Method and system for calculating waveguide invariants in Pekeris waveguide

Abstract

The invention provides a method and a system for calculating waveguide invariants in a Pekeris waveguide. The method and the system are used for reflecting an influence rule of seabed parameters on the waveguide invariants. The waveguide invariant formula is expressed as that the reciprocal of the waveguide invariant is the algebraic sum of the reciprocal of the waveguide invariant formula under the absolute hard seabed condition and the correction of the marine environment parameters. The formula comprises influence parameters such as sound wave frequency, sea depth, seawater sound velocity and density, seabed sound velocity and density and the like. According to the method, the calculation method of the waveguide invariants containing the seabed parameters is innovatively constructed, the formula is simple, and the physical significance is clear; by converting complex marine environment parameters into an algebraic model capable of being quantitatively calculated, quantitative mapping of the marine environment parameters and waveguide invariants is realized, so that the method has the technical advantages of parameter adjustability, influence traceability and rule visualization; the established approximation formula can provide a standardized calculation tool for applications such as underwater sound field characteristic analysis and marine environment parameter inversion.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of underwater acoustics, ocean engineering and underwater acoustic signal processing, and particularly relates to a Pekeris waveguide invariant calculation method and system. BACKGROUND

[0002] Researching the Pekeris shallow sea waveguide invariant approximate formula can be used for theoretical analysis of the interference structure of the sound field and the waveguide invariant, and can also be used for exploring the influence of frequency, ocean environmental parameters and other control variables on β. The core difference between shallow sea acoustics and deep sea acoustics lies in the boundary conditions: the acoustic characteristics of the sea surface and the seabed are significantly different. In shallow sea acoustics, the influence of the sea surface and the seabed on the sound field must be considered at the same time, and the seabed boundary is particularly complex - the differences in density and sound speed of the seabed caused by the impurity content of the seabed base layer, the diversity of the seabed and the stratified structure of the sediment layer are always the key research topics affecting the shallow sea waveguide invariant. With the progress of underwater acoustic measurement technology, it is found that the ocean sound field has a stable space-time interference structure. In the ocean waveguide, the sound field can be characterized as a superposition of discrete modes. Due to the interference between modes, the sound signal often presents an interference structure with certain geometric characteristics in the time domain, frequency domain and spatial domain. This phenomenon is usually manifested as alternating dark and light inclined stripes of sound intensity with distance-frequency change, and the slope of the stripes can define a dimensionless scalar parameter - the waveguide invariant β. This parameter, through the function relationship of group velocity and phase velocity (or slowness), condenses the waveguide dispersion characteristics, and can be approximately taken as 1 under the condition of small angle (θ<20°). As a core parameter that condenses the influence of multiple factors of the ocean sound field, the waveguide invariant has been an important direction of ocean acoustics since it was proposed by Soviet scientists in the mid-20th century. Due to its high sensitivity to seabed parameters, it is of great value to explore the influence of seabed parameters on the waveguide invariant. The relevant research results can be applied to the fields of spatial correlation improvement of underwater acoustic signals, sound source positioning, ocean environment monitoring and seabed geoacoustic inversion, and the application potential based on the waveguide invariant is huge in the future.

[0003] To obtain the variation of waveguide invariant with seabed parameters, the seabed parameters are usually changed by numerical simulation, and then the waveguide invariant is calculated, and finally the summary is condensed. Although this method is simple and fast, numerical simulation has contingency, and it is impossible to derive applicability conclusions. In order to analyze the influence of seabed parameters on waveguide invariant from the formula, Shang team proposed the concept of "effective boundary" in reference ("Relating waveguide invariant and bottom reflection phase-shift parameter Pin a Pekeris waveguide", published in J. Acoust. Soc. Am. 131 (5), 3691 in March 2012), using high-frequency approximation, based on a three-parameter model that can characterize the influence of seabed parameters, a formula is derived with seabed phase shift parameter P as the core. The formula is simple in form and clear in physical meaning, but it is limited by the high-frequency assumption, and its applicability is weak for shallow sea low-frequency scenarios, and its prediction of β value range is limited to 1 to 1.5. In 2022, Gihoon Byun established an approximate formula based on the effective seabed depth as reference ("The waveguide invariant for a Pekeris waveguide", published in J. Acoust. Soc. Am. 151 (1), 846 in February 2022), although it partially considers the influence of seabed parameters, the formula is complex and does not directly clarify the parameter influence law, and the calculation method is also more complex. SUMMARY

[0004] The purpose of the present application is to overcome the defects of low precision and contingency caused by only calculating the waveguide invariant by numerical simulation in the prior art.

