A Bayesian geoacoustic parameter inversion method based on Wasserstein metric

Abstract

The present application provides a Bayesian geoacoustic parameter inversion method, including: obtaining geoacoustic observation data and geoacoustic synthesis data; constructing multiple KRAKENC geoacoustic forward models corresponding to the hierarchical model of the geoacoustic observation data; determining the exponential likelihood distribution of multiple KRAKENC geoacoustic forward models according to the geoacoustic observation data and the geoacoustic synthesis data using the Wasserstein metric form; and calculating the posterior probability distribution of the geoacoustic observation data using the Bayesian algorithm according to the selected exponential likelihood distribution and the prior distribution; using the Markov chain Monte Carlo simulation algorithm, performing random sampling processing on the posterior probability distribution to obtain random sampling data points, calculating the sampling expectation values ​​corresponding to the random sampling data points, and determining the Bayesian geoacoustic inversion results corresponding to the geoacoustic observation data according to the sampling expectation values. The accuracy of sedimentary layer attenuation inversion is improved, and the uncertainty of waveform inversion is significantly reduced.

Description

Technical Field

[0001] The present application relates to the technical field of seabed geoacoustic parameter inversion, and in particular to a Bayesian geoacoustic inversion method, device, electronic device and storage medium based on the Wasserstein metric. Background Art

[0002] Geoacoustic inversion is a technology that infers the acoustic characteristics of the seabed based on the underwater sound field information observed by hydrophones. By establishing physical models and mathematical algorithms, the observed data are used to invert parameters such as seabed sound velocity, seabed density, seabed attenuation and layered structure. Its role is to help predict underwater sound propagation, underwater acoustic communications, earthquake monitoring and many other fields.

[0003] In the process of geoacoustic inversion, the likelihood function is an important basis for parameter estimation. The model parameters that are most likely to produce the observed data are determined by finding the parameter value that makes the likelihood function reach the maximum value, that is, the maximum likelihood estimation. In some complex high-dimensional data generation scenarios, the likelihood function may be difficult to calculate or there may be some problems, which may lead to the problem of low accuracy in geoacoustic parameter inversion. Summary of the invention

[0004] In order to overcome the above technical defects, the present application provides a Bayesian geoacoustic inversion method, storage medium and device based on the Wasserstein metric.

[0005] To achieve the above objectives, this application is implemented according to the following technical solutions:

[0006] In a first aspect, the present application provides a Bayesian geoacoustic inversion method based on the Wasserstein metric.

[0007] A Bayesian geoacoustic inversion method based on Wasserstein metric form includes:

[0008] Acquire geoacoustic observation data and geoacoustic synthesis data;

[0009] Constructing a plurality of KRAKENC geoacoustic forward models corresponding to the hierarchical model of the geoacoustic observation data;

[0010] Determining the exponential likelihood distribution of the plurality of KRAKENC geoacoustic forward models using the Wasserstein metric form according to the geoacoustic observation data and the geoacoustic synthesis data;

[0011] Determining a selected exponential likelihood distribution of the KRAKENC geoacoustic forward model based on the exponential likelihood distribution;

[0012] Obtaining a prior distribution; and calculating the posterior probability distribution of the geoacoustic observation data using a Bayesian algorithm based on the selected exponential likelihood distribution and the prior distribution;

[0013] The Markov chain Monte Carlo simulation algorithm is used to perform random sampling on the posterior probability distribution to obtain a random

[0014] The random sampling data points are sampled, and a sampling expectation value corresponding to the random sampling data points is calculated, and a Bayesian geoacoustic inversion result corresponding to the geoacoustic observation data is determined according to the sampling expectation value.

[0015] Optionally, the step of calculating the exponential likelihood distribution of the KRAKENC geoacoustic forward model based on the geoacoustic observation data and using the Wasserstein metric comprises:

[0016] The geoacoustic observation data and the geoacoustic synthesis data are transformed by Hilbert transformation, and then the geoacoustic observation analysis signal and the geoacoustic synthesis signal are outputted, wherein the analysis signal includes an observation analysis signal and a synthesis analysis signal;

[0017] Based on the analytical signal, the exponential likelihood distribution of the KRAKENC geoacoustic forward model is determined using the Wasserstein metric.

[0018] Optionally, determining the exponential likelihood distribution of the KRAKENC geoacoustic forward model in a Wasserstein metric form according to the analytical signal comprises:

[0019] Solve the module of the observed analytical signal to obtain the observed envelope signal ;

[0020] Solve the module of the synthetic analytical signal to obtain the synthetic envelope signal ;

[0021] The observed envelope signal and synthesized envelope signal Perform softplus transformation to obtain the observed waveform and synthetic field waveform , specifically:

[0022] In the formula, is an adjustable hyperparameter;

[0023] Based on the observed waveform and the synthetic field waveform volume , the Wasserstein metric is used to determine the exponential likelihood distribution of the KRAKENC geoacoustic forward model.

[0024] Optionally, the amount of the observed waveform and the synthetic field waveform volume , using the Wasserstein metric form, the exponential likelihood distribution of the KRAKENC geoacoustic forward model is calculated, including:

[0025] The observed waveform quantity is and the synthetic field waveform volume Calculate the exponential likelihood distribution of the KRAKENC geoacoustic forward model, specifically:

[0026] In the formula, is a hyperparameter that can be estimated in the sampling algorithm. represents the number of geoacoustic observation data, is the second-order Wasserstein distance, represents the FWH observation signal, By receiving the composite signal Operators that generate FWH synthetic fields, and They correspond to the observed waveform and synthetic field waveform that meet the Wasserstein metric requirements after softplus transformation. Represents the model parameter vector included in the KRAKENC geoacoustic forward model.

