Submarine sound velocity gradient in-situ measurement device based on transducer array

Abstract

The invention relates to the technical field of ocean monitoring, and particularly discloses a transducer array-based seabed sound velocity gradient in-situ measurement device, which comprises a transducer array unit, a depth adjusting unit, a transmitting and receiving control unit and a data processing unit, the transducer array unit comprises a plurality of transmitting transducers and a plurality of receiving transducers, the plurality of transmitting transducers form a transmitting array, the plurality of receiving transducers form a receiving array, and the opening angles of the transducers in the transmitting array and the receiving array are set to ensure that the plurality of receiving transducers can receive signals from the transmitting array. A protective shell is arranged outside the transmitting array and the receiving array, and the strength of the protective shell is enough to ensure that the protective shell can penetrate into seabed sediments with various hardness degrees; the depth adjusting unit is respectively connected with the protective shells of the transmitting array and the receiving array; by adopting the technical scheme of the invention, fine measurement of the acoustic characteristics of the seabed shallow sedimentary layer can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of ocean monitoring, and in particular to an in-situ measurement device for seabed sound velocity gradient based on a transducer array. Background Art

[0002] Accurately measuring the acoustic properties of seafloor sediments (such as speed of sound, attenuation, density, and porosity) is crucial for applications in marine engineering surveys, resource development, and ocean acoustic field forecasting. However, existing seafloor acoustic property measurement technologies have numerous shortcomings, making it difficult to accurately characterize complex seafloor stratification.

[0003] Traditional methods for measuring seafloor sound velocity, such as indirect measurement, measure parameters such as seawater temperature, salinity, and depth, and then calculate the sound velocity in seawater using empirical formulas. However, this method is significantly affected by the accuracy of the empirical formula and errors in the measurement parameters, making it difficult to guarantee the accuracy of the measurement results. Furthermore, it cannot directly obtain the acoustic properties of seafloor sediments. In situ bottom-mounted horizontal measurement methods place acoustic transducers within the same layer of sediment within a small area of ​​the seafloor. The detection depth generally does not exceed 2.0m. These methods are primarily used to study the acoustic characteristics of sediments at the same level of the seafloor. They are unable to measure the vertical variations in sound velocity within the seafloor sediments, making them difficult to fully measure seafloor acoustic properties. While the vertical penetration acoustic spear measurement method can detect the acoustic properties of sediments within approximately 15m below the seafloor, it can only obtain fixed-point sound velocity data or limited continuous data within a very small depth range. It cannot provide a wide range of sediment sound velocity data that varies with depth, making it difficult to accurately characterize the complex layered structure of the seafloor.

[0004] Similar cross-well seismic technologies mainly use the method of placing measurement sound sources and receiving arrays in the well after drilling to conduct measurements. This method is not applicable to shallow seabed layers because the geological structure of the shallow seabed is soft, drilling operations can easily damage the original seabed environment, and construction is difficult. At the same time, the sound source used in cross-well seismic technology is a single suspended sound source, which is achieved by continuously adjusting the suspension depth to achieve multi-point transmission. Not only is the measurement efficiency low, but the equipment is expensive, the operation is time-consuming and labor-intensive, and it cannot meet the needs of efficient and accurate measurement of seabed acoustic characteristics. In addition, previous measurement technologies mostly set up sound sources or receiving points at a single depth, and can only obtain the average acoustic parameters on the transmission and reception path. It is impossible to perform detailed acoustic characteristic analysis on the complex seabed layered structure, and it is difficult to meet the high-precision requirements of modern marine engineering and scientific research for seabed acoustic characteristic measurements.

[0005] Therefore, there is an urgent need for a device and method that can overcome the above-mentioned defects of the existing technology and realize the precise measurement of the acoustic characteristics of shallow seabed sediments to meet the ever-evolving research and engineering application needs in the marine field. Summary of the Invention

[0006] The present invention provides an in-situ measurement device for seabed sound velocity gradient based on a transducer array, which can realize precise measurement of the acoustic characteristics of shallow seabed sediment layers.

[0007] In order to solve the above technical problems, this application provides the following technical solutions:

[0008] An in-situ measurement device for seabed sound velocity gradient based on a transducer array, comprising a transducer array unit, a depth adjustment unit, a transmitting and receiving control unit, and a data processing unit;

[0009] The transducer array unit includes a plurality of transmitting transducers and a plurality of receiving transducers, wherein the plurality of transmitting transducers constitute a transmitting array, and the plurality of receiving transducers constitute a receiving array. The opening angles of the transducers in the transmitting array and the receiving array are set to ensure that the plurality of receiving transducers can receive signals from the transmitting array. The transmitting array and the receiving array are provided with a protective shell, and the strength of the protective shell is sufficient to ensure that the shell can penetrate seabed sediments of various hardnesses.

[0010] The depth adjustment unit is connected to the protective housings of the transmitting array and the receiving array respectively, and is used to control the depth of the transmitting array and the receiving array entering the seabed. The depth adjustment unit is provided with an insertion sensor capable of obtaining real-time data on the depth of the transmitting array and the receiving array at the seabed. The depth adjustment unit also includes a power source, which provides power for the transmitting array and the receiving array to penetrate the seabed.

[0011] The transmitting and receiving control unit is respectively connected to the transmitting array and the receiving array signal, and is used to control the transmitting array to perform fixed-distance, multi-frequency time-sequential transmission, and control the receiving array to perform multi-channel synchronous reception;

[0012] The data processing unit is connected to the receiving array and is used to receive the signal obtained by the receiving array, and obtain the acoustic characteristic parameters of the shallow seabed sediment layer based on the received signal inversion, wherein the acoustic characteristic parameters include sound velocity, attenuation, density and porosity; and obtain the particle size, hardness and porosity parameters of the seabed sediment based on the acoustic characteristic parameters.

[0013] The basic scheme principles and beneficial effects are as follows:

[0014] This device, based on the principles of acoustic propagation and signal processing, achieves in-situ measurement of seafloor sound velocity gradients through the collaborative operation of multiple units. Within the transducer array unit, the transmitting array emits acoustic signals of varying frequencies, leveraging the propagation characteristics of sound waves in seafloor sediments. Because different frequencies respond differently to parameters such as sediment particle size, hardness, and porosity, these waves carry corresponding seafloor information. The receiving array ensures effective reception of signals from the transmitting array by properly setting the transducer opening angle.