[0005] In order to achieve the above purpose, the present application proposes a Pekeris waveguide waveguide invariant calculation method, comprising:

[0006] The calculation formula of the waveguide invariant is: the reciprocal of the waveguide invariant is the algebraic sum of the reciprocal of the waveguide invariant formula under the condition of the absolute hard seabed and a correction quantity containing the marine environment parameters.

[0007] As an improvement of the above method, the calculation formula of the waveguide invariant is specifically:

[0008]

[0009] Wherein, β kl represents the waveguide invariant of the interference of the k, l order normal wave; β kl (∞) represents the waveguide invariant of the interference of the k, l order normal wave under the condition of the absolute hard seabed; Δ klrepresents a correction quantity containing marine environment parameters.

[0010] As an improvement of the above method, the correction quantity containing marine environment parameters Δ kl represents:

[0011]

[0012] wherein θ k represents the grazing angle of the k-th normal wave; the intermediate variable F(θ) is represented as:

[0013]

[0014] wherein c w represents the sound speed in water; h represents the depth; ω represents the frequency; m b represents the density ratio of the seabed; n b represents the sound speed ratio of the seabed.

[0015] The application also provides a waveguide invariant calculation system in a Pekeris waveguide, which is realized based on the above method, and the system comprises:

[0016] The waveguide invariant calculation module is configured to calculate the waveguide invariant according to the calculation formula of the waveguide invariant; and the waveguide invariant formula is that the reciprocal of the waveguide invariant is the algebraic sum of the reciprocal of the waveguide invariant formula under the condition of an absolute hard seabed and a correction quantity containing marine environment parameters.

[0017] Compared with the prior art, the application has the following advantages:

[0018] The calculation method of the application is based on the Pekeris shallow sea waveguide invariant approximate formula derived from the normal wave group velocity circulation displacement formula, which has a clear physical image and is a strict formula for the Pekeris model. Compared with the prior art, the application has the following technical advantages: first, based on the strict circulation displacement theory of the Pekeris waveguide normal wave group velocity, the calculation and prediction of the Pekeris shallow sea waveguide invariant are more accurate; second, the formula can strictly prove that the Pekeris shallow sea waveguide invariant is generally not less than 1, and still has high prediction accuracy for the larger waveguide invariant value (> 2) under the condition of shallow sea low frequency; finally, the calculation method of the formula can clearly reflect the influence law of seabed parameters, frequency, sea depth and the like on the Pekeris shallow sea waveguide invariant. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 The waveguide invariant calculation method flowchart in the Pekeris waveguide is shown;

[0020] Figure 2 The eigenray and beam displacement are shown.

[0021] Figure 3 Liquid seabed propagation is shown, wherein c w represents the sound speed in water, p w represents the density, c b represents the seabed sound speed, p b represents the density, and θ represents the grazing angle, and the dashed line represents the beam displacement.

[0022] Figure 4 Density and sound speed distribution in Pekeris waveguide and values are shown, wherein A, B and C respectively represent three waveguides and corresponding density and sound speed, the water body is an isospeed layer, and the seabed is the bottom of an isospeed half-space.

[0023] Figure 5 Waveguide invariants related to mode 1 and mode 2 calculated by KRAKEN and the derived formula and the difference value thereof are shown when p b = 1.58 g / cm 3 , and the seabed sound speed c b = 1580 m / s.

[0024] Figure 6 Waveguide invariants related to mode 1 and mode 2 calculated by KRAKEN and the derived formula and the difference value thereof are shown when p b = 1.87 g / cm 3 , and the seabed sound speed c b = 1697 m / s.

