result can be improved by adopting a forward-pulling simulated annealing algorithm; compared with two types of sound velocity attenuation and density, the uncertainty of longitudinal wave sound velocity and transverse wave sound velocity is smaller; the uncertainty of each parameter in the deposited layer is smaller compared to a semi-infinite substrate.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and drawings.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flow chart of a shallow sea multi-layer seabed geophone parameter inversion method according to the present invention;
FIG. 2 is a schematic illustration of a subsea model to which the present invention relates;
FIG. 3 is a schematic diagram of measured data versus inverted data in accordance with the present invention;
FIG. 4 is a schematic representation of model selection results in accordance with the present invention;
FIG. 5 is a chart of the planing surface structure of longitudinal sonic velocity, transverse sonic velocity and seafloor density as a function of depth in accordance with the present invention;
FIG. 6 is a schematic diagram of a one-dimensional marginal probability distribution of sediment layer seafloor parameters in accordance with the present invention;
FIG. 7 is a schematic diagram of a semi-infinite seafloor parameter one-dimensional marginal probability distribution in accordance with the present invention;
FIG. 8 is a graph of a correlation matrix between inversion parameters in accordance with the present invention;
fig. 9 is a schematic diagram of two-dimensional edge probability distributions of the longitudinal wave sound velocity, the transverse wave sound velocity, and the density according to the depth in the present invention.
Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present 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 protection scope of the present invention.
As shown in fig. 1, the present embodiment provides a shallow sea multilayer seabed geophone parameter inversion method, including: inverting the submarine geoacoustic parameters according to a nonlinear Bayesian inversion method; the sound pressure field is used as a research object, and parameters such as density of each layer of the seabed, longitudinal wave sound velocity, transverse wave sound velocity, two types of sound velocity attenuation and the like and uncertainty of the parameters are estimated by adopting a Bayes method; the maximum posterior probability density (MAP) estimation value and marginal probability distribution of each parameter are respectively obtained by searching in each parameter prior interval through a poke-up simulated annealing algorithm and a Metropolis-Hastings sampling method, and an optimal model is selected from different parametric models according to a Bayesian Information Criterion (BIC); the actual seabed structure can be accurately judged from the actually measured data; the accuracy and resolution of the inversion result can be improved by adopting a forward-pulling simulated annealing algorithm; compared with two types of sound velocity attenuation and density, the uncertainty of longitudinal wave sound velocity and transverse wave sound velocity is smaller; the uncertainty of each parameter in the deposited layer is smaller compared to a semi-infinite substrate.
In this embodiment, the method for inverting the submarine geoacoustic parameters according to the nonlinear bayesian inversion method includes: constructing a subsea model (as shown in FIG. 2, where cp、csAnd ρb，αpAnd alphasRespectively represents longitudinal wave sound velocity, transverse wave sound velocity, seabed density, longitudinal wave sound velocity attenuation and transverse wave sound velocity attenuation, z is water depth, z issThe depth of the sound source, r is the propagation distance, and f0 is the sound source), and obtaining the submarine geophone parameters of the submarine model; the sound pressure can be accurately and rapidly calculated according to a fast field method, and the sound pressure field in the embodiment is calculated by a Fast Field Method (FFM); acquiring experimental data in a scaling experiment; the vector d corresponding to the experimental data in the scaling experiment and the vector m corresponding to the seabed model parameters (seabed ground sound parameters) satisfy the Bayesian theorem:
P(m|d)＝P(d|m)P(m)/P(d)；
wherein P (m | d) is the Posterior Probability Density (PPD); the conditional probability P (d | m) of d is usually expressed by a likelihood function l (m); p (m) is a prior probability density function of the vector m, representing available model parameter prior information independent of the data; p (d) is the probability density function of vector d;
p (d) can be regarded as a constant independently of m, then
P(m|d)∝P(d|m)P(m)；
The likelihood function is determined by the data form and the statistical distribution of the data errors. Considering that in the practical application process, the statistical characteristics of the error are difficult to obtain independently, the assumption of unbiased gaussian error is adopted in the processing process, and the likelihood function l (m) is:
L(m)＝P(d|m)∝exp[-E(m)]；
wherein E (m) is an error function;
normalizing E (m):
Figure BDA0002747291420000091
wherein, the integral domain spans M dimension parameter space, M is the number of the parameter to be inverted; m 'represents an unknown number that can represent any model parameter vector m, m and m' being virtually identical except for habitual writing in the integral term; in Bayes theory, the Posterior Probability Density (PPD) can be used as a solution to the inverse problem.