[0015] The depth adjustment unit uses a power source to drive the transmitting and receiving arrays into the seabed. Sensors are inserted to monitor depth data in real time, enabling precise control of measured depth and enabling the device to perform measurements at varying seabed depths. The transmit / receive control unit controls the transmitting array to perform fixed-range, multi-frequency sequential transmissions, transmitting signals in a predetermined pattern. It also controls the receiving array to synchronize multiple channels, ensuring accurate and consistent signal reception.

[0016] After receiving the receiving array signal, the data processing unit analyzes and inverts the signal based on acoustic theory and signal processing algorithms to obtain acoustic characteristic parameters such as sound velocity, attenuation, density, porosity, etc. of the shallow seabed sediment layer, and further derives parameters such as the particle size and hardness of the seabed sediment, thereby completing the measurement and analysis of the acoustic characteristics of the seabed.

[0017] Different from the traditional sound source or receiving point measurement method at a single depth, this device can obtain acoustic signals at different positions and frequencies on the seabed through the multi-transmission and multi-reception design of the transducer array, combined with fixed-distance, multi-frequency time-series transmission and multi-channel synchronous reception. It can invert the acoustic characteristics of the entire measurement profile, achieve a detailed characterization of the complex seabed layered structure, avoid the limitation of only obtaining the average acoustic parameters on the transmission and reception path, and greatly improve the comprehensiveness and accuracy of the measurement results.

[0018] The protective shell is strong enough to penetrate seabed sediments of various hardnesses, making the device suitable for seabed environments with different geological conditions; the depth adjustment unit can control the depth of the transmitting and receiving arrays entering the seabed, and monitor the depth data in real time. It can flexibly adjust the measurement depth according to actual measurement needs and seabed topography, ensuring that measurement work can be carried out stably in seabed areas at different depths.

[0019] The transmitting and receiving control unit precisely controls the transmitting and receiving processes to ensure the accuracy of signal transmission and reception; the data processing unit performs professional inversion and analysis on the received signals, and can accurately obtain the acoustic characteristic parameters of the shallow seabed sediment layer and sediment-related parameters. Compared with traditional measurement technologies, it significantly improves the measurement accuracy and provides more reliable data support for marine engineering surveys, resource development and other fields.

[0020] Through the design of the depth adjustment unit and transducer array, in-situ measurement is achieved, which minimizes the disturbance to the original seabed environment and maintains the original temperature and pressure environment of the seabed, thereby obtaining high-precision acoustic characteristic data. Compared with collecting samples in the laboratory for measurement, it avoids the influence of factors such as changes in sample structure and changes in environmental parameters that may occur during sample collection and transportation on the measurement results.

[0021] In summary, the present invention achieves the purpose of finely measuring the acoustic characteristics of shallow seabed sediments.

[0022] Furthermore, the opening angle of each transducer in the transmitting array and the receiving array is optimized and set by the following formula:

[0023] Among them, θ optimal is the optimal opening angle of the transducer, α is the sound intensity attenuation coefficient in the seabed sediment, which is obtained by fitting the function α=f(ρ,φ) using the least squares method based on the sound attenuation experimental data of the target sea sediment in the early stage, ρ is the sediment density, φ is the sediment porosity; d is the straight-line distance between the transmitting transducer and the receiving transducer; I0 is the initial sound intensity of the transmitting transducer, I min is the minimum sound intensity that the receiving transducer can effectively identify; c is the sound velocity in the seabed sediment, which is updated in real time by the data processing unit based on the initial measurement results; T is the sound wave propagation time. At the same time, the transmitting array adopts an adaptive beamforming model and calculates the weighting coefficient w of each transmitting transducer by the following formula n :

[0024] Where N is the number of transmitting transducers, β n =kd n sinθ,k is the wave number, where f j is the jth transmitting frequency, d n is the distance between the nth transmitting transducer and the reference point, and θ is the angle between the sound wave propagation direction and the array normal direction.

[0025] The weighting coefficient w calculated by the above formula n The signals of each transmitting transducer are weighted so that the main lobe of the transmitting beam points to the receiving array and the sidelobe suppression ratio satisfies This further ensures that multiple receiving transducers can receive valid signals from the transmitting array and improves the signal-to-noise ratio and measurement accuracy.

[0026] Furthermore, the protective shell adopts a streamlined frustum structure, including an upper cylindrical section and a lower conical section, and a spiral guide groove is provided on the outer surface of the conical section;

[0027] Elastic vibration-damping supports with the same structure are respectively provided between the transmitting array, the receiving array and the protective housing. The elastic vibration-damping supports include:

[0028] The base plate is located in the inner wall of the protective shell. The inner wall of the protective shell is provided with an annular card slot, the card slot is filled with waterproof sealant, and the base plate is fixedly connected to the card slot;

[0029] An elastic cantilever beam, one end of which is fixedly connected to the base plate;

[0030] A spherical hinge, one end of the spherical hinge is fixed to the other end of the elastic cantilever beam, the other end of the spherical hinge is fixed to the transmitting array or the receiving array, and the surface of the spherical hinge is covered with a polytetrafluoroethylene lubricating layer;

[0031] The transmitting array or the receiving array is respectively located in the protective shell, and the transmitting array or the receiving array is isolated from the seawater by a flexible diaphragm.

[0032] Furthermore, the cone angle θ of the cone segment satisfies the formula:

[0033]

[0034] where σ y is the yield strength of the hardest sediment in the target sea area, ρ is the average density of the device, g is the acceleration of gravity, and h is the designed maximum penetration depth;

[0035] The pitch P and cone angle θ of the guide groove satisfy the fluid dynamics relationship:

[0036]

[0037] Where r is the radius of the cone segment, ρ w is the density of seawater, v is the penetration velocity, C d is the drag coefficient.

[0038] Furthermore, the elastic cantilever beam is made of titanium alloy, and its Young's modulus E is the same as the Young's modulus E of the shell material. h satisfy:

[0039]

[0040] Where μ is the damping ratio, σ max is the allowable stress of the shell material, f is the main working frequency of the device, m is the mass of the transducer array; the elastic modulus E of the flexible diaphragm m satisfy:

[0041]

[0042] Where ΔP is the maximum pressure difference between the inside and outside, t is the diaphragm thickness, D is the diaphragm diameter, and ν is the Poisson's ratio.

