Scale test sound pressure compensation method during sound velocity mismatch

Abstract

The invention relates to a scale test sound pressure compensation method during sound velocity mismatch, which comprises the following steps of: 1, determining a scale coefficient N, performing 1 / N scaling on underwater acoustic environment geometric parameters of a non-scale test environment, and determining scale test parameters during non-sound velocity mismatch; 2, calculating the sound velocity mismatch amount delta c according to the sound velocity profiles of the non-scaling test environment and the scaling test environment, and calculating the average value c0 of the sound velocity profiles in the non-sound velocity mismatch environment as a reference sound velocity; and 3, setting a sound velocity mismatch correction coefficient alpha, and calculating a sound pressure field distance phase compensation coefficient beta. According to the invention, by calculating the sound pressure distance phase compensation factor related to the sound velocity mismatch, the nonlinear compensation of the sound pressure error caused by the linear mismatch of the sound velocity profile is realized, the scaling test sound pressure error caused by the linear mismatch of the sound velocity profile can be effectively solved, and more accurate sound field data is provided for scaling test detection performance verification.

Description

Technical field:

[0001] The invention belongs to the technical field of underwater acoustics and underwater acoustic signal processing, and in particular relates to a method for compensating sound pressure in a scaled-down test when sound velocity mismatch occurs. Background technology:

[0002] The scaled-down test is an equivalent test method to study the acoustic scattering characteristics of underwater targets and the detection performance of active sonar targets. Using the scaled-down model of the target, a controllable and repeatable scaled-down test verification study for the actual boat sea test can be carried out in a pool or lake, reducing the complexity of the detection performance verification under the actual test conditions. The scaled-down test requires the guarantee of acoustic similarity, so as to obtain the sound field propagation law and target echo characteristics equivalent to those in the actual marine environment. At present, the underwater acoustic scaled-down test is mainly carried out around the geometric scaled-down of the actual boat target, and according to the principle of acoustic similarity, the frequency of the transmitted signal is increased to keep ka unchanged, so as to obtain the acoustic scattering characteristics of the actual boat target according to the acoustic scattering characteristics of the equivalent target. Since the influence of the underwater acoustic channel can be removed during the measurement of the target acoustic scattering characteristics, the change of the sound speed in the scaled-down test can be ignored.

[0003] The scaled-down test verification of target detection performance requires that the sound velocity profile of the underwater acoustic environment remain consistent to avoid errors introduced by changes in sound pressure after scaling. However, in the actual scaled-down test, it is difficult to ensure that the sound velocity profile of the underwater acoustic environment in the actual ocean environment and the lake / laboratory waveguide are exactly the same. The changes in the underwater acoustic environment after scaling, especially the changes in the sound velocity profile, will cause errors in the sound pressure of the scaled-down test at horizontal distances, resulting in a decrease in the detection performance verification capability that relies on distance propagation loss. Summary of the invention:

[0004] The technical problem to be solved by the present invention is to provide a method for compensating sound pressure in a scaled-down test when there is a sound velocity mismatch. The method proposes a horizontal distance-dimensional sound pressure compensation method based on a simple normal wave model. By calculating a sound pressure distance phase compensation factor related to the sound velocity mismatch, nonlinear compensation for the sound pressure error caused by the linear mismatch of the sound velocity profile is achieved. The scaled-down test sound pressure error caused by the linear mismatch of the sound velocity profile can be effectively solved, and more accurate sound field data can be provided for verification of the detection performance of the scaled-down test.

[0005] The technical solution of the present invention is to provide a method for compensating sound pressure in a scaled-down test when sound velocity mismatch occurs, comprising the following steps:

[0006] Step 1: Determine the reduction coefficient N, scale the geometric parameters of the underwater acoustic environment of the non-reduction test environment by 1 / N, and determine the reduction test parameters when there is no sound speed mismatch;

[0007] Step 2: Calculate the sound speed mismatch Δc according to the sound speed profiles of the non-scaled test environment and the scaled test environment, and calculate the average value c0 of the sound speed profile in the environment without sound speed mismatch as the reference sound speed;

[0008] Step 3: Set the sound speed mismatch correction coefficient α and calculate the sound pressure field distance phase compensation coefficient β;

[0009] Step 4: Determine the distance phase term of the sound pressure field of the reduced ratio test after compensation based on the distance phase compensation coefficient β Resample the horizontal distance r′ to obtain a new horizontal distance sample

[0010] Step 5: Sampling based on horizontal distance Determine the sound pressure data of the reduction ratio test after compensation The expression of is used to calculate the sound pressure data after compensation;

[0011] Step 6: Generate sound pressure data in a non-scaled test environment using a simple normal wave model, and calculate the root mean square error and compensation gain of the sound pressure amplitude before and after compensation;

[0012] Step 7: Adjust the sound speed mismatch correction coefficient α according to the distance phase compensation gain to determine whether to compensate the scaled test sound pressure data again.

