A method and system for calculating waveguide invariants in a pekeris waveguide

Abstract

The application provides a waveguide invariant calculation method and system in a Pekeris waveguide, which is used for reflecting the influence law of seabed parameters on the waveguide invariant. The waveguide invariant formula is expressed as the reciprocal of the waveguide invariant under the condition of an absolute hard seabed, and an algebraic sum containing a marine environment parameter correction. The formula contains influence parameters such as sound wave frequency, sea depth, seawater sound speed and density, seabed sound speed and density. The application innovatively constructs a waveguide invariant calculation method containing seabed parameters, and the formula is simple and has clear physical meaning. Through converting complex marine environment parameters into an algebraic model that can be quantitatively calculated, the quantitative mapping of marine environment parameters and waveguide invariants is realized, so that the method has technical advantages of adjustable parameters, traceable influence and visualized law. The established approximate formula can provide a standardized calculation tool for underwater sound field characteristic analysis, marine environment parameter inversion and the like.

Description

Technical Field

[0001] This application belongs to the fields of underwater acoustic engineering, marine engineering and underwater acoustic signal processing, and specifically relates to a method and system for calculating waveguide invariants in Pekeris waveguides. Background Technology

[0002] The Pekeris approximation formula for shallow-sea waveguide invariants can be used for both theoretical analysis of acoustic field interference structures and waveguide invariants, and for exploring the influence of control variables such as frequency and marine environmental parameters on β. The core difference between shallow-sea and deep-sea acoustics lies in the boundary conditions: the acoustic characteristics of the sea surface and seabed differ significantly. In shallow-sea acoustics, the influence of both the sea surface and seabed on the sound field must be considered simultaneously, with the seabed boundary being particularly complex—differences in seabed density and sound velocity caused by impurity content in the seabed substrate, sediment diversity, and sedimentary layer structure have always been key research topics affecting shallow-sea waveguide invariants. With advancements in underwater acoustic measurement technology, observations have revealed that the ocean acoustic field possesses a stable spatiotemporal interference structure. In ocean waveguides, the sound field can be characterized as a superposition of discrete modes. Due to intermodal interference, the acoustic signal often exhibits an interference structure with certain geometric characteristics in the time, frequency, and spatial domains. This phenomenon typically manifests as alternating bright and dark inclined fringes of sound intensity varying with distance and frequency, the slope of which can be defined as a dimensionless scalar parameter—the waveguide invariant β. This parameter, through the functional relationship between group velocity and phase velocity (or slowness), encapsulates the waveguide dispersion characteristics and can be approximated as 1 under small angle conditions (θ < 20°). As a core parameter condensing the multi-factor influence of the ocean acoustic field, waveguide invariants, since their introduction by Soviet scientists in the mid-to-late 20th century, have become an important direction in marine acoustics research. Given their high sensitivity to seabed parameters, exploring the influence of seabed parameters on waveguide invariants is of great value. Related research results can be applied to fields such as improving the spatial correlation of underwater acoustic signals, sound source localization, marine environmental monitoring, and seabed acoustic inversion, and the future application potential based on waveguide invariants is enormous.

[0003] To obtain the variation law of waveguide invariants with seabed parameters, it is usually necessary to change the seabed parameters through numerical simulation, then calculate the waveguide invariants, and finally summarize and refine the results. Although this method is simple and fast, numerical simulation is subject to randomness and cannot derive applicable conclusions. In order to analyze the influence of seabed parameters on waveguide invariants from the perspective of formulas, Shang's team proposed the concept of "effective boundary" in the 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, they derived an expression with the seabed phase shift parameter P as the core based on a three-parameter model that can characterize the influence law of seabed parameters. The formula is concise and has a clear physical meaning, but it is limited by the high-frequency assumption and has weak applicability to shallow sea low-frequency scenarios. Moreover, its predicted 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 shown in the 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 highly complex and fails to directly explain the law of parameter influence. The calculation method is also relatively complicated. Summary of the Invention

[0004] The purpose of this application is to overcome the shortcomings of existing technologies that rely solely on numerical simulation to calculate waveguide invariants, which result in low accuracy and randomness.

[0005] To achieve the above objectives, this application proposes a method for calculating waveguide invariants in Pekeris waveguides, including:

[0006] The formula for calculating waveguide invariants is: the reciprocal of the waveguide invariant formula under absolutely hard seabed conditions is the algebraic sum of the reciprocal of the waveguide invariant formula and a correction factor that includes marine environmental parameters.