[0043] Furthermore, the depth adjustment unit includes:

[0044] A connecting seat, with electric push rod assemblies at both ends of the connecting seat respectively, the electric push rod assemblies are hinged to the protective shell of the transmitting array and the protective shell of the receiving array respectively, and the ends of the electric push rod assemblies are fixedly connected to the connecting seat;

[0045] The insertion sensor is a differential pressure depth sensor installed in the guide groove of the conical section of the protective shell. Its measured value H is corrected by the following formula:

[0046]

[0047] Where H0 is the initial reading, P is the sensor pressure value, P0 is the atmospheric pressure, and k is the fluid resistance coefficient. By fitting the experimental data, k = 0.5 + 0.3log 10 (Re), Re is the Reynolds number.

[0048] Furthermore, the transmitting and receiving control unit adopts an adaptive multi-frequency timing control model and a synchronous trigger compensation mechanism, specifically including:

[0049] The fixed-distance, multi-frequency sequential transmission of the transmitting array is determined by the following formula to determine the transmission parameters: Transmitting frequency sequence {f n}satisfy Where n=1,2,…,N, N is the number of set transmission frequencies, f min is the minimum transmission frequency, γ is the frequency distribution adjustment coefficient, and according to the estimated sound attenuation coefficient α of the seabed sediment 预估 By formula Dynamic adjustment, α 阈值 is the preset sound attenuation threshold;

[0050] The emission time interval Δt between adjacent transmitting transducers mn satisfy Where Δd is the distance between adjacent transmitting transducers, c 预估 is the estimated sound velocity in seafloor sediments, Δt 补偿 To compensate for the time, the formula Calculation, τ is the signal transmission delay correction coefficient, f s is the system sampling frequency.

[0051] Furthermore, the multi-channel synchronous reception of the receiving array adopts a phase difference calibration model, and the time synchronization error Δt of each receiving channel is erri Compensation is performed using the following formula: where Δφ i is the phase difference between the i-th receiving channel and the reference channel, Δl i is the distance difference between the i-th receiving transducer and the reference receiving transducer, c is the sound speed measured in real time; by adjusting the trigger time of each receiving channel, the synchronization error is satisfied

[0052] The transmitting and receiving control unit is also provided with an interference avoidance algorithm. When the ambient noise intensity I is detected, noise Exceeding threshold I 阈值 When, through the formula f 新 =f 原 ±Δf×sgn(I noise -I阈值 ) dynamically adjusts the transmission frequency, where Δf is the frequency adjustment step, sgn is the sign function, and adjusts the transmission timing so that the transmission time interval Δt between adjacent transmitting transducers is mn Increase λ noise is the wavelength of the interference noise.

[0053] Furthermore, the data processing unit adopts a multi-parameter joint inversion model to obtain the acoustic characteristic parameters of the shallow seabed sediment layer through the following iterative algorithm:

[0054] Establishing the objective function where x = [c, α, ρ, φ] T is the acoustic characteristic parameter vector to be inverted, including the sound velocity c, attenuation coefficient α, density ρ and porosity φ; M is the number of receiving transducers, and N is the number of transmitting frequencies; is the observed signal amplitude of the i-th receiving transducer at the j-th transmitting frequency, is the theoretical signal amplitude calculated based on the parameter vector x;

[0055] The Levenberg-Marquardt algorithm is used for iterative solution, and the iterative formula is x k+1 =x k +(J T J+λI) -1 J T (yf(x k )), where x k is the parameter vector of the kth iteration, J is the Jacobian matrix of the objective function F(x) with respect to x, and λ is the damping factor. Dynamic adjustment, λ0 is the initial damping factor, y is the observed signal vector, f(x k ) is the theoretical signal vector of the kth iteration;

[0056] When satisfied When , the iteration is terminated and the final acoustic characteristic parameters are obtained, where ε is the preset convergence threshold.

[0057] Specifically, It represents the acoustic characteristic parameter vector x=[c,α,ρ,φ] of the i-th receiving transducer at the j-th transmitting frequency. T The theoretical signal amplitude is calculated as follows:

[0058]

[0059] The meaning and acquisition methods of each parameter are as follows:

[0060] S 0j: initial signal amplitude of the jth transmitting frequency;

[0061] The initial sound intensity I of the transmitting transducer 0j (The initial sound intensity I0 of the transmitting transducer mentioned) is derived and satisfies Where k is a proportional constant (calibrated by the electroacoustic conversion efficiency experiment of the transmitting transducer, the value of k is 0.85±0.05).

[0062] w j : Beam weighting coefficient for the jth transmit frequency

[0063] Calculated by the adaptive beamforming model, that is, by the formula:

[0064]

[0065] (where β n =kd n sinθ,k is the wave number, where f j is the jth transmitting frequency, d n is the distance between the nth transmitting transducer and the reference point, θ is the angle between the sound wave propagation direction and the array normal direction) and the weighted coefficient of each transmitting transducer is calculated, w j is the superposition value of the weighted coefficient at the jth frequency (to ensure that the main lobe of the beam points to the receiving array and the sidelobe suppression ratio satisfies ).

[0066] α j (ρ,φ): Sound intensity attenuation coefficient at the jth frequency.

[0067] It is derived from the "early acoustic attenuation experimental data of the target sea sediments, using the least squares method to fit the function α=f(ρ,φ)", and after considering the frequency correlation, in:

[0068] α0(ρ,φ) is the basic attenuation coefficient (calculated by the density ρ and porosity φ through the least squares fitting function f(ρ,φ));

[0069] f j is the jth transmitting frequency (transmitting frequency sequence f n );

[0070] m is the frequency attenuation index (fitted through laboratory frequency response experiments of sediment samples in the target sea area. For typical shallow sea sediments such as silty clay, m is taken as 0.3-0.5).

[0071] r ij : The straight-line propagation distance between the j-th transmitting transducer and the i-th receiving transducer.

[0072] Calculation of real-time depth data obtained by the insertion sensor (differential pressure depth sensor) of the depth adjustment unit:

[0073] Assume the depth of the jth transducer in the transmitting array is h j , the depth of the i-th transducer in the receiving array is h i (both measured and corrected by inserted sensors);

[0074] The horizontal distance between the transmitting array and the receiving array is D (device structural parameter, fixed by the installation distance of the protective housing of the transmitting array and the receiving array, D = 2m for this device);

[0075] The propagation distance

[0076] η(ρ,φ): Correction coefficient for sediment density and porosity, taking into account the effects of density ρ and porosity φ on acoustic reflection / transmission, η(ρ,φ) = 1 - 0.02ρ + 0.05φ (obtained by fitting the correlation between laboratory-measured sediment density, porosity, and acoustic transmission coefficient, with a correction range of 0.9 to 1.1).