[0013] As a preferred embodiment, the specific operation of step 1 is as follows: assuming that the actual target radius is a, under the condition that the acoustic parameter ka remains unchanged, the radius of the scaled target model is a′, and the calculation formula of the scale factor is:

[0014] N=a / a′,

[0015] The scaled-down test parameters when there is no sound velocity mismatch are:

[0016] H′=H / N,

[0017] z′ s =z s / N,

[0018] z′=z / N,

[0019] r′=r / N,

[0020] Among them, H, z s , z, r are the water depth, sound source depth, receiving depth and receiving horizontal distance in the non-scaled test respectively; H′, z′ s , z′, r′ are the water depth, sound source depth, receiving depth and receiving horizontal distance in the scaled-down test respectively.

[0021] As a preferred embodiment, the specific operation of step 2 is as follows: assuming that the sound velocity profile in the scaled-down test environment without sound velocity mismatch is c(z), and the sound velocity profile in the actual scaled-down test environment is c′(z), after smoothing the sound velocity profile, the sound velocity mismatch amount is calculated as

[0022] Δc=c′(z)-c(z)

[0023] The calculation formula for the reference sound speed c0 is:

[0024]

[0025] As a preferred embodiment, the specific operation of step 3 is as follows: in the scaled-down test, under the condition of sound velocity mismatch of Δc, the horizontal wave number Satisfaction relationship

[0026]

[0027] Where ω′ is the angular frequency of the sound source in the scaled-down test, k′ is the horizontal wave number of the sound pressure field in the scaled-down test when there is no sound velocity mismatch. zm is the corresponding vertical wave number, the sound velocity mismatch degree Δ = Δc / c0; α is the sound velocity mismatch correction coefficient, which is used to compensate for the error introduced by the linear approximation process of the horizontal wave number; when the sound velocity mismatch is small, the initial value of the sound velocity mismatch correction coefficient is set to α = 1; thus, the distance phase compensation coefficient of the sound pressure field is calculated as

[0028]

[0029] As a preference, in step 4, after determining the distance phase compensation coefficient β, the scaled-down test sound pressure distance propagation phase term with or without sound speed mismatch satisfies the relationship

[0030]

[0031] Among them, horizontal distance sampling is the unit for the imaginary part of a complex number.

[0032] As a preferred embodiment, in step 5, under the condition of no sound velocity mismatch, the sound pressure field expression of the scaled-down test is:

[0033]

[0034] Among them, Ψ′ m (·) is the depth function of the mth mode excited in the scaled test environment, M is the total number of normal wave modes excited by the sound source in the scaled test environment, ρ(z′ s ) is the water density at the sound source depth, usually 1g / cm 3 ; When there is a sound velocity mismatch, the scaled test sound pressure expression is

[0035]

[0036] Using the distance-phase compensation relationship in step 4, the sound pressure expression of the compensation reduction ratio test can be written as

[0037]

[0038] For distance phase Compensation can offset the sound pressure error on the horizontal distance caused by the sound speed mismatch.

[0039] Compared with the prior art, the present invention has the following advantages:

[0040] In view of the problem that the sound pressure of the underwater acoustic scaled test is inaccurate at the horizontal distance due to the sound velocity mismatch, a sound pressure compensation method for the scaled test when the sound velocity mismatch occurs is proposed. This method uses a simple normal wave model to establish the sound pressure field expression, obtains the mapping relationship between the sound velocity mismatch size and the horizontal wave number change in the scaled environment, and then maps the change of the horizontal wave number to the change of the distance phase term of the sound pressure field at the horizontal distance, determines the distance phase compensation coefficient, and finally uses a nonlinear interpolation method to compensate the sound pressure data, thereby obtaining sound pressure data consistent with that in the non-scaled test environment. The simulation results show that the present invention can obtain sound pressure data that meets the requirements in both different frequencies and different sound velocity mismatch sizes, proving that this method can reduce the sound pressure error caused by inconsistent sound velocity profiles in scaled tests, and provide accurate sound pressure data for scaled test detection performance verification. Description of the drawings:

[0041] Figure 1 The present invention is implemented as a flow chart.