[0025] Figure 7 Waveguide invariants related to mode 1 and mode 2 calculated by KRAKEN and the derived formula and the difference value thereof are shown when p b = 1.97 g / cm 3 , and the seabed sound speed c b = 1753 m / s. DETAILED DESCRIPTION

[0026] The technical solutions of the present application will be described in detail below with reference to the accompanying drawings.

[0027] In order to narrow the gap between the ideal waveguide and the actual environment, the Pekeris waveguide model with a penetrable half-space bottom is adopted in the present application, which can more accurately describe the shallow sea environment. The present application aims to derive a calculation method for reflecting the influence of seabed parameters on waveguide invariants in the Pekeris waveguide, and to lay a foundation for theoretical analysis of ocean acoustic field interference structure.

[0028] The application provides a waveguide invariant calculation method in a Pekeris waveguide, which comprises two parts of formula derivation and simulation verification. First, under the condition of an absolutely hard seabed, the density and sound speed of the seabed tend to infinity, and sound waves cannot penetrate the seabed, so the waveguide invariant calculation formula is formula (1.1). Then, the condition is extended to a liquid seabed, and the density and sound speed of the seabed are considered to be finite values, and sound waves can penetrate the seabed and reflect back to the water body. The new group velocity expression is derived by using the circulating displacement formula of the normal wave group velocity. The expression is substituted into the original definition formula of the waveguide invariant to derive a new explicit expression of the waveguide invariant containing frequency, water depth, seabed density and sound speed and other marine environmental parameters. Further, the expression is simplified to the waveguide invariant expression under the condition of an absolutely hard seabed and an algebraic sum of a correction term containing marine environmental factors. Finally, the formula is programmed to realize the rapid calculation method. The waveguide invariant results under the condition of a specific depth, a specific frequency range and different seabed parameter combinations are calculated by numerical simulation, and the results are compared with the standard results calculated by the KRAKEN program to verify the accuracy of the method.

[0029] The method constructs an approximate calculation method of the waveguide invariant of the Pekeris waveguide containing the influence law of the seabed parameters by the derived waveguide invariant calculation formula. Compared with the traditional waveguide invariant calculation method, the method has the following advantages: 1. Compared with the traditional KRAKEN numerical calculation method, the seabed parameters are directly introduced into the method, which is convenient for program implementation and theoretical characteristic analysis and reveals the internal law. 2. The formula significantly improves the accuracy compared with the previous calculation method under the condition of shallow water and low frequency, and still maintains high prediction accuracy for the case of β>2.

[0030] As shown in Figure 1 , the derivation process of the waveguide invariant calculation method provided by the application comprises:

[0031] Step 1: Derive a new group velocity formula based on the circulating displacement formula of the normal wave group velocity;

[0032] As shown in Figure 2 , under the condition of an absolutely hard seabed (the density and sound speed of the seabed tend to infinity), sound waves cannot penetrate the seabed interface to produce total reflection, and the waveguide invariant formula is as follows (formula 1.1). The circulating displacement formula of the normal wave group velocity is as shown in formula (1.2).

[0033]

[0034] wherein, and are the phase velocity and group velocity of the mth and nth normal waves respectively. l and T l represent the span of the lth normal wave and the time required for the corresponding eigenray to pass through a span, respectively, δl l is the wave beam displacement of the lth mode at the sea bottom and the corresponding time delay. Then, it is extended to the liquid sea bottom, considering the finite density and sound speed of the sea bottom (not infinite anymore), part of the sound wave will penetrate the sea bottom and reflect again. As shown in Fig. 1, the space is divided into two regions: Region I covers the sea surface and the water layer, and Region II is the sea bottom half-space below the water layer. This application does not consider the absorption and attenuation of the sea bottom, and adopts the Pekeris waveguide model with the ability to penetrate the bottom of the half-space, which is more capable of describing the shallow sea environment than the ideal waveguide. Then, based on the group velocity circular displacement formula of the normal mode, a new group velocity expression is derived as follows: Figure 3

[0035]

[0036] where θ l and are the grazing angle and the group velocity of the lth mode under the condition of an absolutely hard sea bottom, respectively.