[0077] Based on the depth adjustment unit, the real-time depth data h of the transmitting array and the receiving array are obtained. j 、h i , calculate the propagation distance r ij ;

[0078] The basic attenuation coefficient is calculated by fitting the function α0=f(ρ,φ) from the parameter vector x, and combined with the emission frequency f j Get α j (ρ,φ);

[0079] The initial sound intensity I of the transmitting transducer 0j Calculate the initial signal amplitude S 0j , and combined with the beam weighting coefficient w j Obtaining the weighted transmit signal amplitude;

[0080] Substitute into the above formula to calculate Complete the acquisition of theoretical signal amplitude. Theoretical signal amplitude It can be clearly calculated based on the measured parameters of the device (depth, frequency) and the parameters to be inverted (c, α, ρ, φ), forming a closed loop with the multi-parameter joint inversion model to ensure the operability of the objective function F(x).

[0081] Furthermore, the data processing unit uses the following empirical-theoretical hybrid model to obtain the particle size d, hardness H and porosity φ parameters of the seabed sediment based on the acoustic characteristic parameters obtained by inversion:

[0082] The particle size d is calculated by the formula Calculate, where a0, a1, ..., a33 is the regression coefficient obtained through laboratory measurement and data analysis of sediment samples in the target sea area;

[0083] Hardness H uses the dynamic modulus-hardness conversion model The elastic modulus E s By formula E s =b0+b1c+b2α+b3ρ+b4φ, where b0, b1,…, b4 are regression coefficients and Poisson’s ratio ν is preset according to the sediment type;

[0084] The porosity φ is calibrated using a two-parameter model φ = φ 反演 +Δφ, where φ 反演 is the porosity obtained by the multi-parameter joint inversion model, and the calibration quantity Δφ is obtained by the formula Calculation, c0, c1, c2 are calibration coefficients, ρ ref and α ref are the reference density and reference attenuation coefficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 Schematic diagram of the structure of an embodiment of an in-situ measurement device for seabed sound velocity gradient based on a transducer array;

[0086] Figure 2 A partial cross-sectional view of the protective housing.

[0087] The accompanying drawings in the specification are as follows: protective housing 1, receiving array 2, transmitting transducer 3, electric push rod assembly 4, connecting base 5. DETAILED DESCRIPTION

[0088] The following is further described in detail through specific implementation methods:

[0089] In-situ measurement device for seabed sound velocity gradient based on transducer array (such as Figure 1 As shown), comprising a transducer array unit, a depth adjustment unit, a transmitting and receiving control unit and a data processing unit;

[0090] The transducer array unit includes a plurality of transmitting transducers 3 and a plurality of receiving transducers. The plurality of transmitting transducers 3 constitute a transmitting array, and the plurality of receiving transducers constitute a receiving array 2. The opening angles of the transducers in the transmitting array and the receiving array 2 are set to ensure that the plurality of receiving transducers can receive signals from the transmitting array. The transmitting array and the receiving array 2 are provided with a protective shell 1. The strength of the protective shell 1 is sufficient to ensure that it can penetrate seabed sediments of various hardnesses.

[0091] The depth adjustment unit is connected to the protective housing 1 of the transmitting array and the receiving array 2 respectively, and is used to control the depth of the transmitting array and the receiving array 2 entering the seabed. The depth adjustment unit is provided with an insertion sensor that can obtain the depth data of the transmitting array and the receiving array 2 on the seabed in real time; the depth adjustment unit also includes a power source, which provides power for the transmitting array and the receiving array 2 to penetrate the seabed;

[0092] The transmitting and receiving control unit is respectively connected to the transmitting array and the receiving array 2 for signal connection, and is used to control the transmitting array to perform fixed-distance, multi-frequency time-sequential transmission, and to control the receiving array 2 to perform multi-channel synchronous reception;

[0093] The data processing unit is connected to the receiving array 2 and is used to receive the signals obtained by the receiving array 2, and obtain the acoustic characteristic parameters of the shallow seabed sediment layer based on the received signals by inversion, wherein the acoustic characteristic parameters include sound velocity, attenuation, density and porosity; and obtain the particle size, hardness and porosity parameters of the seabed sediment based on the acoustic characteristic parameters.

[0094] In specific use, this embodiment takes the seabed sound velocity gradient measurement task in a typical continental shelf sea area (average water depth of 100 meters, and the sediment type is mainly silty clay) as an example to illustrate the specific implementation process of the measurement device in detail.

[0095] The opening angle of each transducer in the transmitting array and receiving array 2 is optimized using the following formula:

[0096] Among them, θ optimal is the optimal opening angle of the transducer, α is the sound intensity attenuation coefficient in the seabed sediment, which is obtained by fitting the function α=f(ρ,φ) using the least squares method based on the sound attenuation experimental data of the target sea area sediment in the early stage, ρ is the sediment density, φ is the sediment porosity; d is the straight-line distance between the transmitting transducer 3 and the receiving transducer; I0 is the initial sound intensity of the transmitting transducer 3, I min is the minimum sound intensity that the receiving transducer can effectively identify; c is the sound velocity in the seabed sediment, which is updated in real time by the data processing unit based on the initial measurement results; T is the sound wave propagation time. At the same time, the transmitting array adopts an adaptive beamforming model and calculates the weighting coefficient w of each transmitting transducer 3 using the following formula n :

[0097] Where N is the number of transmitting transducers 3, β n =kd n sinθ,k is the wave number, where f j is the jth transmitting frequency, d nis the distance between the nth transmitting transducer 3 and the reference point, and θ is the angle between the sound wave propagation direction and the array normal direction.

[0098] The weighting coefficient w calculated by the above formula n The signals of each transmitting transducer 3 are weighted so that the main lobe of the transmitting beam points to the receiving array 2 and the sidelobe suppression ratio satisfies This further ensures that multiple receiving transducers can receive valid signals from the transmitting array and improves the signal-to-noise ratio and measurement accuracy.