[0042] Figure 2 It is a schematic diagram of the scaled-down test under the sound speed mismatch condition of the present invention and a simulated sound speed profile of the non-scaled test environment.

[0043] Figure 3 The figure is a comparison of the horizontal wave number conversion in the scaled-down test environment under the same sound velocity mismatch conditions with different sound source frequencies of the present invention.

[0044] Figure 4 The following is a comparison of the horizontal wave number conversion in the scaled-down test environment under different sound speed mismatch conditions for the present invention.

[0045] Figure 5 The figure is a comparison of compensation results in the case of a sound source frequency of 300 Hz and a sound speed mismatch of 3 m / s in an embodiment of the present invention.

[0046] Figure 6 The figure is a comparison of compensation results in the case of a sound source frequency of 400 Hz and a sound speed mismatch of 3 m / s in an embodiment of the present invention.

[0047] Figure 7The figure is a comparison of compensation results in the case of a sound source frequency of 300 Hz and a sound speed mismatch of 5 m / s in an embodiment of the present invention.

[0048] Figure 8 The figure is a comparison of compensation results in the case of a sound source frequency of 400 Hz and a sound speed mismatch of 5 m / s in an embodiment of the present invention.

[0049] Fig. 9 The figure is a comparison of compensation gains under different sound velocity mismatch conditions of the embodiments of the present invention. Specific implementation method:

[0050] The present invention will be further described below with reference to the accompanying drawings:

[0051] A method for compensating sound pressure in a scaled-down test when sound velocity mismatch occurs, such as Figure 1 The specific implementation process is as follows:

[0052] 1) Determine the scaling factor N, scale the geometric parameters of the underwater acoustic environment of the non-scaling test environment by 1 / N, and determine the scaling test parameters when there is no sound speed mismatch.

[0053] Assuming that the actual target radius is a, under the condition that the acoustic parameter ka remains unchanged, the radius of the scaled target model is a′, and the calculation formula of the scale factor is:

[0054] N=a / a′

[0055] The scaled-down test parameters when there is no sound velocity mismatch are:

[0056] H′=H / N

[0057] z′ s =z s / N

[0058] z′=z / N

[0059] r′=r / N

[0060] Among them, H, z s , z, r are the water depth, sound source depth, receiving depth and receiving horizontal distance in the non-scaled test respectively; H′, z′ s , z′, r′ are the water depth, sound source depth, receiving depth and receiving horizontal distance in the scaled-down test respectively.

[0061] 2) Calculate the sound speed mismatch Δc based on the sound speed profiles of the non-scaled test environment and the scaled test environment, and calculate the average value c0 of the sound speed profile in the environment without sound speed mismatch as the reference sound speed.

[0062] Assuming that the sound velocity profile in the scaled-down test environment without sound velocity mismatch is c(z), and the sound velocity profile in the actual scaled-down test environment is c′(z), after smooth fitting of the sound velocity profile, the magnitude of the sound velocity mismatch is calculated as:

[0063] Δc=c′(z)-c(z)

[0064] The calculation formula for the reference sound speed c0 is:

[0065]

[0066] 3) Set the sound speed mismatch correction coefficient α and calculate the sound pressure field distance phase compensation coefficient β.

[0067] In the scaled-down test, when the sound velocity mismatch is Δc, the horizontal wave number Satisfaction relationship

[0068]

[0069] Where ω′ is the angular frequency of the sound source in the scaled-down test, k′ is the horizontal wave number of the sound pressure field in the scaled-down test when there is no sound velocity mismatch. zm is the corresponding vertical wave number, and the sound velocity mismatch degree Δ = Δc / c0. α is the sound velocity mismatch correction coefficient, which is used to compensate for the error introduced by the horizontal wave number linear approximation process. When the sound velocity mismatch is small, the initial value of the sound velocity mismatch correction coefficient is set to α = 1. Thus, the distance phase compensation coefficient of the sound pressure field is calculated as

[0070]

[0071] 4) Determine the distance phase term of the sound pressure field of the compensation reduction ratio test according to the distance phase compensation coefficient β Resample the horizontal distance r′ to obtain a new horizontal distance sample

[0072] After determining the distance phase compensation coefficient β, the scaled-down test sound pressure distance propagation phase term with and without sound speed mismatch satisfies the relationship

[0073]

[0074] Among them, horizontal distance sampling is the unit for the imaginary part of a complex number.