[0037] Step 2: Substitute the newly derived group velocity formula into the original waveguide invariant expression, and then obtain the new waveguide invariant formula.

[0038] Based on the theoretical framework of the waveguide invariant formula under the condition of an absolutely hard sea bottom and the group velocity circular displacement formula of the normal mode, the interference of the kth and lth modes is introduced, and the new group velocity expression (Formula 1.3) is substituted into the original definition of the waveguide invariant to obtain Formula (1.4).

[0039]

[0040] where and are the phase velocity and group velocity of the kth and lth modes, respectively. θ k and τ k are the grazing angle and the time delay corresponding to the wave beam displacement at the sea bottom of the kth mode, respectively. T k represents the time required for the corresponding eigenray of the kth mode to pass through one span. represents the group velocity of the kth mode under the condition of an absolutely hard sea bottom.

[0041] Next, it is simplified, and under the condition of a small grazing angle, Taylor expansion is used:

[0042]

[0043] Therefore, after final simplification, we have:

[0044]

[0045] where β​​kl (∞) represents the waveguide invariant of the k, l-th normal mode under the condition of an absolutely hard bottom.

[0046] Let:

[0047]

[0048] Simplify Δ kl

[0049]

[0050] where:

[0051]

[0052]

[0053]

[0054] Step 3: Simulation verification is performed on the newly obtained waveguide invariant formula, and the accuracy is determined by comparing it with the waveguide invariant results calculated by KRAKEN;

[0055] The relationship between waveguide invariant β and frequency F under different seabed densities and seabed sound speeds. Three typical Pekeris seabed parameter models (depth h = 100 m, density gradient increasing) are selected, and the marine waveguide and seabed sound speed parameters are as shown in Figure 4 In view of the fact that the KRAKEN normal wave model is applicable to shallow sea low frequency (F = 40-400Hz, and higher frequency environments can also be simulated as h1F1 = h2F2) and homogeneous waveguide environment, the present application calculates the β 12 value by the model and compares it with the theoretical derivation formula (formula 1.9) for verification. It should be particularly noted that when the frequency is lower than 40Hz (F < 40Hz), the sound energy leakage significantly leads to data distortion, so the effective frequency band is analyzed. The basic parameters are set as: water sound speed c w = 1500m / s, density p w = 1.0g / cm 3 , and the waveguide parameters are strictly limited to be homogeneous (i.e. not changing with spatial coordinates).

[0056] Then, a program is written using Matlab to compare the formula calculation results with KRAKEN for verification of its accuracy:

[0057] First, the seabed density is simulated as 1.58g / cm 3 , and the seabed sound speed is 1580m / s (soft seabed environment). This theoretical model is for soft seabed environment. The KRAKEN calculation results (solid line represents) and formula (1.9) (denoted as derived-equation, dashed line represents) β​​12 The values are compared, Figure 5 The left figure shows the results of KRAKEN and the derived formula, and the right figure shows the relative error of the two, integrated Figure 5 From the data, it can be seen that under low frequency conditions (F < 56Hz), even if β 12 >2, the derived formula still has good applicability, and it can be seen that the relative error of the two is slightly greater than 5% at low frequency, when the frequency is higher than 56Hz, the relative error is less than 1% and gradually decreases, and when the frequency is greater than 160Hz, KRAKEN and formula (1.9) are in good agreement, verifying the accuracy of the derived formula in the low frequency soft seabed environment.

[0058] Then increase the seabed density and sound speed, increase the seabed density to 1.87g / cm 3 Increase the seabed sound speed to 1697m / s, and simulate the typical sandy seabed environment by further increasing the seabed density. This parameter setting can effectively reveal the frequency domain response characteristics of β 12 value with density, and accurately evaluate the calculation accuracy of formula (1.9). Figure 6 The simulation results show that: compared with the previous example, the error level is further reduced, KRAKEN (solid line) and formula (1.9) (dashed line) only have a small deviation of less than 1% in the frequency band of 40-100Hz, and thereafter, the relative error asymptotically converges to 0, and the two curves are completely coincident at higher frequencies.