[0007] As an improvement to the above method, the formula for calculating the waveguide invariant is as follows:

[0008]

[0009] Where, β kl β represents the waveguide invariant that represents the interference between the k-th and l-th normal modes; kl (∞) represents the waveguide invariant of the interference between the k-th and l-th normal modes under absolutely hard seabed conditions; Δ klThis indicates the correction amount that includes marine environmental parameters.

[0010] As an improvement to the above method, the correction amount Δ, which includes marine environmental parameters, is... kl Represented as:

[0011]

[0012] Where, θ k The glancing angle of the k-th normal mode is represented by:

[0013]

[0014] Among them, c w The speed of sound in water is represented by h; the depth is represented by ω; the frequency is represented by m. b Indicates the density ratio of the seabed; n b This indicates the ratio of the speed of sound at the seabed.

[0015] This application also provides a system for calculating waveguide invariants in Pekeris waveguides, implemented based on the above method. The system includes:

[0016] The waveguide invariant calculation module is used to calculate waveguide invariants 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 absolutely hard seabed conditions and a correction quantity containing marine environmental parameters.

[0017] Compared with existing technologies, the advantages of this application are:

[0018] The core of the calculation method of this invention is the approximate formula for Pekeris shallow-sea waveguide invariants derived from the cyclic displacement formula of the normal wave group velocity. This formula has a clear physical picture and is a rigorous formula for the Pekeris model. Compared with the prior art, the technical advantages of this invention are as follows: First, based on the cyclic displacement theory that strictly holds for the normal wave group velocity of the Pekeris waveguide, the calculation and prediction of Pekeris shallow-sea waveguide invariants are relatively accurate; second, this formula can rigorously prove that the Pekeris shallow-sea waveguide invariants are generally not less than 1, and still have high prediction accuracy for larger waveguide invariant values ​​(>2) under shallow-sea low-frequency conditions; finally, the calculation method of this formula can clearly reflect the influence of seabed parameters, frequency, sea depth, etc. on the Pekeris shallow-sea waveguide invariants. Attached Figure Description

[0019] Figure 1 The diagram shows the flowchart of the waveguide invariant calculation method in Pekeris waveguides.

[0020] Figure 2 The diagram shows the intrinsic acoustic rays and beam shift.

[0021] Figure 3 The diagram shows the propagation of liquid on the seabed, where c w ρ represents the speed of sound in water. w c represents density. b ρ represents the speed of sound at the bottom of the sea. b The dotted line represents density, θ represents the grazing angle, and the dashed line represents beam displacement.

[0022] Figure 4 The figure shows the density and sound velocity distribution and values ​​in the Pekeris waveguide, where A, B, and C represent three types of waveguides and their corresponding densities and sound velocities, respectively. The water body is an isosonic layer, and the seabed is the bottom of an isosonic half-space.

[0023] Figure 5 The figure shows ρ b =1.58g / cm 3 seabed sound speed c b Waveguide invariants and their differences related to Mode 1 and Mode 2 calculated by KRAKEN and derivation at 1580 m / s;

[0024] Figure 6 The figure shows ρ b =1.87g / cm 3 seabed sound speed c b Waveguide invariants and their differences related to Mode 1 and Mode 2 calculated by KRAKEN and derivation at 1697 m / s;

[0025] Figure 7 The figure shows ρ b =1.97g / cm 3 seabed sound speed c b Waveguide invariants and their differences related to Mode 1 and Mode 2 calculated by KRAKEN and derivation at 1753 m / s. Detailed Implementation

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

[0027] To bridge the gap between ideal waveguides and real-world environments, this application employs a Pekeris waveguide model with a penetrable half-space bottom, which more accurately describes shallow-sea environments. This application aims to derive a calculation method for reflecting the influence of seabed parameters on waveguide invariants in the Pekeris waveguide, laying the foundation for theoretical analysis of marine acoustic field interference structures.