[0027] Optionally, determining a selected exponential likelihood distribution of the KRAKENC geoacoustic forward model based on the exponential likelihood distribution comprises:

[0028] The exponential likelihood distribution is parameterized using the BIC criterion to determine the selected exponential likelihood distribution of the KRAKENC geoacoustic forward model.

[0029] Optionally, determining the Bayesian geoacoustic result corresponding to the geoacoustic observation data according to the sampling expected value includes:

[0030] Comparing the sampled expected value with a preset expected value;

[0031] When the sampling expected value is greater than the preset expected value, the geoacoustic observation data corresponding to the sampling expected value is queried in the geoacoustic forward model, and the geoacoustic observation data is used as the Bayesian geoacoustic inversion result corresponding to the geoacoustic observation data.

[0032] In a second aspect, the present application provides a computer device, comprising a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set or an instruction set, and the at least one instruction, at least one program, a code set or an instruction set is loaded and executed by the processor to implement the Bayesian geoacoustic inversion method based on the Wasserstein metric form as described in any one of the first aspects.

[0033] In a third aspect, the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores at least one instruction, at least one program, code set or instruction set, and the at least one instruction, at least one program, code set or instruction set is loaded and executed by a processor to implement the Bayesian geoacoustic inversion method based on the Wasserstein metric form as described in any one of the first aspects.

[0034] This application has the following beneficial effects:

[0035] In the present application, the Wasserstein metric form is adopted in the process of determining the likelihood function, thereby improving the accuracy of sedimentary layer attenuation inversion and significantly reducing the uncertainty of waveform inversion.

[0036] In addition to the above-described purposes, features and advantages, the present application has other purposes, features and advantages. The present application will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0038] Figure 1 It is a flowchart of a Bayesian geoacoustic inversion method based on the Wasserstein metric provided in this application.

[0039] Figure 2 It is a schematic diagram of the SW06 simulation experiment environment characteristics provided for the experimental verification of this application.

[0040] FIG3( a ) is a diagram of the original waveform signal received by the hydrophone during the experimental verification phase of this application.

[0041] FIG3( b ) is a diagram of the warping signal after warping transformation in the experimental verification phase of this application.

[0042] FIG3( c ) is a diagram of the received signal restored after inverse warping transformation in the experimental verification stage of this application.

[0043] Figure 4(a) Schematic diagram of the spatial distribution of the sound field at 50 Hz in the numerical environment during the experimental verification phase of this application.

[0044] Figure 4 (b) Schematic diagram of the spatial distribution of the sound field at 150 Hz in the numerical environment during the experimental verification phase of this application.

[0045] FIG5( a ) is a spectrum diagram of the Warping signal in the experimental verification stage of this application.

[0046] Figure 5(b) is the spectrum diagram of the warping signal in the 0-50 Hz frequency band during the experimental verification phase of this application.

[0047] FIG5( c ) is a spectrum diagram of the received signal in the experimental verification stage of this application.

[0048] Figure 6 This is a schematic diagram of the posterior prediction distribution of the Bayesian inversion of the dispersion feature at the L2 distance in the experimental verification stage of this application.

[0049] FIG7( a ) is a schematic diagram of the posterior prediction distribution of the L2-FWH-Bayesian inversion in the experimental verification stage of this application.

[0050] FIG7( b ) is a schematic diagram of the posterior prediction distribution of the Was-FWH-Bayesian inversion in the experimental verification stage of this application.

[0051] FIG8( a ) is a schematic diagram of the posterior distribution of the likelihood function under the L2-D-Bayesian inversion method in the experimental verification stage of this application.

[0052] FIG8( b ) is a schematic diagram of the posterior distribution of the likelihood function under the L2-FWH-Bayesian inversion method in the experimental verification stage of this application.

[0053] FIG8( c ) is a schematic diagram of the posterior distribution of the likelihood function under the Was-FWH-Bayesian inversion method (softlpus function b=1.31) in the experimental verification stage of this application.

[0054] FIG8( d ) is a schematic diagram of the posterior distribution of the likelihood function under the Was-FWH-Bayesian inversion method (softlpus function b=0.57) in the experimental verification stage of this application.

[0055] Fig. 9 It is a schematic diagram of the one-dimensional and joint marginal posterior distributions of the L2-D-Bayesian inversion in the experimental verification stage of this application.

[0056] Fig.10 It is a schematic diagram of the one-dimensional and joint marginal posterior distributions of the L2-FWH-Bayeisan inversion in the experimental verification stage of this application.

[0057] Fig.11 It is a schematic diagram of the one-dimensional and joint marginal posterior distributions of the Was-FWH-Bayesian inversion in the experimental verification stage of this application. DETAILED DESCRIPTION

[0058] The embodiments of the present application are described in detail below with reference to the accompanying drawings; however, the present application can be implemented in many different ways as defined and covered by the claims.