In this embodiment, the method for inverting the submarine geoacoustic parameters according to the nonlinear bayesian inversion method further includes: because of the problem of dimensional parameters in inversion, the correlation characteristics among model parameters also need to be researched for more reasonably explaining the inversion result of the parameters;
obtaining the MAP value of the parameter to be inverted:
Figure BDA0002747291420000092
obtaining the mean value of the parameters to be inverted:
Figure BDA0002747291420000093
acquiring one-dimensional probability density distribution of a parameter to be inverted: p (m)i|d)＝∫(mi-mi′)P(m′|d)dm′；
Wherein, a Dirac Delta function;
the interrelationship between the parameters to be inverted can be quantitatively described by normalizing the correlation matrix generated by the covariance:
Figure BDA0002747291420000094
wherein the correlation value RijThe correlation value is between +1 and-1, and when the correlation value is equal to +1, the two parameters to be inverted are completely correlated; when the value is equal to-1, the two parameters to be inverted are completely inversely correlated; when the value is equal to 0, the two parameters to be inverted are completely uncorrelated
Figure BDA0002747291420000095
Respectively, representing the correlation matrix generated by normalizing the covariance between the parameters in the model parameter vector m.
In this embodiment, the method for inverting the submarine geoacoustic parameters according to the nonlinear bayesian inversion method further includes: selecting a proper prior parameter range is the key to the success or failure of inversion, and in order to ensure the completeness of sampling, the prior information in the text considers that each parameter is uniformly distributed in a sufficiently wide range; the MAP estimated value is solved by adopting a Correction Simulated Annealing (CSA), wherein the CSA is an improved Simulated Annealing algorithm and can correct random parameters in an optimization solving process according to the physical characteristics of the upper and lower layers of the seabed; the one-dimensional and two-dimensional edge probability distribution of the parameters is solved by numerical integration of parameter PPD obtained by a Metropolis-Hasting sampling Method (MHS), although the sampling result of the MHS sampling method does not depend on an initial model, if a correct initial value is selected, the accuracy and the speed of inversion can be improved, and a MAP estimated value searched by a CSA method is used as the initial model of MHS sampling;
in Bayes inversion theory, solving parameter PPD needs to obtain likelihood function L (m), wherein the likelihood function is related to statistical distribution of data error (including measurement error and theoretical error) and is an important index for quantitatively describing parameter uncertainty; in this embodiment, assuming that the data errors are independent and uniformly distributed random variables, the likelihood function can be expressed as:
Figure BDA0002747291420000101
wherein p isf meaFor the measured sound pressure received by a single sensor at position k at frequency f, in the same case, pf preIt is indicated that the predicted sound pressure,
Figure BDA0002747291420000102
represents the covariance matrix at frequency f;
predicted sound pressure pf preComprises the following steps:
Figure BDA0002747291420000103
wherein p isf FFMIs the sound pressure calculated by the fast field method; a. thefAnd thetafAmplitude and phase at each frequency for an unknown sound source;
when in use
Figure BDA0002747291420000104
Obtaining a maximum likelihood estimation value of a sound source:
Figure BDA0002747291420000105
wherein, is a conjugate transpose;
processing the corner-line covariance as C ignoring the spatial correlation of the dataf m＝vfI, then the likelihood function is:
Figure BDA0002747291420000106
wherein the variance vfIs frequency dependent; i is a unit array; b isf(m) is normalized Bartlett dispenser:
Figure BDA0002747291420000111
when in use
Figure BDA0002747291420000112
Obtaining the variance vfMaximum likelihood estimation of (2):
Figure BDA0002747291420000113
according to the variance vfSubstituting the maximum likelihood estimation value of (a) into L (m) ═ P (d | m) ocexp [ -E (m)]And
Figure BDA0002747291420000114
obtaining a corresponding error function E (m) when the maximum likelihood function estimation value is satisfied:
Figure BDA0002747291420000115
in this embodiment, the method for inverting the submarine geoacoustic parameters according to the nonlinear bayesian inversion method further includes: the reasonable parameterized model is the key of Bayesian inversion, and the structure cannot be completely analyzed due to the under-parameterized model, so that the uncertainty of the model is low; the over-parameterized model has insufficient constraints on parameters, so that the uncertainty of the model is increased, and the under-parameterized model and the over-parameterized model have certain influence on an inversion result. Bayesian Information Criterion (BIC) is applied herein to select the parameterized model that best fits the measured data. The BIC value is obtained from the normal distribution of the multidimensional variable, is not an accurate value, and is a progressive approximation of bayesian theorem P (d | I) of model I, that is, assuming measurement data d (experimental data in a scaling experiment), a likelihood function of model I (model I refers to different inversion models, that is, a sea-bottom model, and BIC is an inversion model that best meets the experimental data found from different inversion models) has the following expression:
Figure BDA0002747291420000116
wherein, M is a parameter in the model I (corresponding model) (parameter of the subsea model, when the subsea is layered, different subsea layers are layered, and the inversion parameters included in the subsea model are not too many, for example, the number of the one-layer subsea inversion parameter M is 5, and the two-layer subsea model M is 11), and N is the number of data parameters (experimental data in the scaling experiment);
replacing the likelihood function with an error function to obtain:
Figure BDA0002747291420000121
the BIC is a Bayesian information criterion, the model with the smallest BIC value (the BIC is a model which is selected from different models I and best accords with experimental or simulation parameters, and the model is a model selected from the models I) is an optimal model, and the value of the BIC is determined by an error function, the number of model parameters and the number of data together, so that under-parameterization and over-parameterization models are avoided, and the optimal parameterization model is selected more effectively.
In this embodiment, the method for inverting the submarine geoacoustic parameters according to the nonlinear bayesian inversion method further includes: searching MAP values in a prior interval based on an error function is an important step of a Bayesian inversion method, the error function is nonlinear and has multiple dimensions and possibly multiple peak values, so that great challenges are brought to the searching process, and the correlation among parameters aggravates the difficulty of searching; at present, most scholars apply local optimization or global optimization algorithm to the inversion research of the earth sound parameters; the local optimization method iteratively improves the initial model by moving the local gradient downwards, and the methods can effectively move downhill and adapt to relevant parameters, but are easy to fall into local minimum; compared with a local optimization algorithm, the global optimization avoids falling into local minimum in a timely upward moving mode, and the whole parameter space can be directionally and randomly searched;
when MAP value searching is carried out, the selection of parameter intervals is particularly important, and the parameter interval selection becomes difficult as the parameterized model is gradually complicated; in the past, when semi-infinite seabed inversion is performed, the MAP value can be obtained by gradually optimizing under the condition that an error function and an optimization algorithm are selected reasonably, but with the increase of the number of layers of a seabed model, the optimization process becomes more complex due to the addition of the thickness of a deposition layer, the selection of a parameter space is more difficult, the optimization difficulty and accuracy are increased due to the large range of the parameter space, and the fact that the actual value of measured data is contained in an optimization interval cannot be guaranteed due to the small range, so that a poke-up simulated annealing algorithm (CSA) is provided based on the improvement of a simulated annealing algorithm (SA), and is applied to a Bayesian inversion method:
initialization parameter m1，m2(random number random generation);
calculating an error function;
when m is satisfied2>m1Random disturbance calculation is carried out (in the actual physical ocean, the acoustic impedance of the second layer, the density and the sound velocity are larger than those of the first layer, and m is represented by parameters2>m1So that m should be guaranteed when inverting multiple layers of seafloorn+1>mn) Otherwise, performing micro forward interference to make m2>m1Then, random perturbation calculation is carried out (m (i +1) ═ m (i)) + a (m)max-mmin) (ii) a Wherein m ismaxIn order to achieve the upper limit of the optimization interval,mminthe lower limit of the optimizing interval; the expression of the coefficient a is as follows: a 2(T (i))/Tmax)b(-0.5))；
Judging whether the result of the random disturbance calculation meets Metropolis criterion (Metropolis acceptance criterion) or not, and reserving a parameter m when the result meets the Metropolis criterion1，m2Otherwise, judging m again2>m1；
Judging the reserved parameter m1，m2If the end condition (here, the optimization is based on the simulated annealing algorithm, and the end condition is that the temperature T in the model annealing algorithm is 1), is satisfied, the output parameter (m) is output1，m2) Otherwise, judging m again2>m1；
m1，m2Is two adjacent layers of sea floor, m1The sound velocity, density, sound velocity attenuation and sediment layer depth of a layer of seabed close to the sea level; m is2The sound velocity, density, sound velocity attenuation and sediment layer depth of a layer of seabed far away from the sea level;
in underwater acoustics, acoustic impedance increases along with the increase of the depth of the sea bottom, the next layer of optimization is corrected by utilizing the previous layer of optimization result according to the physical law of the sea bottom, and the physical law of the acoustic impedance is as follows: c. Cm+1ρm+1≥cmρm m＝1,…,n；
Where c represents the sound velocity and ρ represents the density; according to the physical law of the acoustic impedance, the acoustic impedance of the second layer is larger than that of the first layer, so that micro forward disturbance is added during optimization, and the inversion process is more in line with the physical law.