[0028] This application proposes a method for calculating waveguide invariants in Pekeris waveguides, comprising two parts: formula derivation and simulation verification. First, under absolutely hard seabed conditions, seabed density and sound velocity tend to infinity, preventing sound waves from penetrating the seabed; the waveguide invariant calculation formula under this condition is Equation (1.1). Then, extending to liquid seabed conditions, considering seabed density and sound velocity as finite values, sound waves will penetrate the seabed and reflect back into the water. Using the cyclic displacement formula for normal wave group velocity, a new group velocity expression is derived. Substituting this expression into the original definition of waveguide invariants, a new explicit expression for waveguide invariants, incorporating marine environmental parameters such as frequency, sea depth, seabed density, and sound velocity, is derived. Furthermore, this expression is simplified to an algebraic sum of the waveguide invariant expression under absolutely hard seabed conditions and a correction term incorporating marine environmental influences. Finally, a rapid calculation method for the formula is implemented through programming. Numerical simulations are used to calculate the waveguide invariants at specific depths and within specific frequency ranges, with different combinations of seabed parameters. The results are compared with standard results calculated using the KRAKEN program to verify the accuracy of the method.

[0029] This method constructs an approximate calculation method for waveguide invariants of the Pekeris waveguide, incorporating the influence of seabed parameters, based on the derived waveguide invariant calculation formula. Compared with traditional waveguide invariant calculation methods, this method has the following advantages: 1. Compared with the traditional KRAKEN numerical calculation method, this method directly incorporates seabed parameters, facilitating programmed implementation and theoretical characteristic analysis, and revealing their inherent laws. 2. This formula significantly improves accuracy under shallow sea and low-frequency conditions compared to previous calculation methods, and maintains high prediction accuracy for the case β>2.

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

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

[0032] like Figure 2 As shown, under absolutely hard seabed conditions (seabed density and sound speed approach infinity), sound waves cannot penetrate the seabed interface and undergo total reflection. The waveguide invariant formula is shown below (Formula 1.1). The cyclic displacement formula for the normal mode group velocity is shown in Formula (1.2).

[0033]

[0034] in, and S represents the phase velocity and group velocity of the m-th and n-th normal modes, respectively. l With T l δ represents the span of the l-th normal mode and the time required for the corresponding eigenline to travel one span, respectively.l τ l Let represent the beam displacement and corresponding time delay of the l-th normal mode at the seabed. This is then generalized to the liquid seabed, considering the finite seabed density and the speed of sound (no longer infinite), where some sound waves will penetrate the seabed and be reflected again. For example... Figure 3 As shown, the space is divided into two regions: Region I encompasses the sea surface and the water layer, while Region II is the seabed half-space below the water layer. This application does not consider seabed absorption and attenuation, and adopts a Pekeris waveguide model with a penetrable bottom of the half-space. This model describes the shallow sea environment better than an ideal waveguide. Then, based on the normal mode group velocity cyclic displacement formula, a new group velocity expression is derived, as shown below:

[0035]

[0036] Where, θ l and denoted as the glancing angle of the l-th normal wave and the group velocity under absolutely hard seabed conditions, respectively.

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

[0038] Based on the theoretical framework of waveguide invariant formulas and normal wave group velocity cyclic displacement formulas under absolutely hard seabed conditions, the interference of the kth and lth normal waves is introduced, and the new group velocity expression (Formula 1.3) is substituted into the original definition of waveguide invariants to obtain Formula (1.4).

[0039]

[0040] in, and θ represents the phase velocity and group velocity of the kth and lth normal modes, respectively. k and τ k T represents the grazing angle of the k-th normal wave and the corresponding time delay of the beam displacement at the seabed, respectively. k This represents the time required for the corresponding eigenline of the k-th normal mode to travel one span. Let represent the group velocity of the k-th algebraic element under absolutely hard seabed conditions.

[0041] Next, we simplify the equation. Using Taylor expansion under small glancing angle conditions, we get:

[0042]

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

[0044]

[0045] Where, βkl (∞) represents the waveguide invariant of the interference between the kth and lth normal modes under absolutely hard seabed conditions.

[0046] make:

[0047]

[0048] Simplify Δ kl have to:

[0049]

[0050] in:

[0051]

[0052] have to:

[0053]

[0054] Step 3: Perform simulation verification on the newly obtained waveguide invariant formula and compare it with the waveguide invariant results calculated by KRAKEN to determine its accuracy;

[0055] The relationship between waveguide invariant β and frequency F under different seabed densities and seabed sound velocities is shown. Three typical Pekeris seabed parameter models (depth h = 100 m, increasing density gradient) are selected, and their ocean waveguide and seabed sound velocity parameters are as follows: Figure 4 As shown. Given that the Kraken normal mode model is applicable to shallow, low-frequency (F = 40-400Hz, and from h1F1 = h2F2, it can simulate even lower frequency environments with increasing depth) and horizontally uniform waveguide environments, this application uses this model to calculate β. 12 The values ​​were compared and verified with the theoretical derivation (Formula 1.9). It should be noted that when the frequency is below 40Hz (F<40Hz), significant acoustic energy leakage leads to data distortion; therefore, the analysis focuses on the effective frequency band. The basic parameters are set as follows: water sound velocity c... w =1500m / s, density ρ w =1.0g / cm 3 Furthermore, the waveguide parameters are strictly limited to be horizontally uniform (i.e., do not change with spatial coordinates).