[0075] 5) Sampling based on horizontal distance Determine the sound pressure data of the reduction ratio test after compensation The expression of is used to calculate the sound pressure data after compensation.

[0076] Under the condition of no sound velocity mismatch, the sound pressure field expression of the scaled-down test is:

[0077]

[0078] Among them, Ψ′ m (·) is the depth function of the mth mode excited in the scaled test environment, M is the total number of normal wave modes excited by the sound source in the scaled test environment, ρ(z′ s ) is the water density at the sound source depth, usually 1g / cm 3 When there is a sound velocity mismatch, the scaled test sound pressure expression is

[0079]

[0080] Using the distance-phase compensation relationship in step 4), the sound pressure expression of the compensation reduction ratio test can be written as

[0081]

[0082] Therefore, for the distance phase term The compensation can offset the sound pressure error on the horizontal distance caused by the sound speed mismatch. The present invention uses a nonlinear interpolation method to perform distance phase compensation on the scaled test sound pressure p' on the horizontal distance, and to perform sound pressure amplitude compensation on the scaled test sound pressure p' on the horizontal distance. Convert and obtain the sound pressure after compensation

[0083] 6) The sound pressure data in the non-scaled test environment is generated using the simple normal wave model, and the root mean square error and compensation gain of the sound pressure amplitude before and after compensation are calculated.

[0084] The sound pressure data p is generated according to the non-scaled test environment parameters, and the N-fold amplitude conversion is performed to obtain the sound pressure in the scaled test environment. Then the formula for calculating the root mean square error of the sound pressure amplitude after the distance phase compensation reduction ratio test is:

[0085]

[0086] By Substituting p′ for the root mean square error of the sound pressure amplitude in the scaled-down test before compensation, e(z), the distance-phase compensation gain G can be calculated by:

[0087]

[0088] 7) Adjust the sound speed mismatch correction coefficient α according to the distance phase compensation gain to determine whether to compensate the scaled test sound pressure data again.

[0089] Determine whether to correct α based on the distance phase compensation gain G. When G < 0dB, adjust the sound speed mismatch correction coefficient to α = 1 + Δ / 10, recalculate the horizontal wave number change coefficient β of the sound pressure field, repeat 3) to 7), and calculate the sound pressure data after distance phase compensation. Reduce the impact of sound velocity mismatch and provide accurate sound pressure data for scaled test detection performance verification.

[0090] Simulation and sea trial data test results

[0091] Based on the above implementation process, the processing results of the present invention are given through simulation. The simulation processing is as follows: Figures 2 to 9 shown.

[0092] Computer simulation 1: Use the KRAKEN acoustic simulation tool to generate sound pressure data under the condition of sound velocity mismatch. The simulation environment is as follows: Figure 2 The simulation parameters are as follows: for the non-scaled test environment, the water depth is 106m and the water density is 1g / cm 3 , the sound velocity profile is as follows Figure 2 (a) shows that under the water body is a sediment layer with a thickness of 20m and a density of 1.5g / cm 3 , the sound velocity of the sediment layer is 1800m / s, and the attenuation is 0.5dB / λ. The base is an acoustic half-space bottom with a density of 2.6g / cm 3 , sound velocity 5200m / s, attenuation 1.8dB / λ. Sound source depth 40m, receiving depth 50m, horizontal receiving distance is set to 1m interval up to 5km. Sound source frequencies are 300Hz and 400Hz respectively. Figure 2 (b) shows a scaled-down test environment with linear mismatch of sound velocity profile, with a sound velocity mismatch of Δc = 3 m / s and a scale factor of N = 5. In the scaled-down test environment, the water depth is changed to 21.2 m, the sound source depth is changed to 8 m, the receiving depth is changed to 10 m, and the horizontal receiving distance is changed to an interval of 0.2 m up to 1 km. Figure 3 The comparison results of the horizontal wavenumber changes in the sound pressure field when the sound source frequency is 300Hz and 400Hz under the mismatch condition of Δc=3m / s are given. It can be seen that after N=5 times conversion, when the sound source frequency increases, the horizontal wavenumber error caused by the sound velocity mismatch becomes larger, resulting in an increase in the sound pressure field error. Figure 4 The comparison results of the horizontal wave number changes when the sound source frequency is 300Hz and the sound velocity mismatch is Δc=3m / s and Δc=5m / s are given. It can be seen that the larger the sound velocity mismatch is, the larger the horizontal wave number error is. The simulation results show that both the sound source frequency and the sound velocity mismatch will cause errors in the sound pressure of the scaled-down test when the sound velocity mismatch occurs, and the sound pressure error is mainly introduced by the change in the horizontal wave number.