In this example, a shallow sea wave guide environment having an elastic deposition layer and an elastic semi-infinite sea bottom was simulated by laying fine sand on a PVC plate (Polyvinyl Chloride, measured density of (1.20 g. cm-3)) having a size of 1.5 m.times.1.1 m.times.0.105 m (length. times.1 m. times.width. times.height, measurement error. + -. 1mm) to simulate an elastic sea bottom, and a sound depth zs200mm, receiving depth zr200mm, depth of water z1300mm, and the sound velocity in water calculated from the room temperature is 1450.212/m · s-1. High frequency waterSound is emitted by a sound source at a fixed position, and a receiving hydrophone measures every fixed distance; in order to improve the measurement accuracy, the transmitting transducer is fixed in water at one end, the receiving hydrophone is fixed on a movable micro-workbench, the workbench moves by 2mm each time, and the measurement error is less than 20 um; controlling the mobile workbench by using a computer, measuring and acquiring data; after the measurement at one position is finished, the workbench automatically moves to the next position, the average value is obtained after 10 times of measurement at each position, and 500 points are measured in the experiment process; during measurement, a home-made transmitting transducer (with the diameter of about 8 mm) is used as a high-frequency sound source (with the center frequency of 155kHz), and a TC4038 standard hydrophone is used for receiving signals. Establishing a proper forward model is one of key factors for improving inversion speed and accuracy, regarding the seabed as a uniform and isotropic multilayer medium aiming at a shallow sea environment, and taking the longitudinal wave sound velocity, the transverse wave sound velocity, the density, the longitudinal wave attenuation, the transverse wave attenuation and the depth of each layer as a text inversion object. Fig. 3 is a propagation loss comparison graph of inversion data and actual measurement data of a scaling experiment, and it can be seen from the graph that the trends of the inversion data and the actual measurement data are basically consistent, and the comparison result is better. Table 1 gives the inversion prior interval and the mean and variance of the inversion results; the density of the PVC sheet simulating a semi-infinite seabed is known to be 1.20g cm-3The thickness of the sediment layer simulated by the fine sand is about 250mm, and the density mean value of the semi-infinite seabed obtained by inversion is 1.205g cm-3The mean deposit thickness was 249.694mm, indicating that the inversion results are substantially consistent with the experiments. In the prior art, a PVC plate made of the same material is adopted to simulate a scaling experiment of a semi-infinite seabed, and the longitudinal wave sound velocity obtained by inversion of the scaling experiment is 2399.364m & s-1The transverse wave sound velocity is 1242.978m · s-1In consideration of the facts that fine sand replaces a settled layer in the experimental process and uncertain factors such as the uniformity of fine sand laying are more, the longitudinal wave velocity and the transverse wave velocity of the semi-infinite seabed obtained through inversion in the embodiment are basically consistent with the results in the prior art, and the effect of the shallow sea multilayer seabed ground sound parameter inversion method in the embodiment is verified.
Table 1: inversion results
Figure BDA0002747291420000151
In model research, 3 groups of different models are considered, the models are 1-3 layers of isotropic uniform seabed distribution models respectively, and data error values, parameter numbers and BIC values corresponding to MAP values of each model solved by CSA are given.
As can be seen from (a) in fig. 4, (m1, m2, m3, respectively representing 1-layer, 2-layer, 3-layer uniform seabed distribution model, i.e. seabed model), the error value of the model (seabed model) in question gradually decreases as the number of layers increases, and the whole model shows a descending trend, which is consistent with the actual physical situation; as can be seen from (b) in fig. 4, as the number of layers increases, the parameters to be considered also increase, which increases the uncertainty of the inversion result; the BIC fully considers the balance among the error value, the number of parameters and the number of data of the model, and selects the parameterized model which is most consistent with the measured data. As can be seen from (c) of fig. 4, the optimal model finally determined by the BIC criterion is a 2-uniform seafloor distribution model.
