International and domestic research progress in theory and experiment and applications of the air-to-water sound transmission are presented in this paper. Four classical numerical methods of calculating the underwater...International and domestic research progress in theory and experiment and applications of the air-to-water sound transmission are presented in this paper. Four classical numerical methods of calculating the underwater sound field gener- ated by an airborne source, i.e., the ray theory, the wave solution, the normal-mode theory and the wavenumber integration approach, are introduced. Effects of two special conditions, i.e., the moving airborne source or medium and the rough air-water interface, on the air-to-water sound transmission are reviewed. In experimental studies, the depth and range distributions of the underwater sound field created by different kinds of airborne sources in near-field and far-field, the longitudinal horizontal correlation of underwater sound field and application methods for inverse problems are reviewed.展开更多
A propagation experiment was conducted in the South China Sea in 2014 with a flat bottom and seamounts respectively by using explosive sources. The effects of seamounts on sound propagation are analyzed by using the b...A propagation experiment was conducted in the South China Sea in 2014 with a flat bottom and seamounts respectively by using explosive sources. The effects of seamounts on sound propagation are analyzed by using the broadband signals. It is observed that the transmission loss (TL) decreases up to 7 dB for the signals in the first shadow zone due to the seamount reflection. Moreover, the TL might increase more than 30 dB in the converge zone due to the shadowing by seamounts. Abnormal TLs and pulse arrival structures at different ranges are explained by using the ray and wave theory. The experimental TLs and arrival pulses are compared with the numerical results and found to be in good agreement.展开更多
There are so many Isolated Islands (inhabited islands) in the world, including Japan. However, at present islanders, there have been faced with the decline of industries, serious concerns of rapid aging and very low b...There are so many Isolated Islands (inhabited islands) in the world, including Japan. However, at present islanders, there have been faced with the decline of industries, serious concerns of rapid aging and very low birthrate without children and water scarcity issues etc. It can be said that these situations are under the environment which shows a microcosm of Japanese and/or world survival society in the near future. In this paper, the experimental data on the reduction of the mixed water (seawater & rainwater) salinity by the sound wave when changing the volume ratio were first shown, taking into the characteristics of the Isolated Islands. Next, the main analysis result on the water qualities of mixed water with which sound wave was irradiated was shown and the consideration mainly based on the WHO drinking water quality standards was carried out. Finally, through a simple water quality improvement apparatus using small hydroelectric power, a consideration regarding a possibility of the purification of the water (to be a drinking water) based on the solar circulation energy (regenerative type’s natural energy) such as small hydropower utilization, natural sunlight utilization, natural gravity utilization, natural oscillation utilization has been described in the paper.展开更多
This study investigates the use of dynamic a priori error information according to atmospheric moistness and the use of quality controls in temperature and water vapor profile retrievals from hyperspectral infrared ...This study investigates the use of dynamic a priori error information according to atmospheric moistness and the use of quality controls in temperature and water vapor profile retrievals from hyperspectral infrared (IR) sounders. Temperature and water vapor profiles are retrieved from Atmospheric InfraRed Sounder (AIRS) radiance measurements by applying a physical iterative method using regression retrieval as the first guess. Based on the dependency of first-guess errors on the degree of atmospheric moistness, the a priori first-guess errors classified by total precipitable water (TPW) are applied in the AIRS physical retrieval procedure. Compared to the retrieval results from a fixed a priori error, boundary layer moisture retrievals appear to be improved via TPW classification of a priori first-guess errors. Six quality control (QC) tests, which check non-converged or bad retrievals, large residuals, high terrain and desert areas, and large temperature and moisture deviations from the first guess regression retrieval, are also applied in the AIRS physical retrievals. Significantly large errors are found for the retrievals rejected by these six QCs, and the retrieval errors are substantially reduced via QC over land, which suggest the usefulness and high impact of the QCs, especially over land. In conclusion, the use of dynamic a priori error information according to atmospheric moistness, and the use of appropriate QCs dealing with the geographical information and the deviation from the first-guess as well as the conventional inverse performance are suggested to improve temperature and moisture retrievals and their applications.展开更多
By using the expressions for the maximum absorption per wavelength (αλ),and the relaxation frequency fr of the boric acid relaxation derived previously by the author and employing the related oceanographic literatur...By using the expressions for the maximum absorption per wavelength (αλ),and the relaxation frequency fr of the boric acid relaxation derived previously by the author and employing the related oceanographic literatures, the effects of pressure, temperature, pH and salinity on (αλ)r and ∫r of the boric acid relaxation in sea water have been estimated. Results show that ( αλ), not only increases with pH but also increases approximately linearly with pressure and temperature, and is nearly proportional to the 1. 35 power of salinity. However, pressure, pH and salinity have negligible effect on ∫r; therefore, ∫r, can be approximately expressed as a function of temperature only. Comparisons of the predicted with the measured ( αλ)r and ∫r in different ocean areas are given.展开更多