[0093] Computer simulation 2: Calculate the distance phase compensation coefficient β and the corresponding horizontal distance resampling according to the size of the sound speed mismatch Δc The distance phase compensation of the sound pressure data is completed by using a one-dimensional nonlinear interpolation method. According to the sound velocity profile in the non-scaled test environment, the reference sound velocity c0 = 1533.9 m / s can be calculated. When the sound velocity mismatch Δc = 3 m / s and Δc = 5 m / s, the correction coefficient α = 1 is taken, and the distance phase compensation coefficients β = 0.9980 and β = 0.9968. Figure 5 The compensation results are compared when the sound source frequency is 300Hz and the sound velocity mismatch Δc = 3m / s. It can be seen that when the sound velocity mismatch occurs, there is an obvious error in the horizontal distance between the sound pressure field of the scaled test and the sound pressure field of the non-scaled test. After distance phase compensation, the sound pressure after compensation is consistent with the sound pressure change of the non-scaled test, and the compensation effect is good. Figure 6 The compensation results are compared when the sound source frequency is 400Hz and the sound speed mismatch Δc=3m / s. It can be seen that the sound pressure data of the scaled-down test after distance phase compensation is consistent with the sound pressure results in the non-scaled test environment, proving that the method proposed in the present invention is effective under different sound source frequencies. Figure 7 and Figure 8 The compensation results of the sound pressure data of the scaled-down test with different sound source frequencies under the condition of sound velocity mismatch Δc = 5m / s are compared. Figure 5 and Figure 6 The results show that under the same sound source frequency, the distance phase compensation method proposed in the present invention is effective under different sound speed mismatch sizes, and can obtain sound pressure data consistent with the non-scaled test environment. The above results prove that the method of the present invention can obtain sound pressure field data that meets the requirements under different sound source frequencies and different sound speed mismatch conditions, reducing the impact of sound pressure field errors caused by sound speed mismatch in scaled tests.

[0094] Computer simulation 3: Set the sound speed mismatch size Δc from 0 to 8m / s, and calculate the distance phase compensation gain G under different Δc conditions. The sound source frequency is 300Hz and 400Hz respectively, and the results are as follows Fig. 9 As shown. It can be seen that when Δc = 0m / s, the compensation gain at both sound source frequencies is 0dB. At this time, there is no sound velocity mismatch problem in the scaled-down test environment. The method of the present invention is suitable for scaled-down tests without sound velocity mismatch. When Δc≠0, the compensation gain after compensating the scaled-down test sound pressure data using the method of the present invention can reach more than 0dB, and when the sound velocity mismatch becomes larger, the compensation gain increases accordingly, proving that the method of the present invention is effective.

[0095] The above simulation analysis results show that the sound field compensation method for the scaled-down test when the sound velocity mismatch is proposed in the present invention can effectively reduce the sound pressure field error caused by the sound velocity mismatch in the scaled-down test, and the sound pressure data obtained by the compensation method under different sound source frequencies and different sound velocity mismatch sizes are consistent with the sound pressure data in the non-scaled test environment. The invention provides an effective method to counteract the influence of sound velocity mismatch in the signal processing application of underwater acoustic scaled-down test, which can obtain accurate scaled-down test sound pressure data and has good application prospects.

[0096] The above is only an explanation of the preferred embodiments of the present invention, which should not be construed as a limitation on the claims. Any equivalent process changes made using the present invention specification are included in the patent protection scope of the present invention.