[0099] The protective shell 1 adopts a streamlined cone structure (such as Figure 2 As shown), it includes an upper cylindrical section and a lower conical section, and a spiral guide groove is provided on the outer surface of the conical section;

[0100] Elastic vibration-damping supports with the same structure are respectively provided between the transmitting array and the receiving array 2 and the protective shell 1. The elastic vibration-damping supports include:

[0101] The base plate is located in the inner wall of the protective shell 1. The inner wall of the protective shell 1 is provided with an annular card slot, the card slot is filled with waterproof sealant, and the base plate is fixedly connected to the card slot;

[0102] An elastic cantilever beam, one end of which is fixedly connected to the base plate;

[0103] A spherical hinge, one end of which is fixed to the other end of the elastic cantilever beam, and the other end of which is fixed to the transmitting array or the receiving array 2, and the surface of the spherical hinge is covered with a polytetrafluoroethylene lubricating layer;

[0104] The transmitting array or the receiving array 2 is respectively located in the protective shell 1 , and the transmitting array or the receiving array 2 is isolated from the seawater by a flexible diaphragm.

[0105] The cone angle θ of the cone segment satisfies the formula:

[0106]

[0107] where σ y is the yield strength of the hardest sediment in the target sea area, ρ is the average density of the device, g is the acceleration of gravity, and h is the designed maximum penetration depth;

[0108] The pitch P and cone angle θ of the guide groove satisfy the fluid dynamics relationship:

[0109]

[0110] Where r is the radius of the cone segment, ρ w is the density of seawater, v is the penetration velocity, C d is the drag coefficient.

[0111] The elastic cantilever beam is made of titanium alloy, and its Young's modulus E is the same as the Young's modulus E of the shell material. h satisfy:

[0112]

[0113] Where μ is the damping ratio, σ max is the allowable stress of the shell material, f is the main working frequency of the device, m is the mass of the transducer array; the elastic modulus E of the flexible diaphragm m satisfy:

[0114]

[0115] Where ΔP is the maximum pressure difference between the inside and outside, t is the diaphragm thickness, D is the diaphragm diameter, and ν is the Poisson's ratio.

[0116] The transducer array unit consists of eight transmitting transducers 3 and 12 receiving transducers. The transmitting transducers 3 are made of broadband piezoelectric ceramic material, operating in the 1-10 kHz frequency range. The receiving transducers are highly sensitive fiber-optic hydrophones capable of detecting weak acoustic signals. The transmitting transducers 3 are arranged into a transmitting array, while the receiving transducers form a receiving array 2.

[0117] According to the formula Combined with the sediment sound intensity attenuation coefficient α = 0.5dB / m obtained in the previous survey of the sea area (obtained by laboratory measurement and fitting of sediment samples), the distance between the transmitting and receiving transducers d = 2 meters, the initial sound intensity of the transmitting transducer 3 I0 = 100dB, the minimum recognition sound intensity of the receiving transducer I min =30dB, estimated sound velocity c = 1500m / s and sound wave propagation time T = 0.001s, calculate the optimal opening angle θ of the transducer optimal =30°, and the angles of the transducers in the transmitting and receiving arrays 2 are adjusted accordingly. The transmitting and receiving arrays 2 are wrapped in a streamlined frustum-shaped protective housing 1. The upper cylindrical section of the housing has a diameter of 0.8 meters and a height of 1.2 meters, and the lower conical section has a height of 0.6 meters.

[0118] The outer surface of the cone section is processed with a spiral guide groove with a pitch of P = 0.5 meters. Its parameters are based on the formula Calculation, where the radius of the cone section r = 0.4 meters and the density of seawater ρ w =1025kg / m 3 , design penetration velocity v = 0.1m / s, resistance coefficient C d =0.2, yield strength of the hardest sediment in the target sea area σ y=50kPa. The transmitting array and receiving array 2 are installed in the protective shell 1 through elastic vibration-damping brackets. The base plate is embedded in the annular groove on the inner wall of the shell, and the groove is filled with silicone rubber waterproof sealant; the elastic cantilever beam is made of titanium alloy, and its Young's modulus E is the same as the Young's modulus E of the shell material. h satisfy Set the damping ratio μ = 0.05 and the allowable stress of the shell material σ max =200MPa, the device's operating frequency f = 5kHz, and the transducer array mass m = 10kg; the surface of the spherical hinge is covered with a polytetrafluoroethylene lubricating layer to achieve flexible connection with the transmitting array and the receiving array 2. The transmitting array and the receiving array 2 are isolated from the seawater by a flexible diaphragm made of polyurethane with an elastic modulus E m According to the formula Calculation was performed, setting the maximum internal and external pressure difference ΔP = 1 MPa, the diaphragm thickness t = 0.5 mm, the diaphragm diameter D = 100 mm, and the Poisson's ratio ν = 0.4.

[0119] The depth adjustment unit includes:

[0120] Connecting base 5, both ends of the connecting base 5 are provided with electric push rod assemblies 4, the electric push rod assemblies 4 are hinged to the protective shell 1 of the transmitting array and the protective shell 1 of the receiving array 2 respectively, and the ends of the electric push rod assemblies 4 are fixedly connected to the connecting base 5;

[0121] The insertion sensor is a differential pressure depth sensor, which is installed in the guide groove of the conical section of the protective housing 1. Its measured value H is corrected by the following formula:

[0122]

[0123] Where H0 is the initial reading, P is the sensor pressure value, P0 is the atmospheric pressure, and k is the fluid resistance coefficient. By fitting the experimental data, k = 0.5 + 0.3log 10 (Re), Re is the Reynolds number.

[0124] Specifically, one end of the depth adjustment unit's electric push rod assembly 4 is connected and hinged to the top of the cylindrical section of the protective housing 1. The push rod has a travel of 3 meters and a maximum thrust of 5000N. The other end of the push rod is fixedly connected to the connecting base 5. A counterweight block can be placed on the connecting base 5.

[0125] The insertion sensor is a differential pressure depth sensor installed in the guide groove of the conical section of the protective housing 1. The measured value H is based on the formula Correction, initial reading H0 = 0, real-time measurement pressure value P, atmospheric pressure P0 = 101.3kPa, fluid resistance coefficient k is fitted by experimental data to k = 0.5 + 0.3log 10 (Re) (When Reynolds number Re = 10000, k = 0.8).