[0056] Then, a program was written in Matlab to compare the calculation results with those of KRAKEN to verify its accuracy:

[0057] First, the simulated seabed density is 1.58 g / cm³. 3 The sound speed on the seabed is 1580 m / s (soft seabed environment). This theoretical model is designed for a soft seabed environment. The results calculated by KRAKEN (solid line) and formula (1.9) (denoted as derived-equation, dashed line) β are compared.12 Compare the values. Figure 5 The left figure shows the calculation results of KRAKEN and the derivation, and the right figure shows the relative error between the two. Figure 5 The data shows that under low-frequency conditions (F < 56Hz), even β 12 >2. The derivation formula still maintains good applicability. It can be seen that the relative error between the two is slightly greater than 5% at low frequencies. When the frequency is higher than 56Hz, the relative error is less than 1% and gradually decreases. When the frequency is higher than 160Hz, KRAKEN and formula (1.9) are in good agreement, which verifies the accuracy of the derivation formula in the low-frequency soft seabed environment.

[0058] Subsequently, the density of the seabed and the speed of sound were increased, raising the density of the seabed to 1.87 g / cm³. 3 The speed of sound on the seabed was increased to 1697 m / s, and the density of the seabed was further increased to simulate a typical sandy seabed environment. This parameter setting can effectively reveal β 12 The frequency domain response characteristics of the value as a function of density are determined, and the calculation accuracy of formula (1.9) is accurately evaluated. Figure 6 Simulation results show that, compared with the previous example, the error level is further reduced. KRAKEN (solid line) and Equation (1.9) (dashed line) have only a small deviation of less than 1% in the 40-100Hz frequency band. After that, the relative error asymptotically converges to 0, and the two curves completely overlap in the higher frequency band.

[0059] Finally, the density of the seabed was increased to 1.97 g / cm³. 3 The speed of sound on the seabed is 1753 m / s, and the seabed density is further increased to simulate a typical hard seabed environment. This parameter setting can systematically reveal β 12 The frequency domain response under high-density seabed conditions is studied, and the calculation accuracy of formula (1.9) is evaluated more accurately. Figure 7 Simulation results show that β calculated by KRAKEN (solid line) and the derived formula (dashed line) is consistent with the results calculated by the KRAKEN formula. 12 The inter-value error level was further reduced compared to the previous example; the relative error across the entire frequency band (40-400Hz) was less than 0.5%; the two curves eventually overlapped completely, further verifying the accuracy of formula (1.9) in the hard seabed scenario.

[0060] Verification analysis revealed that the relative error between the results calculated by KRAKEN and the derived formula was less than 5% at its maximum, generally less than 2%, and eventually approached 0. This indicates that the derived formula has high accuracy and is well applicable to shallow sea low-frequency conditions. Thus, the formula verification was completed.

[0061] Step 4: Based on the findings in Step 3, the new formula is found to have higher accuracy in calculating waveguide invariants. Then, by changing the seabed density, sound velocity, and frequency, the variation of waveguide invariants with these variables is analyzed.

[0062] Preliminary analysis revealed the following variation of waveguide invariants with seabed parameters: First, as the frequency increases from 40Hz to 400Hz, the waveguide invariant value gradually decreases, eventually approaching 1. Then, seabed density and sound velocity increase sequentially. Verification showed that the derived formula has high accuracy, and it was also observed that the waveguide invariant value gradually decreases with increasing seabed density and sound velocity, eventually approaching 1. Finally, the effects of seabed density and sound velocity alone were examined. For sound velocity, the waveguide invariant value decreases linearly with increasing seabed sound velocity at different frequencies, and the amplitude of change gradually decreases with increasing frequency. However, for seabed density, it is difficult to directly decouple the single seabed density parameter (ρ) from the theoretical formula. b The independent action mechanism of the waveguide invariant β is investigated, therefore, this study employs limiting analysis to explore its influence. Under normal conditions, the waveguide invariant β is typically greater than 1; however, as the density of the seabed medium approaches infinity (ρ... b When the boundary condition is β→∞, it is an absolutely hard seabed boundary condition. At this time, the waveguide invariant formula can be simplified to the product of the cosines of the grazing angles of the two normal modes. Mathematical derivation shows that the value of β asymptotically converges to 1. From this, it can be inferred that as the seabed density increases from its normal value to infinity, the waveguide invariant β exhibits a decreasing characteristic. The above completes the preliminary analysis of the variation law of waveguide invariants with seabed parameters.