This study was aimed at mapping the subsurface extent of saline water intrusions into aquifers at the eastern part of Dahomey basin, Nigeria. The study adopted geoelectric sounding methods. 108 vertical electrical sou...This study was aimed at mapping the subsurface extent of saline water intrusions into aquifers at the eastern part of Dahomey basin, Nigeria. The study adopted geoelectric sounding methods. 108 vertical electrical soundings (VES) and 9 induced polarization soundings (IPS) data were acquired using Schlumberger array technique. Three aquifer units were delineated across the study area. The resistivity of the first, second and third aquifer layers varies from 0.2 to 1569 ohm-m, 0.5 to 904 ohm-m and 0.4 to 665 ohm-m respectively, while depth to the top of first, second and third aquifer varies respectively from 0.7 to 151.5 m, 1.4 to 305.5 m and 12.9 to 452.9 m. The depth to the first aquifer layer is shallow (less than 5 m) in the coastal area which makes this area to be highly vulnerable to anthropogenic pollution while their proximity to Atlantic Ocean makes them susceptible to saline water intrusion. In all the three aquifer units, the coastal area, Agbabu and other few locations in the mainland are characterized by low resistivity values (below 60 ohm-m) indicating possible presence of brackish or saline water. IP sounding results showed that all the low resistive layers in the mainland are characterized by clayey materials. The integration of VES and IPS results enabled the delineation of the saline water lateral extent across the study area. There is a strong direct correlation (r2 = 0.8564) between location distance from the saline water source and depth to saline water in the study area. This can therefore serve as a predictive model to determine depth to saline water at any location within the saline water zone in the study area.展开更多
Cognitive-inspired computational systems play a crucial role in designing intelligent health monitoring systems which help both patients and hospitals.It also helps in early and consistent decision-making for various ...Cognitive-inspired computational systems play a crucial role in designing intelligent health monitoring systems which help both patients and hospitals.It also helps in early and consistent decision-making for various health issues including human psychological health.Water fountains built in parks and public spaces are used as decorative instruments which not only give appealing visuals but also provide a relaxing environment to the visitors.These natural sounds have a direct effect on the psychological health of visitors.Very few research works are reported on developing the relationship between water sounds and their corresponding psychological impact.This assessment needs trained manpower and a lot of experimental time which is costly and may not be always available.In this paper,to access the from the pleasantness from human health-friendly water fountain sounds,a perceptually weighted functional link artificial neural network(P-FLANN)model is developed.To reduce the computational complexity of training and for faster convergence,swam intelligence-based optimization algorithm is used for updating the weights.It is observed from the comparative simulation results that the proposed P-FLANN model can effectively perform prediction tasks which is not only cost-effective but also 95%accurate and can play a crucial role in designing human health-friendly water fountains in smart cities.展开更多
It is complicated to model the acoustic field in stratified ocean for airborne aircraft,due to high speed of the source and air-to-water sound transmission.To our knowledge,there are very few papers in the open litera...It is complicated to model the acoustic field in stratified ocean for airborne aircraft,due to high speed of the source and air-to-water sound transmission.To our knowledge,there are very few papers in the open literature dealing with this complicated problem;but,in our opinion,they all require great amount of computation.We now propose a different method that requires much less computation.We improve the wavenumber integration method to model the received temporal signal for a moving source in stratified ocean and sum up in a concise form the core of our paper as follows:(A) Eq.(11) can be calculated by means of fast Chirp Z transform and the signals at all N time points are generated simultaneously;(B) direct numerical evaluation of the wavenumber integral in Eq.(4) produces large numerical errors;so it is necessary to shift the integration slightly below the real axis;(C) we compare the computation cost of direct calculation method with that of our fast calculation method;from the results presented in table 1,we can see that the fast calculation method consumes much less computation time,particularly for long duration signals;(D) for an airborne rapidly moving source,we compute the Doppler-shifted signals in shallow water and analyze their short-time Fourier transform;from Fig.1b,we can see that the received signals have multiple frequency components for a tonal source due to source motion and that each component corresponds to an arrival path.展开更多
To unlearn the meaning of a sustainable water resource conservation is now an essential issue in using of sustained, sound, and high-quality water in the world. In this paper, a water quality purification by the Schum...To unlearn the meaning of a sustainable water resource conservation is now an essential issue in using of sustained, sound, and high-quality water in the world. In this paper, a water quality purification by the Schumann frequencies was first considered through the murmuring sound of upper reach at the mountain stream (Kyoto Pref., Japan) regarding the conservation of water resources. Second, water is changing freely and easily accepting the wavelength of all the sounds. We therefore referred to a flow and dynamic equilibrium to realize and understand the water quality purification process. Finally, a “consciousness only Buddhist philosophy” of water quality as an analogical approach was introduced to realize and understand the water purification process. As a result, we have confirmed the water purification capability by Schmann frequencies in an experiment on water quality. And through the experiment, we have realized the importance/significance to find the meaning for a person’s primary meaningless such as 1) meaning connection among life, environment, and economics as a condition of human life, 2) energy, entropy and fluctuation under law of thermodynamics, 3) a metaphor between water quality and mutual possession of the ten worlds based on conscious-only theory, and 4) sense of wonder through the water purification process.展开更多