Fig. 5 shows the section structures of the corresponding longitudinal wave sound velocity, transverse wave sound velocity and density varying with depth obtained by inversion (m1, m2 and m3 represent 1-layer, 2-layer and 3-layer uniform seabed distribution inversion models, namely seabed models). Usually, the acoustic impedance (rho c, where rho is density c and is sound velocity) and the depth are in a direct proportional relation, that is, the acoustic impedance increases with the increase of the depth, and it can be seen from the result that the trends of the seabed distribution models of 1, 2 and 3 layers all conform to the physical rule, and as the seabed layering increases, the parameter distribution does not have the phenomenon of 'folding back', thereby verifying the key role of the poking-in simulation annealing algorithm in searching the parameter prior interval. It can be seen from the sectional structure that the 1000mm boundary is used, and the values of the boundary include the structure division with obvious longitudinal wave sound velocity, transverse wave sound velocity and density, and the boundary tends to a certain value, wherein the longitudinal wave sound velocity trend is more obvious.
The nonlinear Bayes inversion method can analyze the uncertainty of the inversion result, and since the earth-sound parameter inversion is a complex problem of nonlinear multi-parameter optimization and is obviously unreasonable only by taking a group of optimal solutions as the inversion result, the uncertainty analysis of the inversion result is particularly important.
Selecting a 3-layer uniformly distributed optimal model determined by a BIC criterion, searching an estimated value obtained by using a CSA method as a sampled initial model, and obtaining a PPD numerical integration solution of parameters by using a Metropolis-Hasting sampling method, wherein a one-dimensional probability distribution diagram of the parameters corresponding to the 2-layer uniform seabed distribution model is given in the figures 6 and 7, wherein a red solid line represents an MAP value of each parameter; as can be seen from the figure, the one-dimensional marginal probability distribution of each parameter in the sedimentary deposit and the semi-infinite seabed conforms to normal distribution in the prior interval, and the distribution of each parameter is narrower compared with that of the semi-infinite seabed sedimentary deposit, which indicates that the sedimentary deposit parameters are more sensitive; from a single parameter point of view, cp2、cs2And cs3The distribution is narrow, which indicates that the parameter can be well distinguished, and the uncertainty is small; c. Cp3And the sound velocity attenuation distribution result of each layer is poor, which shows that the parameter uncertainty is relatively large and is not easy to be identified.
Considering that the earth-sound parameter inversion is a multi-parameter optimization problem, parameters are coupled with each other, and the correlation between the parameters can directly influence the inversion result, so that the uncertainty of the parameters to be inverted is increased, and therefore, the correlation between the inversion parameters is analyzed, as shown in fig. 8. As can be seen from the results, αs2And cp3And cs3And alphap3Has stronger positive correlation; c. Cp2And ρ2Also has positive correlation; alpha is alphap2And ρ2And cs3And ρ3Has stronger negative correlation; h is2And ρ2、ρ3Has strong negative correlation between the two.
In order to more intuitively and accurately represent the relationship between the longitudinal wave sound velocity, the transverse wave sound velocity and the density along with the change of the depth, a two-dimensional marginal probability distribution map of the longitudinal wave sound velocity, the transverse wave sound velocity, the density and the depth is given in fig. 9, because the inversion parameters are the sedimentary deposit and the parameters of the lower seabed, namely the two-dimensional marginal probability density distribution starts from the sedimentary deposit. From the results it can be seen that: compared with a semi-infinite seabed, the probability distribution of the longitudinal wave sound velocity, the transverse wave sound velocity and the density of the sediment layer is narrower, the uncertainty is smaller, and the parameters of the sediment layer are further shown to be more sensitive.
The sea floor parameters can be obtained by carrying out Bayesian inversion by utilizing the sound pressure field, and the optimal model determined by the BIC criterion is a 3-layer uniform distribution model and is consistent with the experimental result; aiming at the nonlinear Bayesian inversion method of the multilayer submarine model, the correcting simulated annealing algorithm provided by the invention can efficiently and accurately obtain the MAP estimated value, and avoids the parameter 'retracing' phenomenon in the multilayer submarine model. Through uncertain analysis of the inversion result, when the acoustic pressure field inversion is carried out, compared with longitudinal wave attenuation, transverse wave attenuation and density, the uncertainty of the longitudinal wave sound velocity and the transverse wave sound velocity is smaller, and the sensitivity is stronger; compared with a semi-infinite seabed sedimentary deposit, the method has the advantages that each parameter is more sensitive and uncertainty is smaller.