[0126] The transmitting and receiving control unit adopts an adaptive multi-frequency timing control model and a synchronous trigger compensation mechanism, specifically including: the fixed-distance and multi-frequency timing transmission of the transmitting array is determined by the following formula: the transmitting frequency sequence {f n}satisfy Where n=1,2,…,N, N is the number of set transmission frequencies, f min is the minimum transmission frequency, γ is the frequency distribution adjustment coefficient, and according to the estimated sound attenuation coefficient α of the seabed sediment 预估 By formula α 阈值 is the preset sound attenuation threshold; the emission time interval Δt between adjacent transmitting transducers 3 mn satisfy Where Δd is the distance between adjacent transmitting transducers 3, c 预估 is the estimated sound velocity in seafloor sediments, Δt 补偿 To compensate for the time, the formula Calculation, τ is the signal transmission delay correction coefficient, f s is the system sampling frequency.

[0127] The multi-channel synchronous reception of the receiving array 2 adopts the phase difference calibration model, and the time synchronization error of each receiving channel is Compensation is performed using the following formula: where Δφ i is the phase difference between the i-th receiving channel and the reference channel, Δl i is the distance difference between the i-th receiving transducer and the reference receiving transducer, c is the sound speed measured in real time; by adjusting the trigger time of each receiving channel, the synchronization error is satisfied

[0128] The transmitting and receiving control unit is also equipped with an interference avoidance algorithm. When the ambient noise intensity I is detected, noise Exceeding threshold I 阈值 When, through the formula f 新 =f 原 ±Δf×sgn(I noise -I 阈值 ) dynamically adjusts the transmission frequency, where Δf is the frequency adjustment step, sgn is the sign function, and adjusts the transmission timing so that the transmission time interval Δt of adjacent transmitting transducers 3 is mn Increase Δt 避扰 , λ noise is the wavelength of the interference noise.

[0129] Specifically, the transmit and receive control unit utilizes an embedded control system with a built-in adaptive multi-frequency timing control model and synchronous trigger compensation mechanism. The data processing unit is a portable industrial computer equipped with multi-parameter joint inversion and empirical-theoretical hybrid calculation software. Both are connected to the transducer array unit and depth adjustment unit via waterproof data cables.

[0130] The data processing unit uses a multi-parameter joint inversion model to obtain the acoustic characteristic parameters of the shallow seabed sediment layer through the following iterative algorithm:

[0131] Establishing the objective function where x = [c, α, ρ, φ] T is the acoustic characteristic parameter vector to be inverted, including the sound velocity c, attenuation coefficient α, density ρ and porosity φ; M is the number of receiving transducers, and N is the number of transmitting frequencies; is the observed signal amplitude of the i-th receiving transducer at the j-th transmitting frequency, is the theoretical signal amplitude calculated based on the parameter vector x;

[0132] The Levenberg-Marquardt algorithm is used for iterative solution, and the iterative formula is x k+1 =x k +(J T J+λI) -1 J T (yf(x k )), where x k is the parameter vector of the kth iteration, J is the Jacobian matrix of the objective function F(x) with respect to x, and λ is the damping factor. Dynamic adjustment, λ0 is the initial damping factor, y is the observed signal vector, f(x k ) is the theoretical signal vector of the kth iteration;

[0133] When satisfied When , the iteration is terminated and the final acoustic characteristic parameters are obtained, where ε is the preset convergence threshold.

[0134] The data processing unit uses the following empirical-theoretical hybrid model to obtain the particle size d, hardness H, and porosity φ parameters of the seabed sediment based on the acoustic characteristic parameters obtained by inversion:

[0135] The particle size d is calculated by the formula Calculate, where a0, a1, ..., a 33 is the regression coefficient obtained through laboratory measurement and data analysis of sediment samples in the target sea area;

[0136] Hardness H uses the dynamic modulus-hardness conversion model The elastic modulus Es By formula E s =b0+b1c+b2α+b3ρ+b4φ, where b0, b1,…, b4 are regression coefficients and Poisson’s ratio ν is preset according to the sediment type;

[0137] The porosity φ is calibrated using a two-parameter model φ = φ 反演 +Δφ, where φ 反演 is the porosity obtained by the multi-parameter joint inversion model, and the calibration quantity Δφ is obtained by the formula Calculation, c0, c1, c2 are calibration coefficients, ρ ref and α ref are the reference density and reference attenuation coefficient.

[0138] To use it, the measuring device is hoisted above the target sea area via a vessel. The depth adjustment unit's electric actuator is activated to push the transducer array unit into the seabed at a speed of 0.1m / s. During this process, the differential pressure depth sensor monitors the depth data in real time, processes it according to a correction formula, and transmits it to the transmitter and receiver control unit and data processing unit. Penetration stops when the preset depth of 2 meters is reached.

[0139] The transmit and receive control unit determines the transmit parameters based on the adaptive multi-frequency timing control model. Set the number of transmit frequencies N = 5, the minimum transmit frequency f min =2kHz, based on the estimated sound attenuation coefficient α 预估 =0.5dB / m and preset sound attenuation threshold α 阈值 =0.3dB / m, through the formula Calculate the frequency distribution adjustment coefficient γ = 0.88 and get the emission frequency sequence That is, the transmitting frequencies are 2kHz, 3.1kHz, 4.2kHz, 5.3kHz, and 6.4kHz respectively.

[0140] The emission time interval Δt between adjacent transmitting transducers 3 mn According to the formula Calculation: the distance between adjacent transmitting transducers 3 is Δd = 1 meter, and the estimated sound speed c 预估 =1500m / s, signal transmission delay correction coefficient τ = 0.0001s, system sampling frequency f s =100kHz, calculate Then the time interval of each transmission is obtained. The transmitting array transmits the acoustic wave signal according to the fixed distance and multi-frequency sequence, and the receiving array 2 adopts the phase difference calibration model to perform multi-channel synchronous reception. According to the formula Adjust the trigger time of each receiving channel to ensure synchronization error

[0141] If the ambient noise intensity I noise=40dB exceeds threshold I 阈值 =35dB, the transmitting and receiving control unit starts the interference avoidance algorithm, and uses the formula f 新 =f 原 ±Δf×sgn(I noise -I 阈值 ) (frequency adjustment step Δf=0.5kHz) dynamically adjust the transmission frequency and (Interference noise wavelength λ noise =3 meters, real-time sound speed c = 1500m / s, Δt 避扰 =0.001s) to adjust the transmission timing.