[0059] Finally, increase the seabed density to 1.97g / cm 3 The seabed sound speed is 1753m / s, and the seabed density is further increased to simulate the typical hard seabed environment. This parameter setting can systematically reveal the frequency domain response law of β 12 in the high-density seabed condition, and more accurately evaluate the calculation accuracy of formula (1.9). Figure 7 The simulation results show that: the error level between the β 12 values calculated by KRAKEN (solid line) and the derived formula (dashed line) is further reduced compared with the previous example; the relative error is less than 0.5% in the full frequency band (40-400Hz); the two curves are finally completely coincident, further verifying the accuracy of formula (1.9) in the hard seabed scenario.

[0060] Through verification analysis, it is found that the relative error between the results calculated by KRAKEN and the derived formula is less than 5% at most, basically less than 2%, and finally tends to 0, indicating that the calculation accuracy of the derived formula is high, and the formula has good applicability for shallow sea low frequency conditions, thus completing the formula verification.

[0061] Step 4: Through step 3, it is found that the new formula has high accuracy in calculating waveguide invariants, and then by changing the seabed density and sound speed and frequency, the variation law of waveguide invariants with these variables is analyzed.

[0062] The preliminary analysis of the variation of waveguide invariant with seabed parameters is as follows: firstly, the frequency increases from 40 Hz to 400 Hz, and the waveguide invariant gradually decreases to 1. Then, the seabed density and the seabed sound speed increase, and the verification shows that the accuracy of the derived formula is high. It is also found that the waveguide invariant gradually decreases to 1 as the seabed density and the seabed sound speed increase. Finally, the single seabed density and the seabed sound speed affect the waveguide invariant. For the seabed sound speed, the waveguide invariant decreases linearly with the increase of the seabed sound speed at different frequencies, and the change amplitude of the waveguide invariant gradually decreases with the increase of the frequency. For the seabed density, it is difficult to directly decouple the independent action mechanism of the single seabed density parameter (ρ b ) on the waveguide invariant β from the theoretical formula. Therefore, the limit analysis method is used to explore the influence law. Under normal conditions, the waveguide invariant β is usually greater than 1; when the seabed medium density tends to infinity (ρ b →∞), it is an absolute hard seabed boundary condition, and the waveguide invariant formula can be simplified to the product form of the cosine of the grazing angle of the second-order normal wave. Mathematical derivation shows that the value of β converges to 1. It can be inferred that the waveguide invariant β decreases as the seabed density increases from the normal value to infinity. The above completes the preliminary analysis of the variation of the waveguide invariant with the seabed parameters.

[0063] Step 5: Based on the simulation analysis in step 4, this step further analyzes the value range of the waveguide invariant and its variation law with the seabed parameters.

[0064] Based on step 4, we have preliminarily understood the variation of the waveguide invariant with the seabed parameters through simulation. Next, we analyze the variation of the waveguide invariant with the seabed parameters from the formula level. Firstly, the value range of the waveguide invariant is discussed based on the derivation formula of the waveguide invariant. As can be seen from the derivation formula in step 2, the main factor affecting the value of β is F(θ). Therefore, F(θ) is discussed next.

[0065]

[0066] Expand tanθ:

[0067]

[0068]

[0069] Then move outside the brackets, inside the brackets to get:

[0070]

[0071] Next, discuss the increase or decrease of F(θ

[0072]

[0073] is a decreasing function, so F(θ

[0074]

[0075] Since it is a Pekeris waveguide, so β kl >0, and under the condition of small grazing angle From the above, we can get the general conclusion that β kl >1, thus ending the derivation of the range of β.