[0059] In order to solve the problems raised by the above background technology, Figure 1 As shown, this application proposes a Bayesian geoacoustic inversion method based on the Wasserstein metric form, the steps are as follows:

[0060] Step S1: Acquire geoacoustic observation data and geoacoustic synthesis data;

[0061] Hydroacoustic observation data containing seabed acoustic information refers to the data obtained by monitoring and recording the acoustic signals emitted by cooperative or non-cooperative sound sources propagating through ocean waveguides at specific underwater locations through an acoustic array containing hydrophone elements. These data reflect the information of underwater broadband sound propagation and scattering, seawater sound velocity structure and seabed acoustic parameters. For example, in earthquake monitoring, geoacoustic observation data records the sound generated by crustal movement before and after an earthquake; in volcano monitoring, it is the sound record generated by magma activity, gas eruption and other processes inside the volcano. For example, in passive acoustic monitoring of shallow sea areas, marine environmental noise, random source radiation noise, etc. are often used for geoacoustic parameter inversion; and in acoustic detection of controlled sound sources, especially under broadband conditions, hydroacoustic signal waveform pulses, seabed reflection coefficients and propagation losses are often used for geoacoustic parameter inversion.

[0062] Geoacoustic synthetic data is data that simulates the characteristics of geoacoustic signals generated through theoretical models, computer simulations or other artificial construction methods. It is not a real signal directly obtained from actual geoacoustic observations, but a data set generated according to certain physical or mathematical rules based on parameterized assumptions and mathematical descriptions of factors such as ocean environment waveguide characteristics, sound source characteristics, and underwater sound propagation.

[0063] It should be noted that the geoacoustic observation data mentioned above is also geoacoustic synthesis data. Since signals are also a kind of data, geoacoustic observation data can also be called geoacoustic observation signals, and geoacoustic synthesis data can also be called geoacoustic observation signals. Generally, they include sound velocity parameters, density parameters, attenuation coefficients and seabed stratification parameters.

[0064] In the present application, a single hydrophone is used to receive the above-mentioned geoacoustic observation signal and the simulated synthetic signal.

[0065] Step S2: constructing a plurality of KRAKENC geoacoustic forward models corresponding to the hierarchical model of the geoacoustic observation data;

[0066] After the geoacoustic observation data are obtained, it is necessary to construct multiple KRAKENC geoacoustic forward models corresponding to the hierarchical model of the geoacoustic observation data based on the obtained geoacoustic observation data.

[0067] Since this application is mainly used for the inversion of broadband waveforms, the seabed is parameterized. When parameterizing the seabed, a layered model is used, which means that the geological structure of the seabed is regarded as consisting of multiple different layers. It's like imagining the seabed as a multi-layered "cake", each layer has its own characteristics. This layered approach helps to describe the complex acoustic characteristics of the seabed more finely, because different strata may differ in terms of sound speed, density, attenuation coefficient and thickness. Then, multiple KRAKENC geoacoustic forward models corresponding to different layered models are determined. Due to different layered models, it means that there are different parameterization schemes, and the parameterization schemes between different layered models are different. This means that there are multiple KRAKENC geoacoustic forward models, and each KRAKENC geoacoustic forward model has different parameters, and thus the corresponding parameterization schemes are also different. In order to facilitate calculation and understanding, we assume that the number of parameters of each KRAKENC geoacoustic forward model is , and then we can get the corresponding model parameter vector KRAKENC, one of the underwater acoustic models, requires a mesh to simulate a 3D environment. In the field of underwater sound modeling, KRAKENC has been applied to many environmental studies. Therefore, the forward model KRAKENC is not described in detail.

[0068] Taking the hierarchical model ( The seafloor is parameterized by the sound velocity parameter, density parameter, attenuation coefficient and thickness ( The parameter sound velocity of the sedimentary layer in the two-layer model is a negative gradient structure, and the bottom layer is a homogeneous uniform layer. Therefore, the two-layer model is divided into two cases when the parameterization scheme is selected: one is that the upper layer sound velocity is a negative gradient structure, which is defined by the sound velocity at the top and bottom of the layer, and is recorded as a "2+1" layer model; the other is a "2" layer model with uniform stratification.

[0069] Step S3: Determine the exponential likelihood distribution of the multiple KRAKENC geoacoustic forward models according to the geoacoustic observation data and the geoacoustic synthesis data using the Wasserstein metric form;

[0070] The Wasserstein metric, also known as the Earth Mover's Distance (EMD), is a metric used to measure the distance between two probability distributions.

[0071] After determining multiple KRAKENC geoacoustic forward models, due to the presence of noise in geoacoustic observation data and geoacoustic synthesis data, in order to improve the accuracy of the signal processing algorithm, the Wasserstein (bulldozer distance) metric with low noise sensitivity is used to determine the selected exponential likelihood distribution of the KRAKENC geoacoustic forward model. The selected exponential likelihood distribution is to determine the corresponding exponential likelihood distribution for multiple KRAKENC geoacoustic forward models, and then use the BIC criterion method to determine an exponential likelihood distribution with the minimum BIC value. The specific process of solving the selected exponential likelihood function is as follows:

[0072] Since the geoacoustic observation signal and geoacoustic synthesis signal finally received in the above are hydroacoustic signals, and hydroacoustic signals cannot meet the requirements of Wasserstein metric, it is necessary to preprocess the signal. The main difficulty in applying Wasserstein metric to hydroacoustic waveform structure is that the signal does not meet the mass conservation and non-negativity constraints. Since Hilbert transform can be used to calculate the instantaneous properties of time series, especially amplitude and frequency. Therefore, we use Hilbert transform to transform the geoacoustic observation data and geoacoustic synthesis data, and output the geoacoustic observation analysis signal and geoacoustic synthesis analysis signal.