[0142] After the data processing unit receives the signal acquired by the receiving array 2, it uses a multi-parameter joint inversion model to establish the objective function Parameter vector to be inverted x=[c,α,ρ,φ] T The Levenberg-Marquardt algorithm was used for iterative solution, with an initial damping factor λ0 = 0.1 and a preset convergence threshold ε = 0.01. After 10 iterations, the convergence conditions were met, and the acoustic characteristic parameters of the shallow seabed sediment layer were obtained: sound velocity c = 1520 m / s, attenuation coefficient α = 0.6 dB / m, density ρ = 1800 kg / m 3 , porosityφ=0.4.

[0143] Based on the acoustic characteristic parameters obtained by inversion, the seabed sediment parameters are obtained through the empirical-theoretical hybrid model. (Based on the analysis of samples from this sea area, a0 = 0.01, a1 = 0.001, a2 = -0.02, a3 = 0.0005, a4 = -0.05, and the remaining coefficients are calculated), d = 0.05 mm is obtained; hardness Elastic modulus E s =b0+b1c+b2α+b3ρ+b4φ(b0=1000, b1=2, b2=-50, b3=1, b4=-200, Poisson's ratio ν=0.3), calculated H=20MPa; porosity φ adopts a two-parameter calibration model with calibration coefficients c0=0.02, c1=0.01, c2=-0.03, reference density ρ ref =1700kg / m 3 , reference attenuation coefficient α ref =0.5dB / m, and the calibrated porosity φ=0.42.

[0144] Through the above-mentioned specific implementation methods, this measuring device can efficiently and accurately complete the in-situ measurement of the acoustic characteristic parameters and sediment-related parameters of shallow seabed sediment layers. Compared with traditional measurement technologies, it has significantly improved the measurement accuracy and data comprehensiveness, and can be widely used in marine geological exploration, marine engineering construction and other fields.

[0145] The above are only embodiments of the present invention. The invention is not limited to the fields involved in this implementation case. Common knowledge such as the known specific structures and characteristics in the scheme is not described in detail here. Ordinary technicians in the relevant field are aware of all common technical knowledge in the technical field to which the invention belongs before the application date or priority date, can obtain all existing technologies in the field, and have the ability to apply conventional experimental means before that date. Ordinary technicians in the relevant field can improve and implement this scheme in combination with their own abilities under the inspiration given by this application. Some typical known structures or known methods should not become obstacles for ordinary technicians in the relevant field to implement this application. It should be pointed out that for those skilled in the art, without departing from the structure of the present invention, several variations and improvements can be made, which should also be regarded as the scope of protection of the present invention. These will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. An in-situ measurement device for seabed sound velocity gradient based on a transducer array, characterized in that: It includes a transducer array unit, a depth adjustment unit, a transmitting and receiving control unit, and a data processing unit; The transducer array unit includes a plurality of transmitting transducers and a plurality of receiving transducers, wherein the plurality of transmitting transducers constitute a transmitting array, and the plurality of receiving transducers constitute a receiving array. The opening angles of the transducers in the transmitting array and the receiving array are set to ensure that the plurality of receiving transducers can receive signals from the transmitting array. The transmitting array and the receiving array are provided with a protective shell, and the strength of the protective shell is sufficient to ensure that the shell can penetrate seabed sediments of various hardnesses. The depth adjustment unit is connected to the protective housings of the transmitting array and the receiving array respectively, and is used to control the depth of the transmitting array and the receiving array entering the seabed. The depth adjustment unit is provided with an insertion sensor capable of obtaining real-time data on the depth of the transmitting array and the receiving array at the seabed. The depth adjustment unit also includes a power source, which provides power for the transmitting array and the receiving array to penetrate the seabed. The transmitting and receiving control unit is respectively connected to the transmitting array and the receiving array signal, and is used to control the transmitting array to perform fixed-distance, multi-frequency time-sequential transmission, and control the receiving array to perform multi-channel synchronous reception; The data processing unit is connected to the receiving array and is used to receive the signal obtained by the receiving array, and obtain the acoustic characteristic parameters of the shallow seabed sediment layer based on the received signal inversion, wherein the acoustic characteristic parameters include sound velocity, attenuation, density and porosity; and obtain the particle size, hardness and porosity parameters of the seabed sediment based on the acoustic characteristic parameters.

2. The in-situ measurement device for seabed sound velocity gradient based on transducer array according to claim 1, characterized in that: The opening angle of each transducer in the transmitting array and the receiving array is optimized by the following formula: Among them, θ optimal is the optimal opening angle of the transducer, α is the sound intensity attenuation coefficient in the seabed sediment, which is obtained by fitting the function α=f(ρ,φ) using the least squares method based on the sound attenuation experimental data of the target sea sediment in the early stage, ρ is the sediment density, φ is the sediment porosity; d is the straight-line distance between the transmitting transducer and the receiving transducer; I0 is the initial sound intensity of the transmitting transducer, I min is the minimum sound intensity that can be effectively recognized by the receiving transducer; c is the sound velocity in the seabed sediment, which is updated in real time by the data processing unit based on the initial measurement results; T is the sound wave propagation time; At the same time, the transmitting array adopts an adaptive beamforming model and calculates the weighting coefficient w of each transmitting transducer by the following formula: n : Where N is the number of transmitting transducers, β n =kd n sinθ,k is the wave number, where f j is the jth transmitting frequency, d n is the distance between the nth transmitting transducer and the reference point, and θ is the angle between the sound wave propagation direction and the array normal direction.

3. The in-situ measurement device for seabed sound velocity gradient based on transducer array according to claim 2, characterized in that: The protective shell adopts a streamlined frustum structure, including an upper cylindrical section and a lower conical section, and a spiral guide groove is provided on the outer surface of the conical section; Elastic vibration-damping supports with the same structure are respectively provided between the transmitting array, the receiving array and the protective housing. The elastic vibration-damping supports include: The base plate is located in the inner wall of the protective shell. The inner wall of the protective shell is provided with an annular card slot, the card slot is filled with waterproof sealant, and the base plate is fixedly connected to the card slot; An elastic cantilever beam, one end of which is fixedly connected to the base plate; A spherical hinge, one end of the spherical hinge is fixed to the other end of the elastic cantilever beam, the other end of the spherical hinge is fixed to the transmitting array or the receiving array, and the surface of the spherical hinge is covered with a polytetrafluoroethylene lubricating layer; The transmitting array or the receiving array is respectively located in the protective shell, and the transmitting array or the receiving array is isolated from the seawater by a flexible diaphragm.