[0063] Step 5: Based on the simulation analysis in Step 4, this step further analyzes the range of waveguide invariants and their variation with seabed parameters from a formula perspective.

[0064] Based on step 4, we have gained a preliminary understanding of the variation law of waveguide invariants with seabed parameters through simulation. Next, we will analyze the variation law of waveguide invariants with seabed parameters from the perspective of formulas. First, regarding the range of values ​​of waveguide invariants, we will discuss the range of values ​​of β based on the derivation formula of waveguide invariants. As can be seen from the derivation formula in step 2, the main factor affecting the value of β is F(θ). Therefore, we will discuss F(θ) next.

[0065]

[0066] Expand tanθ:

[0067]

[0068]

[0069] Then Move it outside the parentheses. Move it into the parentheses to get:

[0070]

[0071] Next discussion The monotonicity of the property can be simplified to the following form:

[0072]

[0073] achievable Since F(θ) is a decreasing function, it is an increasing function, leading to the following conclusion:

[0074]

[0075] Because it is a Pekeris waveguide, therefore β kl >0, and under small sweep angle conditions From the above, we can obtain the β in the Pekeris waveguide kl The general conclusion that β > 1 concludes the derivation of the range of values ​​for β.

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

[0077]

[0078] Next discussion Monotonicity with respect to frequency ω:

[0079]

[0080] achievable For a single variable, the frequency ω is an increasing function, i.e., F(θ) k )-F(θ l For a single variable, frequency ω is a decreasing function. Combining this with formulas 1.11 and 1.12, we can see that when other parameters remain constant, as the frequency increases, F(θ)... k )-F(θ l ) gradually decreases, |Δ kl | Gradually decreases and as frequency ω→∞, F(θ) k )-F(θ l )→0, that is, Δ kl If the frequency F increases to 0, then β gradually decreases as the frequency F increases, eventually approaching 1.

[0081] Similarly, we can deduce the relationship between β and depth h, and draw a similar conclusion: as the depth increases, β gradually decreases and eventually approaches 1.

[0082] Next, we will discuss β as a function of the seabed sound velocity ratio n. b and density ratio The relationship between the changes is complex, making it difficult to isolate a single variable for study. Therefore, the limiting method is adopted. When the seabed density and seabed sound speed are infinite, the seabed is approximately absolutely hard, β = cos(θ). k)·cos(θ l At this time, β takes the value of 1. Through simulation analysis of seabed density, it was found that the greater the frequency, the less obvious the influence of seabed density on β becomes.

[0083] Step 6: Compare with existing results and summarize and analyze the advantages and applicability of our formula.

[0084] Based on the normal group velocity cyclic displacement formula, the expression for the waveguide invariant β in the Pekeris waveguide (Formula 1.9) was successfully derived. This theoretical breakthrough is mainly reflected in two aspects:

[0085] First, the general conclusion that β>1 under the small grazing angle condition of the Pekeris waveguide is rigorously demonstrated, proving the theoretical universality of this conclusion. Although Shang et al. have proposed similar conclusions, their use of high-frequency approximation assumptions limits their applicability to low frequencies. In contrast, this derivation maintains good accuracy even under the extreme condition of β>>2, providing a new theoretical analysis tool for the study of acoustic field interference and waveguide invariant theory.