[0073] After obtaining the geoacoustic observation analytical signal and the geoacoustic synthetic analytical signal, the selected exponential likelihood distribution of the KRAKENC geoacoustic forward model is calculated using the Wasserstein metric form according to the geoacoustic observation analytical signal and the geoacoustic synthetic analytical signal. That is, the modulus of the observed analytical signal is solved to obtain the observed envelope signal ; Solve the module of the synthetic analytical signal to obtain a synthetic envelope signal .

[0074] For the mass conservation constraint, converting the signal into a probability distribution is the key to satisfying the conservation property, which directly affects the convexity of the objective function. Considering that the seismic signal is similar to the hydroacoustic signal, the scaling function softplus function used in the related work of seismic acoustic waveform inversion is selected here to observe the envelope signal. and synthesized envelope signal Perform softplus transformation to obtain the observed waveform and synthetic field waveform , specifically:

[0075] (1)

[0076] In the formula, is an adjustable hyperparameter; the hyperparameter can be adjusted automatically during the actual transformation process. It is related to the convexity of the objective function.

[0077] The Wasserstein metric is less sensitive to noise, so in the subsequent signal processing process, the lower noise sensitivity helps to improve the accuracy of the signal processing algorithm. This paper constructs the Wasserstein metric-likelihood function based on the exponential function, which can ensure that when the Bayesian posterior takes the negative logarithm, the mismatch function of the Wasserstein metric form in the likelihood function is restored. , written as:

[0078] (2)

[0079] In the formula, is a hyperparameter that can be estimated in the sampling algorithm. represents the number of geoacoustic observation data, is the second-order Wasserstein distance, and They correspond to the observed waveform and synthetic field waveform that meet the Wasserstein metric requirements after softplus transformation. Represents the model parameter vector included in the KRAKENC geoacoustic forward model.

[0080] Substituting formula (2) into formula (1), we get the following formula (3). By using formula (3), we can calculate and determine the exponential likelihood distribution of multiple KRAKENC geoacoustic forward models corresponding to different hierarchical models.

[0081] (3)

[0082] In the formula, is a hyperparameter that can be estimated in the sampling algorithm. represents the number of geoacoustic observation data, is the second-order Wasserstein distance, Represents the FWH (Full Width at Half-Maximum) observed (including Hilbert transform process) signal, By receiving the composite signal Operators that generate FWH synthetic fields, and They correspond to the observed waveform and synthetic field waveform that meet the Wasserstein metric requirements after softplus transformation. Represents the model parameter vector included in the KRAKENC geoacoustic forward model.

[0083] It should be noted that the Wasserstein metric can be calculated in any dimension by numerically solving the Monge–Ampère form. For the case where the dimension is greater than 1 and there are multiple signals, such as the waveform signal matching problem of a multi-hydrophone array, considering the computational cost, a "track-by-track" method can be used to add the one-dimensional Wasserstein distances of multiple hydrophones.

[0084] Step S4: determining a selected exponential likelihood distribution of the KRAKENC geoacoustic forward model based on the exponential likelihood distribution;

[0085] In practical problems, the parameterization scheme of the geoacoustic model (such as the number of seafloor layers) cannot be directly determined. Using too few parameters will lead to insufficient data fitting, parameter estimation bias, and inaccurate parameter uncertainty estimation. Using too many parameters will overfit the data, resulting in large parameter variance.

[0086] Therefore, after using formula (3) to calculate the exponential likelihood distribution of multiple KRAKENC geoacoustic forward models corresponding to the hierarchical model, the BIC criterion is then used to calculate the exponential likelihood distribution of multiple KRAKENC geoacoustic forward models, and the selected exponential likelihood distribution of the KRAKENC geoacoustic forward model is determined, and then the model with the selected exponential likelihood distribution is determined as the forward model with the best inversion effect. The calculation process is as follows:

[0087] (4)

[0088] Where, is the Wasserstein metric-likelihood function value, is the number of model parameters, is the number of geoacoustic observation data;

[0089] The above formula (4) can be written as (5)

[0090] In the formula, To represent the specified parameterization scheme, each KRAKENC geoacoustic forward model corresponds to a specified parameterization scheme.

[0091] The above calculation process can also be understood as determining the hierarchical parameterization scheme of the seabed acoustic model based on the BIC criterion, and realizing the forward calculation based on the KRAKENC model of the simple normal wave theory. The parameterization scheme with the minimum BIC value is selected as the most suitable model (minimizing BIC is a regularization scheme). The first term on the right side of the formula is used to match the model with a smaller error, that is, as As increases, the mismatch decreases; the second term is balanced by imposing a penalty term on the free parameters to prevent over-parameterization.

[0092] Step S5: taking a prior distribution, and calculating the posterior probability distribution of the geoacoustic observation data using a Bayesian algorithm based on the selected exponential likelihood distribution and the prior distribution;

[0093] After the selected exponential likelihood distribution is determined, the model corresponding to the optimal parameterization scheme is determined. Then, based on the selected exponential likelihood distribution and the prior distribution, the Bayesian algorithm is used to calculate the posterior probability distribution of the geoacoustic observation data.

[0094] Prior distribution is a concept in Bayesian statistics. In Bayesian reasoning, we describe the uncertainty of an unknown parameter (or multiple parameters) before observing data in a probabilistic way. This probability distribution is the prior distribution. It reflects our estimate of the possible range of parameter values ​​and their probabilities based on previous experience, theoretical knowledge or subjective judgment before conducting experiments, observing or collecting data. Prior distribution can reduce the uncertainty in the inversion process to a certain extent. In a complex geoacoustic system, relying solely on observed data may lead to greater uncertainty in the inversion results because the observed data may be interfered by noise or incomplete. Prior distribution constrains the inversion parameters by providing additional information, making the inversion results more stable. At the same time, it also helps to prevent overfitting, that is, prevent the model from over-relying on observed data and producing complex results that do not conform to the actual situation. It should be noted that this article does not make specific restrictions on the way to obtain the prior distribution and its specific form of expression. You can choose the appropriate prior distribution according to the actual situation on site.