[0076] Next, we discuss the relationship between β and frequency ω:

[0077]

[0078] Next, we discuss the monotonicity of frequency ω:

[0079]

[0080] F(θ is an increasing function of the single variable frequency ω, that is, F(θ k )-F(θ l ) is a decreasing function of the single variable frequency ω, and combining formulas 1.11 and 1.12, we get that when the remaining parameters are unchanged, F(θ k )-F(θ l ) gradually decreases as the frequency increases, |Δ kl | gradually decreases, and when the frequency ω→∞, F(θ k )-F(θ l )→0, that is, Δ kl →0, so β gradually decreases as the frequency F increases, and finally tends to 1.

[0081] Similarly, we can deduce the relationship between β and the increase of depth h, and also get similar conclusions, that is, as the depth increases, β gradually decreases, and finally tends to 1.

[0082] Next, we discuss the relationship between β and the change of the ratio of seabed sound speed n b and the ratio of density Since the original formula structure is complex, it is difficult to separate a single variable for study, so we use the limit method, when the seabed density and seabed sound speed are infinite, the seabed is approximately an absolute hard seabed β = cos(θ k ​)·cos(θ l ), when β is 1, through the simulation analysis of the seabed density, it is found that the greater the frequency, the less obvious the influence of the seabed density on β.

[0083] Step 6: Compared with the existing results, the advantages and applicability of our formula are summarized and analyzed.

[0084] Based on the normal mode group velocity circulating displacement formula, the expression of the waveguide invariant β in the Pekeris waveguide (formula 1.9) is successfully derived, and the theoretical breakthrough mainly embodies in two aspects:

[0085] Firstly, the general conclusion of β>1 under the condition of small grazing angle in the Pekeris waveguide is strictly proved, and the theoretical universality of the conclusion is proved. Although Shang and other scholars have proposed similar conclusions, the low-frequency applicability is limited due to the high-frequency approximation assumption, and the derived formula still maintains good accuracy under the extreme condition of β>>2, which provides a new theoretical analysis tool for the study of sound field interference and waveguide invariant theory.

[0086] Secondly, the influence law of seabed parameters on waveguide invariant is systematically analyzed: numerical simulation shows that the influence of sound frequency (F) on β is the largest, the influence of seabed sound speed (c b ) is the second, and the influence of seabed density (ρ b ) is not obvious, which mainly reflects the joint influence of multiple parameters. Specifically, the increase of F and c b parameters makes the β value monotonically decrease and converge to the theoretical lower limit (β→1), which is consistent with the existing numerical research conclusion. The derived formula effectively avoids the randomness of pure numerical method through strict mathematical derivation, and reveals the internal physical nature of the parameter influence mechanism from the wave theory level. The core value of the analytical model lies in: while accurately describing the parameter response law of β(F, c b , ρ b ), a generalizable theoretical analysis framework is established. Future research can extend the model to complex ocean waveguide environments (such as sloping seabed, three-dimensional non-uniform waveguide, etc.), improve the boundary conditions and medium model, and construct a waveguide invariant calculation method suitable for different marine scenarios, providing theoretical support for underwater target detection, seabed geoacoustic parameter inversion and other applications.

[0087] The application also provides a waveguide invariant calculation system in a Pekeris waveguide, which is realized based on the above method, and the system comprises:

[0088] A waveguide invariant calculation module is configured to calculate the waveguide invariant according to the waveguide invariant calculation formula. The waveguide invariant formula is that the reciprocal of the waveguide invariant is the algebraic sum of the reciprocal of the waveguide invariant under the condition of absolute hard seabed and a correction quantity containing marine environment parameters.

[0089] The application can also provide a computer device, comprising: at least one processor, a memory, at least one network interface and a user interface. The various components in the device are coupled together by a bus system. It can be understood that the bus system is used to realize the connection communication between the components. In addition to including a data bus, the bus system also includes a power supply bus, a control bus and a status signal bus.

[0090] The user interface can include a display, a keyboard or a clicking device. For example, a mouse, a trackball, a touchpad or a touch screen, etc.

[0091] It can be understood that the memory in the embodiments of the application can be a volatile memory or a non-volatile memory, or can include both volatile and non-volatile memories. The non-volatile memory can be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically EPROM (EEPROM) or a flash memory. The volatile memory can be a random access memory (RAM) used as an external cache. By way of example, and not limitation, many forms of RAM can be used, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM) and direct Rambus RAM (DRRAM). The memory described herein is intended to include, without being limited to, these and any other suitable types of memory.