In conclusion, the method and the device realize accurate judgment of the actual seabed structure from the measured data by inverting the seabed ground sound parameters according to the nonlinear Bayesian inversion method; the accuracy and resolution of the inversion result can be improved by adopting a forward-pulling simulated annealing algorithm; compared with two types of sound velocity attenuation and density, the uncertainty of longitudinal wave sound velocity and transverse wave sound velocity is smaller; the uncertainty of each parameter in the deposited layer is smaller compared to a semi-infinite substrate.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method can be implemented in other ways. The apparatus embodiments described above are merely illustrative, and for example, the flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
In addition, the functional modules in the embodiments of the present invention may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.
The functions, if implemented in the form of software functional modules and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.

Claims (6)

1.一种浅海多层海底地声参数反演方法，其特征在于，包括：1. a shallow sea multi-layer submarine geoacoustic parameter inversion method, is characterized in that, comprises: 根据非线性贝叶斯反演方法对海底地声参数进行反演。The seafloor geoacoustic parameters are inverted according to the nonlinear Bayesian inversion method. 2.如权利要求1所述的浅海多层海底地声参数反演方法，其特征在于，2. shallow sea multi-layer seabed geoacoustic parameter inversion method as claimed in claim 1, is characterized in that, 所述根据非线性贝叶斯反演方法对海底地声参数进行反演的方法包括：The method for inverting the submarine geoacoustic parameters according to the nonlinear Bayesian inversion method includes: 构建海底模型，并获取海底模型的海底地声参数；Build a seabed model and obtain the seabed geoacoustic parameters of the seabed model; 获取缩比实验中的实验数据；Obtain the experimental data in the scaled experiment; 缩比实验中的实验数据对应的向量d和海底模型参数对应的向量m满足贝叶斯定理：The vector d corresponding to the experimental data in the scaling experiment and the vector m corresponding to the parameters of the seabed model satisfy Bayes' theorem: P(m|d)＝P(d|m)P(m)/P(d)；P(m|d)=P(d|m)P(m)/P(d); 其中，P(m|d)为后验概率密度；d的条件概率P(d|m)用似然函数L(m)来表示；P(m)是向量m的先验概率密度函数；P(d)是向量d的概率密度函数；Among them, P(m|d) is the posterior probability density; the conditional probability P(d|m) of d is represented by the likelihood function L(m); P(m) is the prior probability density function of the vector m; P (d) is the probability density function of the vector d; P(d)与m无关，则P(d) is independent of m, then P(m|d)∝P(d|m)P(m)；P(m|d)∝P(d|m)P(m); 似然函数L(m)为：The likelihood function L(m) is: L(m)＝P(d|m)∝exp[-E(m)]；L(m)=P(d|m)∝exp[-E(m)]; 其中，E(m)为误差函数；Among them, E(m) is the error function; 将E(m)进行归一化：Normalize E(m):
Figure FDA0002747291410000011
Figure FDA0002747291410000011
 其中，积分域跨越M维参数空间，M为待反演参数的个数；m′为表示任意模型参数向量m的未知数。Among them, the integral domain spans the M-dimensional parameter space, M is the number of parameters to be inverted; m' is the unknown representing the parameter vector m of any model. 3.如权利要求2所述的浅海多层海底地声参数反演方法，其特征在于，3. shallow sea multi-layer seabed geoacoustic parameter inversion method as claimed in claim 2, is characterized in that, 所述根据非线性贝叶斯反演方法对海底地声参数进行反演的方法还包括：The method for inverting the submarine geoacoustic parameters according to the nonlinear Bayesian inversion method further includes: 获取待反演参数的MAP值：
Figure FDA0002747291410000021
Get the MAP value of the parameter to be inverted:
Figure FDA0002747291410000021
 获取待反演参数的均值：
Figure FDA0002747291410000022
Get the mean of the parameters to be inverted:
Figure FDA0002747291410000022
 获取待反演参数的一维概率密度分布：P(mi|d)＝∫δ(mi-mi′)P(m′|d)dm′；Obtain the one-dimensional probability density distribution of the parameters to be inverted: P(m i |d)=∫δ(m i -m i ′)P(m′|d)dm′; 其中，δ狄拉克Delta函数；Among them, the delta Dirac Delta function; 获取待反演参数的相互关系：Get the interrelationship of the parameters to be inverted:
Figure FDA0002747291410000023
Figure FDA0002747291410000023
 其中，相关值Rij介于+1和-1之间，当相关值等于+1时，表示两个待反演参数完全相关；等于-1时表示两个待反演参数完全负相关；等于0时，表示两个待反演参数完全不相关；
Figure FDA0002747291410000024
分别表示模型参数向量m中参数间通过标准化协方差产生的相关矩阵。Among them, the correlation value R ij is between +1 and -1. When the correlation value is equal to +1, it means that the two parameters to be inverted are completely correlated; when it is equal to -1, it means that the two parameters to be inverted are completely negatively correlated; When it is 0, it means that the two parameters to be inverted are completely unrelated;
Figure FDA0002747291410000024
Respectively represent the correlation matrix generated by the standardized covariance between the parameters in the model parameter vector m. 4.如权利要求3所述的浅海多层海底地声参数反演方法，其特征在于，4. shallow sea multi-layer seabed geoacoustic parameter inversion method as claimed in claim 3, is characterized in that, 所述根据非线性贝叶斯反演方法对海底地声参数进行反演的方法还包括：The method for inverting the submarine geoacoustic parameters according to the nonlinear Bayesian inversion method further includes: 当数据误差为独立同分布的随机变量时似然函数为：When the data errors are independent and identically distributed random variables, the likelihood function is:
Figure FDA0002747291410000025
Figure FDA0002747291410000025
 其中，
Figure FDA0002747291410000026
为在频率为f下单个传感器在位置k接收到的测量声压，在相同情况下，
Figure FDA0002747291410000027
表示预测声压，
Figure FDA0002747291410000028
表示频率f下的协方差矩阵；in,
Figure FDA0002747291410000026
is the measured sound pressure received by a single sensor at position k at frequency f, under the same conditions,
Figure FDA0002747291410000027
represents the predicted sound pressure,
Figure FDA0002747291410000028
represents the covariance matrix at frequency f; 预测声压
Figure FDA0002747291410000029
为：
Figure FDA00027472914100000210
predict sound pressure
Figure FDA0002747291410000029
for:
Figure FDA00027472914100000210
 其中，
Figure FDA00027472914100000211
为通过快速场方法计算的声压；Af和θf为未知声源在每一个频率上的幅度和相位；in,
Figure FDA00027472914100000211
is the sound pressure calculated by the fast field method; A f and θ f are the amplitude and phase of the unknown sound source at each frequency; 当
Figure FDA00027472914100000212
获取声源的最大似然估计值：when
Figure FDA00027472914100000212
Obtain the maximum likelihood estimate for a sound source:
Figure FDA00027472914100000213
Figure FDA00027472914100000213
 其中，*为共轭转置；Among them, * is the conjugate transpose; 将角线协方差处理为
Figure FDA0002747291410000031
则似然函数为：Treat the corner covariance as
Figure FDA0002747291410000031
Then the likelihood function is:
Figure FDA0002747291410000032
Figure FDA0002747291410000032
 其中，方差vf与频率有关；I为单位阵；Bf(m)为归一化Bartlett失配器：Among them, the variance v f is related to the frequency; I is the identity matrix; B f (m) is the normalized Bartlett mismatcher:
Figure FDA0002747291410000033
Figure FDA0002747291410000033
 当
Figure FDA0002747291410000034
获取方差vf的最大似然估计值：when
Figure FDA0002747291410000034
Obtain the maximum likelihood estimate of variance v f :
Figure FDA0002747291410000035
Figure FDA0002747291410000035
 根据方差vf的最大似然估计值获取满足最大似然函数估计值时对应的误差函数E(m)：Obtain the corresponding error function E(m) when the estimated value of the maximum likelihood function is satisfied according to the maximum likelihood estimation value of the variance v f :
Figure FDA0002747291410000036
Figure FDA0002747291410000036
 5.如权利要求4所述的浅海多层海底地声参数反演方法，其特征在于，5. shallow sea multi-layer seabed geoacoustic parameter inversion method as claimed in claim 4, is characterized in that, 所述根据非线性贝叶斯反演方法对海底地声参数进行反演的方法还包括：The method for inverting the submarine geoacoustic parameters according to the nonlinear Bayesian inversion method further includes: 当测量数据d时，相应模型的似然函数为：When measuring data d, the likelihood function of the corresponding model is:
Figure FDA0002747291410000037
Figure FDA0002747291410000037
 其中，M是相应模型中参数的个数，N为数据参数个数；Among them, M is the number of parameters in the corresponding model, and N is the number of data parameters; 用误差函数代替似然函数以获取：Substitute the error function for the likelihood function to obtain:
Figure FDA0002747291410000038
Figure FDA0002747291410000038
 其中，BIC为贝叶斯信息准则，BIC值最小的模型即为最优模型。Among them, BIC is the Bayesian information criterion, and the model with the smallest BIC value is the optimal model. 6.如权利要求5所述的浅海多层海底地声参数反演方法，其特征在于，6. shallow sea multi-layer seabed geoacoustic parameter inversion method as claimed in claim 5, is characterized in that, 所述根据非线性贝叶斯反演方法对海底地声参数进行反演的方法还包括：The method for inverting the submarine geoacoustic parameters according to the nonlinear Bayesian inversion method further includes: 基于误差函数在先验区间搜索MAP值，并基于声阻抗的物理规律进行微正向扰动，即Based on the error function, the MAP value is searched in the prior interval, and the slight forward disturbance is performed based on the physical law of acoustic impedance, namely 初始化参数m1，m2；initialization parameters m 1 , m 2 ; 计算误差函数；Calculate the error function; 当满足m2>m1时进行随机扰动计算，否则进行微正向干扰使m2>m1后进行随机扰动计算；When m 2 >m 1 is satisfied, the random disturbance calculation is performed, otherwise, the micro forward disturbance is performed to make m 2 >m 1 , and then the random disturbance calculation is performed; 判断随机扰动计算的结果是否满足Metropolis准则，满足时保留参数m1，m2，否则重新判断m2>m1；Judge whether the result of random perturbation calculation satisfies the Metropolis criterion, keep the parameters m 1 , m 2 if so, otherwise re-judg m 2 >m 1 ; 判断保留的参数m1，m2是否满足终止条件，满足则输出参数，否则重新判断m2>m1；Determine whether the reserved parameters m 1 , m 2 satisfy the termination condition, and output the parameters if they are satisfied, otherwise re-judg m 2 >m 1 ; m1，m2为相邻两层海底，m1为靠近海平面一层海底的声速、密度、声速衰减以及沉积层深度；m2为远离海平面一层海底的声速、密度、声速衰减以及沉积层深度；m 1 , m 2 are the two adjacent seabed layers, m 1 is the sound velocity, density, attenuation of sound velocity and the depth of the sedimentary layer of a sea floor near the sea level; m 2 is the sound velocity, density, attenuation of sound velocity and the depth of the sedimentary layer; 所述声阻抗的物理规律为：cm+1ρm+1≥cmρm m＝1,…,n；The physical law of the acoustic impedance is: c m+1 ρ m+1 ≥c m ρ m m=1,...,n; 其中，c表示声速，ρ表示密度。where c is the speed of sound and ρ is the density.
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CN113330439A (en) * 2021-04-29 2021-08-31 浙江海洋大学 Shallow sea multilayer seabed ground sound parameter inversion method and device, computer equipment and storage medium
WO2022226856A1 (en) * 2021-04-29 2022-11-03 浙江海洋大学 Method and apparatus for inverting geoacoustic parameters of multilayer seabed in shallow sea, and computer device and storage medium
CN113176609B (en) * 2021-04-29 2023-10-10 中北大学 Underground shallow target positioning method based on earth sound field
CN113553773A (en) * 2021-08-16 2021-10-26 吉林大学 Inversion method of ground-air electromagnetic data based on Bayesian framework combined with neural network
CN113553773B (en) * 2021-08-16 2023-01-24 吉林大学 Ground-air electromagnetic data inversion method based on Bayesian framework combined with neural network
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CN115824458A (en) * 2023-02-22 2023-03-21 自然资源部第一海洋研究所 Method and device for inverting water temperature of bottom layer of seabed
CN116559943A (en) * 2023-05-06 2023-08-08 中国人民解放军国防科技大学 A joint inversion method and system for geoacoustic parameters based on Pearson correlation constraints
CN119272608A (en) * 2024-08-28 2025-01-07 浙江海洋大学 Inversion method of seafloor sediment parameters based on multi-layer perceptron

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Application publication date: 20210101