[0095] The Bayesian algorithm used above is: ;

[0096] Among them, P(m|d) represents the posterior probability distribution of the geoacoustic observation data, and P′(m) represents the probability distribution of the geoacoustic observation data.

[0097] The prior distribution, P(d|m) represents the selected exponential likelihood distribution of the geoacoustic observation data, ∝ represents a Bayesian function, and d represents the number of geoacoustic observation data.

[0098] Step S6: Using the Markov Chain Monte Carlo simulation algorithm, randomly sample the posterior probability distribution to obtain random sampling data points, calculate the sampling expectation values ​​corresponding to the random sampling data points, and determine the Bayesian geoacoustic inversion results corresponding to the geoacoustic observation data based on the sampling expectation values.

[0099] This step mentions using a Markov chain Monte Carlo simulation algorithm to perform random sampling on the posterior probability distribution to obtain randomly sampled data points, which is a common method in this field. Therefore, you can choose it at your own discretion and the process will not be elaborated on in detail.

[0100] In this application, the sampling expected value corresponding to the random sampling data point is calculated using the following formula, including:

[0101] (6)

[0102] in, represents the expected value of the distribution corresponding to the randomly sampled data point, represents the value corresponding to the randomly sampled data point, represents the number of convergence steps, represents the number of iteration steps, Represents the first of the randomly sampled data points Sample points.

[0103] Furthermore, the embodiment of the present application determines the Bayesian seismic inversion result corresponding to the geoacoustic observation data according to the sampling expected value, so as to use the geoacoustic observation data with a higher expected value as the final inversion result. Compared with the conventional Bayesian seismic inversion method that uses other calculation methods to determine the exponential likelihood distribution, the Bayesian seismic inversion method based on the Wasserstein metric can obtain more accurate inversion results of the geoacoustic observation data.

[0104] In some embodiments, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the processor implements the Bayesian geoacoustic parameter inversion method based on the Wasserstein metric provided in the first aspect.

[0105] It will be understood by those skilled in the art that all or some of the steps, systems, and functional modules / units in the methods disclosed above may be implemented as software, firmware, hardware, and appropriate combinations thereof. In a hardware implementation, the division between the functional blocks / units mentioned in the above description does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed by several physical components in cooperation. Some or all physical components may be implemented as software executed by a processor, such as a central processing unit, a digital signal processor, or a microprocessor, or may be implemented as hardware, or may be implemented as an integrated circuit, such as an application-specific integrated circuit. Such software may be distributed on a computer-readable storage medium, which may include a computer-readable storage medium (or a non-transitory medium) and a communication medium (or a transient medium).

[0106] As is known to those of ordinary skill in the art, the term computer-readable storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storing information such as computer-readable instructions, data structures, program modules, or other data. Computer-readable storage media include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tapes, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store the desired information and can be accessed by a computer. In addition, as is known to those of ordinary skill in the art, communication media typically contain computer-readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave or other transport mechanism, and may include any information delivery media.

[0107] Exemplarily, the computer-readable storage medium may be an internal storage unit of the network management device described in the foregoing embodiment, such as a hard disk or memory of the network management device. The computer-readable storage medium may also be an external storage device of the network management device, such as a plug-in hard disk, a smart memory card (SmartMediaCard, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc., equipped on the network management device.

[0108] In some embodiments, a device is provided, including a processor and a memory, wherein the memory is used to store a computer program; the processor is used to execute the computer program and implement the Bayesian geoacoustic parameter inversion method based on the Wasserstein metric form provided in the first aspect of the present application when executing the computer program.

[0109] It should be understood that the processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. Among them, the general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0110] Experimental verification:

[0111] This paper chooses to simulate the SW06 experimental environment for numerical experiments. The numerical environment construction and signal generation simulation considers the environment that is not related to distance. The environmental characteristics are based on the SW06 measured results and combined with the inversion estimation results of existing studies. The simulation environment parameters are shown in Figure 2 , the water depth is 80 m, and the sound speed of the water body adopts the real measured sound speed profile (SSP). The SW06 experimental area is affected by strong internal waves (including internal tides), and the sound speed in the water body changes strongly and rapidly. The bathymetric and seabed sediment characteristics do not change with horizontal distance, and have a flat seabed environment. The seabed parameterization scheme selects a 2-layer model with a 25m thick sediment layer covering the basement half space. Consider 7 seabed parameters to be estimated: the compression wave speed of the sediment layer is always equal to 1600 m / s, the density is 1.7 , the attenuation coefficient is 0.15 . Basal layer sound speed 2100 , density is 2.5 , the attenuation coefficient is 0.6 The corresponding geoacoustic inversion parameters and uniform distribution prior intervals are shown in Table 1. The rate parameter takes the Gamma prior. In addition, according to Hamilton's

[66] empirical relationship (7)

[0112] (8)

[0113] Determine the density (unit: ) and the speed of sound (unit: )’s lower and upper limits.