[0086] Secondly, the influence of seabed parameters on waveguide invariants was systematically analyzed: numerical simulations show that the acoustic frequency (F) has the largest influence on β, and the seabed sound velocity (c) b Secondly, the density of the seabed (ρ) b The influence of a single variable on β is not obvious; it is mainly reflected in the combined influence of multiple parameters. Specifically, F and c b Increasing the parameter always leads to a monotonically decreasing β value that converges to the theoretical lower limit (β→1). This pattern is consistent with existing numerical research findings. This derivation effectively avoids the randomness of purely numerical methods through rigorous mathematical derivation, revealing the intrinsic physical essence of the parameter influence mechanism from the perspective of wave theory. The core value of this analytical model lies in its accurate characterization of β(F,c) b ,ρ b While identifying the parameter response patterns, a generalizable theoretical analysis framework was established. Future research could extend this model to complex marine waveguide environments (such as sloping seabeds and three-dimensional non-uniform waveguides), and by improving boundary conditions and medium models, construct waveguide invariant calculation methods adapted to different marine scenarios, providing theoretical support for applications such as underwater acoustic target detection and seabed acoustic parameter inversion.

[0087] This application also provides a system for calculating waveguide invariants in Pekeris waveguides, implemented based on the above method. The system includes:

[0088] The waveguide invariant calculation module is used to calculate waveguide invariants 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 absolutely hard seabed conditions and a correction quantity containing marine environmental parameters.

[0089] This application may also provide a computer device, including: at least one processor, memory, at least one network interface, and a user interface. The various components in this device are coupled together via a bus system. It is understood that the bus system is used to implement communication between these components. In addition to a data bus, the bus system also includes a power bus, a control bus, and a status signal bus.

[0090] The user interface can include a display, keyboard, or clicking device. Examples include a mouse, trackball, touchpad, or touchscreen.

[0091] It is understood that the memory in the embodiments disclosed in this application may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory may be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate Synchronous DRAM (DDRSDRAM), Enhanced Synchronous DRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memories described herein are intended to include, but are not limited to, these and any other suitable types of memory.

[0092] In some implementations, the memory stores elements such as executable modules or data structures, or subsets thereof, or extended sets thereof: operating systems and applications.

[0093] The operating system includes various system programs, such as the framework layer, core library layer, and driver layer, used to implement various basic business functions and handle hardware-based tasks. The application programs include various applications, such as media players and browsers, used to implement various application functions. Programs implementing the methods of the embodiments of this disclosure can be included in the application programs.

[0094] In the above embodiments, the processor can also invoke programs or instructions stored in memory, specifically programs or instructions stored in an application program, for the following purposes:

[0095] Follow the steps described above.

[0096] The above methods can be applied to or implemented by a processor. The processor may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above methods can be completed by integrated logic circuits in the processor's hardware or by software instructions. The processor 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, or discrete hardware components. It can implement or execute the disclosed methods, steps, and logic block diagrams. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the disclosed methods can be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0097] It is understood that the embodiments described in this application can be implemented using 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, microcontrollers, microprocessors, other electronic units for performing the functions described in this application, or combinations thereof.

[0098] For software implementation, the technology of this application can be implemented by executing the functional modules (e.g., procedures, functions, etc.) of this application. The software code can be stored in memory and executed by a processor. The memory can be implemented in the processor or externally.

[0099] This application may also provide a non-volatile storage medium for storing a computer program. When the computer program is executed by a processor, it can implement the steps in the above method embodiments.

[0100] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. Although this application has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of this application do not depart from the spirit and scope of the technical solutions of this application, and should all be covered within the scope of the claims of this application.

Claims

1. A method for calculating waveguide invariants in a Pekeris waveguide, comprising: The formula for calculating waveguide invariants is: the reciprocal of the waveguide invariant formula under absolutely hard seabed conditions is the algebraic sum of the reciprocal of the waveguide invariant formula and a correction factor that includes marine environmental parameters; The specific formula for calculating the waveguide invariant is as follows: ； in, Indicates the first k , l Waveguide invariants for interference of the first normal mode; Indicates the first k , l Waveguide invariants that cause interference of normal modes under absolutely hard seabed conditions; This indicates the correction amount that includes marine environmental parameters; The correction amount includes marine environmental parameters. Represented as: ； in, Indicates the first k The glancing angle of the first normal mode wave; Indicates the first l The glancing angle of the first normal wave; intermediate variable Represented as: ； in, c w Indicates the speed of sound in water; h Indicates depth; ω Indicates frequency; m b Indicates the density ratio of the seabed; n b This indicates the ratio of the speed of sound at the seabed.

2. A system for calculating waveguide invariants in a Pekeris waveguide, implemented based on the method described in claim 1, characterized in that, The system includes: The waveguide invariant calculation module is used to calculate waveguide invariants 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 absolutely hard seabed conditions and a correction quantity containing marine environmental parameters.

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