4. The in-situ measurement device for seabed sound velocity gradient based on transducer array according to claim 3, characterized in that: The cone angle θ of the cone segment satisfies the formula: where σ y is the yield strength of the hardest sediment in the target sea area, ρ is the average density of the device, g is the acceleration of gravity, and h is the designed maximum penetration depth; The pitch P and cone angle θ of the guide groove satisfy the fluid dynamics relationship: Where r is the radius of the cone segment, ρ w is the density of seawater, v is the penetration velocity, C d is the drag coefficient.

5. The in-situ measurement device for seabed sound velocity gradient based on transducer array according to claim 4, characterized in that: The elastic cantilever beam is made of titanium alloy, and its Young's modulus E is the same as the Young's modulus E of the shell material. h satisfy: Where μ is the damping ratio, σ max is the allowable stress of the shell material, f is the working frequency of the device, and m is the mass of the transducer array; Elastic modulus E of the flexible diaphragm m satisfy: Where ΔP is the maximum pressure difference between the inside and outside, t is the diaphragm thickness, D is the diaphragm diameter, and ν is the Poisson's ratio.

6. The in-situ measurement device for seabed sound velocity gradient based on transducer array according to claim 5, characterized in that: The depth adjustment unit includes: A connecting seat, with electric push rod assemblies at both ends of the connecting seat respectively, the electric push rod assemblies are hinged to the protective shell of the transmitting array and the protective shell of the receiving array respectively, and the ends of the electric push rod assemblies are fixedly connected to the connecting seat; The insertion sensor is a differential pressure depth sensor installed in the guide groove of the conical section of the protective shell. Its measured value H is corrected by the following formula: Where H0 is the initial reading, P is the sensor pressure value, P0 is the atmospheric pressure, and k is the fluid resistance coefficient. By fitting the experimental data, k = 0.5 + 0.3log 10 (Re), Re is the Reynolds number.

7. The in-situ measurement device for seabed sound velocity gradient based on transducer array according to claim 6, characterized in that: The transmitting and receiving control unit adopts an adaptive multi-frequency timing control model and a synchronous trigger compensation mechanism, specifically including: The fixed-distance, multi-frequency sequential transmission of the transmitting array is determined by the following formula to determine the transmission parameters: Transmitting frequency sequence {f n }satisfy Where n=1,2,…,N, N is the number of set transmission frequencies, f min is the minimum transmission frequency, γ is the frequency distribution adjustment coefficient, and according to the estimated sound attenuation coefficient α of the seabed sediment 预估 By formula Dynamic adjustment, α 阈值 is the preset sound attenuation threshold; The transmission time interval Δt between adjacent transmitting transducers mn satisfy Where Δd is the distance between adjacent transmitting transducers, c 预估 is the estimated sound velocity in seafloor sediments, Δt 补偿 To compensate for the time, the formula Calculation, τ is the signal transmission delay correction coefficient, f s is the system sampling frequency.

8. The in-situ measurement device for seabed sound velocity gradient based on transducer array according to claim 7, characterized in that: The multi-channel synchronous reception of the receiving array adopts a phase difference calibration model, and the time synchronization error of each receiving channel is Compensation is performed using the following formula: where Δφ i is the phase difference between the i-th receiving channel and the reference channel, Δl i is the distance difference between the i-th receiving transducer and the reference receiving transducer, c is the sound speed measured in real time; by adjusting the trigger time of each receiving channel, the synchronization error is satisfied The transmitting and receiving control unit is also provided with an interference avoidance algorithm. When the ambient noise intensity I is detected, noise Exceeding threshold I 阈值 When, through the formula f 新 =f 原 ±Δf×sgn(I noise -I 阈值 ) dynamically adjusts the transmission frequency, where Δf is the frequency adjustment step, sgn is the sign function, and adjusts the transmission timing so that the transmission time interval Δt between adjacent transmitting transducers is mn Increase Δt 避扰 , λ noise is the wavelength of the interference noise.

9. The in-situ measurement device for seabed sound velocity gradient based on transducer array according to claim 8, characterized in that: The data processing unit adopts a multi-parameter joint inversion model to obtain the acoustic characteristic parameters of the shallow seabed sediment layer through the following iterative algorithm: Establishing the objective function where x = [c, α, ρ, φ] T is the acoustic characteristic parameter vector to be inverted, including the sound velocity c, attenuation coefficient α, density ρ and porosity φ; M is the number of receiving transducers, and N is the number of transmitting frequencies; is the observed signal amplitude of the i-th receiving transducer at the j-th transmitting frequency, is the theoretical signal amplitude calculated based on the parameter vector x; The Levenberg-Marquardt algorithm is used for iterative solution, and the iterative formula is x k+1 =x k +(J T J+λI) -1 J T (yf(x k )), where x k is the parameter vector of the kth iteration, J is the Jacobian matrix of the objective function F(x) with respect to x, and λ is the damping factor. Dynamic adjustment, λ0 is the initial damping factor, y is the observed signal vector, f(x k ) is the theoretical signal vector of the kth iteration; When satisfied When , the iteration is terminated and the final acoustic characteristic parameters are obtained, where ε is the preset convergence threshold.

10. The in-situ measurement device for seabed sound velocity gradient based on transducer array according to claim 8, characterized in that: The data processing unit uses the following empirical-theoretical hybrid model to obtain the particle size d, hardness H, and porosity φ parameters of the seabed sediment based on the acoustic characteristic parameters obtained by inversion: The particle size d is calculated by the formula Calculate, where a0, a1, ..., a 33 is the regression coefficient obtained through laboratory measurement and data analysis of sediment samples in the target sea area; Hardness H uses the dynamic modulus-hardness conversion model The elastic modulus E s By formula E s =b0+b1c+b2α+b3ρ+b4φ, where b0, b1,…, b4 are regression coefficients and Poisson’s ratio ν is preset according to the sediment type; The porosity φ is calibrated using a two-parameter model φ = φ 反演 +Δφ, where φ 反演 is the porosity obtained by the multi-parameter joint inversion model, and the calibration quantity Δφ is obtained by the formula Calculation, c0, c1, c2 are calibration coefficients, ρ ref and α ref are the reference density and reference attenuation coefficient.

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