[0114] The sound source signal is composed of a four-cycle sine wave weighted by Hanning, which is used to simulate the pulse source. The sound source depth is 22 m. The single hydrophone receives the signal at a distance of 7 km from the signal source and a depth of 55 m. As can be seen from the spectrum shown in Figure 3, the signal energy is well controlled between 50-150 Hz. The received signal is also plotted in the figure. The signal is generated according to the simulation generation method in the Workshop'97Benchmark example, and the frequency response of every 1 Hz in the range of 50 to 150 Hz is generated according to the SAFARI model. Horizontal calculation step , the minimum phase velocity is set to , but according to ( The calculation frequency is adjusted in real time to ensure a positive calculation wave number. The received signal is then synthesized based on the frequency response of the complex sound pressure and the pulse signal, and the received signal is superimposed with a noise with an SNR of 6dB to simulate actual observation. The SNR can be expressed as the logarithmic ratio of the signal power to the Gaussian white noise power under the same bandwidth:

[0115] (9)

[0116]

[0117] Figure 4 (a) is the distribution diagram of the sound field at 50 Hz. Figure 4 (b) is the distribution diagram of 150 Hz. The low-frequency field of 50 Hz can penetrate the entire waveguide distance between the sound source and the hydrophone, and the low-frequency field can penetrate the sediment layer to reach the half space; at a higher frequency of 150 Hz, the sound field can still penetrate the sediment layer within the first 2 km distance after the sound source is emitted, and the sound field after 4 km is limited to the upper part of the water / sediment and degenerates to be sensitive only to the characteristics of the seabed interface. Therefore, according to the sound field, the broadband modeling inversion adopted in this paper is necessary.

[0118] Feature extraction and posterior predictive distribution

[0119] Extraction and prediction of normal wave modal dispersion curves

[0120] Figure 3 (a) is the original waveform signal received by the hydrophone, Figure 3 (b) is the warped signal after the warping transformation of the original waveform signal received by the hydrophone, and Figure 3 (c) shows that the main energy broadening range of the original signal is about 0.4 s. According to Figure 3 (b), the main energy broadening of the warped signal in the warping time domain is about 1.8 s, which is mainly due to the linear transformation of the signal phase. The dots in Figure 3 (c) show that the received signal is restored by the inverse warping function, which proves that the warping transformation is reversible and robust, ensuring the conservation of mass before and after the transformation.

[0121] The spectrum in Figure 5(c) is obtained by performing a time-frequency transform on the time series in Figure 3(a). It can be clearly seen from the spectrum that the energy of the signal is effectively limited below 150 Hz. However, since the coupling between the first and second modes is too significant, the conventional modal filtering method cannot be used directly to separate the dispersion curves. The Warping transform shows good superiority, as shown in Figure 5(a). Although the four warping modes are not completely stable, they can also be separated in the time-frequency domain by manual flooding extraction. This theory is consistent with the theory because it can be found that the warping function is approximated by an ideal constant velocity waveguide, rather than the nonlinear sound velocity profile in this experiment ( Figure 2 ), so the energy and warping frequency in the warping domain appear to be "approximately linearized".

[0122] Then, a custom mask is created for the warped signal in the time-frequency domain. (The more prominent polygon in Figure 5 (a)) separates the single warping mode. The dispersion curve is estimated by performing an inverse short-time Fourier transform on these warping modes to achieve modal filtering. The results show that for a single hydrophone receiving signal, the modes can be separated by the warping transform even when there are different modal peaks interlaced on the spectrum diagram. In summary, the warping transform successfully separates the first four coupled normal wave modes in the 50-150 Hz band. According to the amplitude of the warping signal in the frequency domain, it can be found that the fourth-order modal energy is significantly lower than the first three orders. The extracted dispersion curve can be applied to the next step of dispersion inversion research.

[0123] The dispersion inversion results based on L2-Bsayesian are as follows Figure 6 As shown in the figure, the matching relationship between the observed data (red solid line), the posterior prediction (blue dashed line on the far right) and the MAP prediction (green dashed line) is shown, where the shaded gray area represents the 95% posterior interval. According to the matching degree of the dispersion curve, it can be found that the dispersion curves of the first to third order modes match well. It is worth noting that the uncertainty of the predicted distribution of the low-frequency part below 95 Hz of the fourth mode is very large. By combining the extraction results of the dispersion curve in Figure 5, it can be inferred that the estimation of the Airy phase is inaccurate due to the large extraction deviation of the fourth order mode.

[0124] Broadband FWH waveform calculation and prediction distribution

[0125] Figure 7 shows the FWH observation field, MAP prediction, posterior prediction distribution, and average distribution results of the L2-FWH-Bayesian inversion and Was-FWH-Bayesian inversion. Overall, the FWH signal achieves good matching results in both distance (metric) cases, but the confidence interval of the posterior prediction distribution of the L2-FWH-Bayesian inversion is wider and increases with the time series, and the confidence interval widening is inconsistent within the entire sampling. In contrast, the overall uncertainty range of the posterior prediction of the Was-FWH-Bayesian inversion is lower than that of the L2-FWH-Bayesian inversion method. In the 4-6 s range, the RMSE of the posterior prediction and observed FWH of the former is only 0.0108, while the RMSE of the latter is 0.102.