Claims

1. A method for compensating sound pressure in a scaled-down test when sound velocity mismatch occurs, characterized in that: The following steps are included: Step 1: Determine the reduction coefficient N, scale the geometric parameters of the underwater acoustic environment of the non-reduction test environment by 1 / N, and determine the reduction test parameters when there is no sound speed mismatch; Step 2: Calculate the sound speed mismatch Δc according to the sound speed profiles of the non-scaled test environment and the scaled test environment, and calculate the average value c0 of the sound speed profile in the environment without sound speed mismatch as the reference sound speed; Step 3: Set the sound speed mismatch correction coefficient α and calculate the sound pressure field distance phase compensation coefficient β; Step 4: Determine the distance phase term of the sound pressure field of the reduced ratio test after compensation based on the distance phase compensation coefficient β Resample the horizontal distance r′ to obtain a new horizontal distance sample Step 5: Sampling based on horizontal distance Determine the sound pressure data of the reduction ratio test after compensation The expression of is used to calculate the sound pressure data after compensation; Step 6: Generate sound pressure data in a non-scaled test environment using a simple normal wave model, and calculate the root mean square error and compensation gain of the sound pressure amplitude before and after compensation; Step 7: Adjust the sound speed mismatch correction coefficient α according to the distance phase compensation gain to determine whether to compensate the scaled test sound pressure data again.

2. The method for compensating sound pressure in a scaled-down test when sound velocity mismatch occurs according to claim 1, characterized in that: The specific operation of step 1 is as follows: Assuming that the actual target radius is a, under the condition that the acoustic parameter ka remains unchanged, the radius of the scaled target model is a′, and the calculation formula of the scale factor is: N=a / a′, The scaled-down test parameters when there is no sound velocity mismatch are: H′=H / N, With' s =from s / N, z′=z / N, r′＝r / N, Among them, H, z s , z, r are the water depth, sound source depth, receiving depth and receiving horizontal distance in the non-scaled test respectively; H′, z′ s , z′, r′ are the water depth, sound source depth, receiving depth and receiving horizontal distance in the scaled-down test respectively.

3. The sound pressure compensation method for scaled-down test when sound velocity mismatch occurs according to claim 1, characterized in that: The specific operation of step 2 is as follows: Assuming that the sound velocity profile in the scaled-down test environment without sound velocity mismatch is c(z), and the sound velocity profile in the actual scaled-down test environment is c′(z), after smoothing the sound velocity profile, the magnitude of the sound velocity mismatch is calculated as Δc=c′(z)-c(z) The calculation formula for the reference sound speed c0 is:

4. The method for compensating sound pressure in a scaled-down test when sound velocity mismatch occurs according to claim 1, characterized in that: The specific operation of step 3 is as follows: In the scaled-down test, under the condition of sound velocity mismatch of Δc, the horizontal wave number Satisfaction relationship Where ω′ is the angular frequency of the sound source in the scaled-down test, k′ is the horizontal wave number of the sound pressure field in the scaled-down test when there is no sound velocity mismatch. zm is the corresponding vertical wave number, the sound velocity mismatch degree Δ = Δc / c0; α is the sound velocity mismatch correction coefficient, which is used to compensate for the error introduced by the linear approximation process of the horizontal wave number; when the sound velocity mismatch is small, the initial value of the sound velocity mismatch correction coefficient is set to α = 1; thus, the distance phase compensation coefficient of the sound pressure field is calculated as 5. The method for compensating sound pressure in a scaled-down test when sound velocity mismatch occurs according to claim 1, characterized in that: In step 4, after determining the distance phase compensation coefficient β, the scaled-down test sound pressure distance propagation phase term with and without sound speed mismatch satisfies the relationship Among them, horizontal distance sampling is the unit for the imaginary part of a complex number.

6. The method for compensating sound pressure in a scaled-down test when sound velocity mismatch occurs according to claim 1, characterized in that: In step 5, under the condition of no sound velocity mismatch, the sound pressure field expression of the scaled-down test is: Among them, Ψ′ m (·) is the depth function of the mth mode excited in the scaled test environment, M is the total number of normal wave modes excited by the sound source in the scaled test environment, ρ(z′ s ) is the water density at the sound source depth, usually 1g / cm 3 ; When there is a sound velocity mismatch, the scaled test sound pressure expression is Using the distance-phase compensation relationship in step 4, the sound pressure expression of the compensation reduction ratio test can be written as For distance phase Compensation can offset the sound pressure error on the horizontal distance caused by the sound speed mismatch.

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