[0092] In some embodiments, the memory stores elements, executable modules or data structures, or a subset thereof, or an extended set thereof: an operating system and an application program.

[0093] The operating system includes various system programs, such as a framework layer, a core library layer, a driver layer, and the like, for implementing various basic services and processing hardware-based tasks. The application programs include various application programs, such as a media player (Media Player), a browser (Browser), and the like, for implementing various application services. The program for implementing the method of the embodiments of the present disclosure can be included in the application programs.

[0094] In the above-described embodiments, the processor can be configured to, by invoking the program or the instruction stored in the memory, specifically, the program or the instruction stored in the application program:

[0095] perform the steps of the above-described method.

[0096] The above-described method can be applied to the processor or implemented by the processor. The processor can be an integrated circuit chip having a signal processing capability. In the implementation process, the steps of the above-described method can be completed by hardware integrated logic circuits in the processor or by the instructions in the form of software. The processor described above can be a general-purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. The above-disclosed methods, steps and logic block diagrams can be implemented or executed by the processor. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor. The steps of the above-disclosed method can be directly embodied in hardware code executed by the processor, or a combination of hardware and software modules in the processor. The software module can be located in the random access memory (RAM), the flash memory, the read-only memory (ROM), the programmable read-only memory (PROM), the electrically programmable read-only memory (EPROM), the electrically erasable programmable read-only memory (EEPROM), the register, or other mature storage media in the art. The memory is located in the storage medium, and the processor reads information in the memory and combines the hardware to complete the steps of the above-described method.

[0097] It can be understood that the embodiments described in the present application can be realized by hardware, software, firmware, middleware, microcode or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), general purpose processors, controllers, micro-controllers, microprocessors, other electronic units designed to perform the functions described in the present application, or a combination thereof.

[0098] For software implementation, the present application can be implemented by executing the functional modules (such as processes, functions, etc.) described in the present application. The software code can be stored in a memory and executed by a processor. The memory can be implemented in the processor or outside the processor.

[0099] The present application can also provide a non-volatile storage medium for storing a computer program. When the computer program is executed by a processor, each step of the above method embodiments can be implemented.

[0100] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit. Although the present application is described in detail with reference to the embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced by equivalents without departing from the spirit and scope of the present application, and they should be covered in the scope of the claims of the present application.

Claims

1. A method for calculating waveguide invariants in a Pekeris waveguide, comprising: The calculation formula of the waveguide invariant is: the reciprocal of the waveguide invariant is the algebraic sum of the reciprocal of the waveguide invariant formula under absolute hard seabed conditions and a correction factor containing ocean environment parameters.

2. The method for calculating waveguide invariants in a Pekeris waveguide according to claim 1, characterized in that: The calculation formula of the waveguide invariant is specifically: Among them, β kl represents the waveguide invariant of the interference between the kth and lth normal waves; β kl (∞) represents the waveguide invariant of the interference between the kth and lth normal waves under the condition of absolute hard seabed; Δ kl Indicates the correction amount including ocean environment parameters.

3. The method for calculating waveguide invariants in a Pekeris waveguide according to claim 1, wherein: The correction value Δ including the ocean environment parameters kl Expressed as: Among them, θ k represents the grazing angle of the kth normal wave; the intermediate variable F(θ) is expressed as: Among them, c w represents the speed of sound in water; h represents depth; ω represents frequency; m b represents the seabed density ratio; n b Represents the seabed sound speed ratio.

4. A waveguide invariant calculation system in a Pekeris waveguide, implemented based on the method according to any one of claims 1 to 3, characterized in that: The system comprises: The waveguide invariant calculation module is used to calculate the waveguide invariant according to the waveguide invariant calculation formula; the waveguide invariant formula is: the reciprocal of the waveguide invariant is the algebraic sum of the reciprocal of the waveguide invariant formula under absolute hard seabed conditions and a correction variable containing ocean environment parameters.

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