[0126] Posterior Probability Distribution and Uncertainty Analysis

[0127] Table 2 gives the MAP results and average inversion results of the three inversion methods. It can be seen that the L2-D and Was-FWH-Bayesian methods have achieved good estimates of the sedimentary layer thickness, sound velocity and density, while the L2-FWH-Bayesian method's estimation result for the sedimentary layer thickness is less than the true value, with a MAP deviation of 2.48 m and a mean deviation of 2.44 m. Overall, the parameter accuracy of the dispersion inversion is greater than that of the waveform structure inversion. This is related to the fact that the warping transform can ensure the accuracy of the group velocity dispersion curve extraction under a certain noise level, while the waveform structure is more susceptible to noise interference. In addition, the small number of parameters in the dispersion inversion also reduces the uncertainty of the parameter search space. For the basement sound velocity, the MAP result of the Was-FWH-Bayesian method has the largest deviation from the true value, which is 59.10 m / s. The MAP result of the L2-FWH-Bayesian method is completely consistent with the true value, which is consistent with Figure 4 The result that the basement layer does not contain acoustic field information is inconsistent. This shows that the estimation result alone is not enough to support the inversion result, and the uncertainty of the estimation must also be considered.

[0128]

[0129] Figure 8 shows the PPD distribution of the likelihood functions of the four inversion methods. Figure 8 (a) and Figure 8 (b) represent the PPD distribution of the likelihood functions of L2-D-Bayesian and L2-FWI-Bayesian inversion, respectively. It can be found that although there are many local minimum points in both methods, the specific details are different. The likelihood function posterior of the L2-D-Bayesian inversion has a high acoustic velocity along the sediment layer. The distribution of the axis is ridge-like, while in the L2-FWH-Bayesian inversion, this distribution is indeed irregular and has many local peaks, which shows that the likelihood function based on the dispersion curve is not very accurate for the parameter The change of is more sensitive than the likelihood function of FWH. Figure 8 (c) and Figure 8 (d) represent the posterior distribution of the likelihood function of Was-FWH-Bayesian inversion under two softplus function parameters. By comparing the inversion method based on L2, it can be found that the likelihood function based on Wasserstein metric is dominant in overall convexity, and there is no local peak like the likelihood posterior of L2-FWH-Bayesian method. Even when the Bartlett matching field likelihood function takes into account the global signal characteristics, it cannot change the situation that the L2 distance uses point-by-point fitting of the matching field and observation field errors, that is, the same L2 distance may correspond to a variety of different waveform distributions, such as the local peak shown in Figure 8 (b). The peaks in the area far away from the true value will reduce the efficiency of the algorithm, while the peaks near the true value will bring more uncertainty distribution to the sampling results. Under the condition of ensuring mass conservation, the matching field and the observation field are converted into distribution forms, and the difference between the two is measured by Wasserstein metric, which can obtain a more stable and more convex likelihood function space. It is worth noting that different hyperparameters in the softplus function will change the convexity of the likelihood function. Specifically, when b=0.57, the posterior distribution of the likelihood function has multiple local extreme values ​​in the range of 1423 m / s to 1697 m / s for the sedimentary layer sound velocity and 1800 m / s to 2195 m / s for the basement layer sound velocity, while the convexity of the posterior distribution of the likelihood function when b=1.31 is better than the former. Therefore, different hyperparameters of the softplus function will lead to different posterior distributions of the likelihood function.

[0130] The interrelationships between parameters can be studied using the joint marginal probability density. Fig. 9 The one-dimensional and two-dimensional marginal posterior distributions of L2-FWH inversion are given. First, the most notable feature of the one-dimensional marginal distribution is that the sedimentary layer parameters have a higher kurtosis than the basement layer parameters and are thin-tailed (except for the density parameter), while the sedimentary layer sound velocity It is shown as a multi-peak thick-tailed distribution. and sediment density shows a strong correlation, which is logical. The modal cutoff frequency will be reduced and the dispersion curve will be contracted. However, the increase in sound velocity can be compensated by the increase in density, so that the dispersion curve returns to its original position. Speed ​​of sound From the joint margin of , Therefore, although MAP agrees well with the true value, the actual uncertainty is large, which also illustrates the necessity of Bayesian inversion to estimate parameter uncertainty.

[0131] Compared with the large uncertainty of the basement parameters in the L2-D-Bayesian inversion, the L2-FWH-Bayeisan inversion has a larger uncertainty for the basement, e.g. Fig.10 Here, the uncertainty interval is described by the 95% highest probability density (HPD) credible interval. The HPD range exceeds 200m / s, and the base layer density HPD ranges from 2.31 to 2.67 For broadband waveform inversion, the most important parameters are the attenuation parameter and the sedimentary layer parameter. The marginal distribution of shows a significant flatness in the central region [0.169, 0.172], showing a relatively high probability density, and a sharp drop in the right tail of the distribution, indicating that the decay parameter falls into 0.17. The local optimum is near the surface. Except for attenuation and density, the overall uncertainty of other sedimentary parameters is small.

[0132] Fig.11 The one-dimensional and joint marginal posterior distributions of Was-FWH inversion are shown. Overall, the marginal distributions of the parameters are unimodal, especially the sediment thickness. A relatively accurate inversion result was obtained with an uncertainty of HPD = [25.03, 25.19]. The confidence interval is 0.019, which is larger than 0.003 in L2-FWH-Bayeisan, but the relative deviation of the MAP result to the true value is 0.015 smaller than that in L2-FWH-Bayeisan inversion. This shows that the inversion method based on Wasserstein metric is effective in ensuring the attenuation of sedimentary layers. , sediment layer sound velocity and thickness parameters Accuracy, reduced deposition density and attenuation However, the uncertainty of the basement parameters for the Was-FWH-Bayesian inversion is similar to that for the L2-FWH-Bayeisan, which indicates that the basement parameters are insensitive to the broadband FWH waveform structure in this environment.

[0133] The above experimental results show that: The experimental results show that the dispersion inversion method is significantly better than the waveform inversion in terms of the accuracy of estimating sedimentary layer parameters, and the confidence interval of the dispersion curve prediction distribution is narrower than the confidence interval of the waveform prediction distribution. Both cannot estimate the basement parameters well. Although the waveform inversion has poor estimation results for sedimentary layer parameters, compared with the dispersion inversion, it has increased the invertible parameters (attenuation), and the Was-FWH-Bayesian inversion has higher accuracy for sedimentary layer attenuation inversion. For waveform inversion, the method based on Wasserstein metric is similar to the traditional L2 distance inversion method in terms of MAP posterior results, but the average posterior result deviation of L2-FWH-Bayesian inversion is larger, the confidence interval of the posterior prediction distribution is wider, and the joint marginal distribution of sedimentary layer density and sound velocity is larger, which shows that the uncertainty of waveform inversion is significantly reduced based on Wasserstein metric.

[0134] The above description is only the preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A Bayesian geoacoustic parameter inversion method based on Wasserstein metric, characterized in that: include: Acquire geoacoustic observation data and geoacoustic synthesis data; Constructing a plurality of KRAKENC geoacoustic forward models corresponding to the hierarchical model of the geoacoustic observation data; Determining the exponential likelihood distribution of the plurality of KRAKENC geoacoustic forward models using the Wasserstein metric form according to the geoacoustic observation data and the geoacoustic synthesis data; Determining a selected exponential likelihood distribution of the KRAKENC geoacoustic forward model based on the exponential likelihood distribution; Obtaining a prior distribution, and calculating the posterior probability distribution of the geoacoustic observation data using a Bayesian algorithm based on the selected exponential likelihood distribution and the prior distribution; The Markov chain Monte Carlo simulation algorithm is used to perform random sampling processing on the posterior probability distribution to obtain random sampling data points, and the sampling expectation values ​​corresponding to the random sampling data points are calculated. According to the sampling expectation values, the Bayesian geoacoustic inversion results corresponding to the geoacoustic observation data are determined.

2. The method according to claim 1, characterized in that The method of calculating the exponential likelihood distribution of the KRAKENC geoacoustic forward model based on the geoacoustic observation data and using the Wasserstein metric form includes: The geoacoustic observation data and the geoacoustic synthesis data are transformed by Hilbert transformation, and then a geoacoustic observation analysis signal and a geoacoustic synthesis analysis signal are outputted, wherein the analysis signal includes an observation analysis signal and a synthesis analysis signal; Based on the analytical signal, the exponential likelihood distribution of the KRAKENC geoacoustic forward model is determined using the Wasserstein metric.

3. The method according to claim 2, characterized in that Determining the exponential likelihood distribution of the KRAKENC geoacoustic forward model using the Wasserstein metric form according to the analytical signal includes: Solve the module of the observed analytical signal to obtain the observed envelope signal ; Solve the module of the synthetic analytical signal to obtain the synthetic envelope signal ; The observed envelope signal and synthesized envelope signal Perform softplus transformation to obtain the observed waveform and synthetic field waveform , specifically: In the formula, is an adjustable hyperparameter; Based on the observed waveform and the synthetic field waveform volume , the Wasserstein metric is used to determine the exponential likelihood distribution of the KRAKENC geoacoustic forward model.

4. The method according to claim 3, characterized in that The amount based on the observed waveform and the synthetic field waveform quantity, and using the Wasserstein metric form, calculating the exponential likelihood distribution of the KRAKENC geoacoustic forward model, including: The observed waveform quantity is and the synthetic field waveform volume Calculate the exponential likelihood distribution of the KRAKENC geoacoustic forward model, specifically: In the formula, is a hyperparameter that can be estimated in the sampling algorithm. represents the number of geoacoustic observation data, is the second-order Wasserstein distance, represents the FWH observation signal, By receiving the composite signal Operators that generate FWH synthetic fields, and They correspond to the observed waveform and synthetic field waveform that meet the Wasserstein metric requirements after softplus transformation. Represents the model parameter vector included in the KRAKENC geoacoustic forward model.

5. The method according to claim 4, characterized in that Determining the selected exponential likelihood distribution of the KRAKENC geoacoustic forward model based on the exponential likelihood distribution includes: The exponential likelihood distribution is parameterized using the BIC criterion to determine the selected exponential likelihood distribution of the KRAKENC geoacoustic forward model.

6. The method according to claim 1, characterized in that Determining the Bayesian geoacoustic result corresponding to the geoacoustic observation data according to the sampling expectation value includes: Comparing the sampled expected value with a preset expected value; When the sampling expected value is greater than the preset expected value, the geoacoustic observation data corresponding to the sampling expected value is queried in the geoacoustic forward model, and the geoacoustic observation data is used as the Bayesian geoacoustic inversion result corresponding to the geoacoustic observation data.

7. A computer device, characterized in that: The computer device includes a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set or an instruction set, and the at least one instruction, at least one program, a code set or an instruction set is loaded and executed by the processor to implement the Bayesian geoacoustic inversion method based on the Wasserstein metric form as described in any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that: The readable storage medium stores at least one instruction, at least one program, code set or instruction set, and the at least one instruction, at least one program, code set or instruction set is stored in the processor. The processor loads and executes to implement the Bayesian geoacoustic inversion method based on the Wasserstein metric form as described in any one of claims 1 to 6.

Images