Authors have conducted an experiment of irradiation using sound waves (frequency) including ultrasonic waves into water such as drinking water, sea water and forest water and wastewater so far. As a result, almost the...Authors have conducted an experiment of irradiation using sound waves (frequency) including ultrasonic waves into water such as drinking water, sea water and forest water and wastewater so far. As a result, almost the same effect of improvement of water quality was confirmed for each sound wave. Then, an environmental anthropological study of watershed management based on the sound was carried out assuming that a water quality management using the sound could be possible. The Goulburn River basin in the southern part of Australia in which indigenous peoples (Yorta Yorta) have been concerned with the management for a long time so far was selected as an objective drainage basin this time. As a result, a couple of environmental anthropological perspectives on watershed management were proposed.展开更多
The current research focuses on the detection of sea water intrusion in Rashid area which is located about 75 km east to Alexandria, Egypt. For this purpose, geoelectrical survey was carried out using the Schlumberger...The current research focuses on the detection of sea water intrusion in Rashid area which is located about 75 km east to Alexandria, Egypt. For this purpose, geoelectrical survey was carried out using the Schlumberger Vertical Electric Sounding (VES) to identify freshwater thickness, sea water intrusion and estimate subsurface lithology. Seventeen VES stations were measured with current electrode separation (AB/2) ranging from 1.5 m to 100 m. Then, the VES data was interpreted using 1-D and 2-D inversion schemes of DC resistivity data based on least squares method with smoothness constrains. The inverted resistivity distribution at relatively shallow depth shows an important low resistivity zone that probably reflects salt water alteration zone (northern parts). Depth to the freshwater bearing layer reaches its maximum at the south and decreases towards the north. From quantitative interpretation, invasion of salt water started at depth about 10 m at north in the thickness of freshwater bearing layer ranging from 15 to 25 m, while at depth of about 120 m all the layers were saturated with salt water.展开更多
There is a new method of calculating the trajectory of sound waves (rays) in layered stratified speed of sound in ocean without dispersion. A sound wave in the fluid is considered as a vector. The amplitudes occurring...There is a new method of calculating the trajectory of sound waves (rays) in layered stratified speed of sound in ocean without dispersion. A sound wave in the fluid is considered as a vector. The amplitudes occurring at the boundary layers of the reflected and refracted waves are calculated according to the law of addition of vectors and using the law of conservation of energy, as well as the laws that determine the angles of reflection and refraction. It is shown that in calculating the trajectories, the reflected wave must be taken into account. The reflecting wave’s value may be about 1 at certain angles of the initial wave output from the sours. Reflecting wave forms the so-called water rays, which do not touch the bottom and the surface of the ocean. The conditions of occurrence of the water rays are following. The sum of the angles of the incident and refracted waves (rays) should be a right angle, and the tangent of the angle of inclination of the incident wave is equal to the refractive index. Under these conditions, the refracted wave amplitude vanishes. All sound energy is converted into the reflected beam, and total internal reflection occurs. In this paper, the calculation of the amplitudes and beam trajectories is conducted for the canonical type of waveguide, in which the speed of sound is asymmetric parabola. The sound source is placed at the depth of the center of the parabola. Total internal reflection occurs in a narrow range of angles of exit beams from the source 43° - 45°. Within this range of angles, the water rays form and not touch the bottom and surface of ocean. Outside this range, the bulk of the beam spreads, touching the bottom and the surface of the ocean. When exit corners, equal and greater than 77°, at some distance the beam becomes horizontal and extends along the layer, without leaving it. Calculation of the wave amplitudes excludes absorption factor. Note that the formula for amplitudes of the sound waves applies to light waves.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11434012 and 11674349)
文摘International and domestic research progress in theory and experiment and applications of the air-to-water sound transmission are presented in this paper. Four classical numerical methods of calculating the underwater sound field gener- ated by an airborne source, i.e., the ray theory, the wave solution, the normal-mode theory and the wavenumber integration approach, are introduced. Effects of two special conditions, i.e., the moving airborne source or medium and the rough air-water interface, on the air-to-water sound transmission are reviewed. In experimental studies, the depth and range distributions of the underwater sound field created by different kinds of airborne sources in near-field and far-field, the longitudinal horizontal correlation of underwater sound field and application methods for inverse problems are reviewed.
基金Supported by the National Nature Science Foundation of China under Grant Nos 11434012 and 11174312
文摘A propagation experiment was conducted in the South China Sea in 2014 with a flat bottom and seamounts respectively by using explosive sources. The effects of seamounts on sound propagation are analyzed by using the broadband signals. It is observed that the transmission loss (TL) decreases up to 7 dB for the signals in the first shadow zone due to the seamount reflection. Moreover, the TL might increase more than 30 dB in the converge zone due to the shadowing by seamounts. Abnormal TLs and pulse arrival structures at different ranges are explained by using the ray and wave theory. The experimental TLs and arrival pulses are compared with the numerical results and found to be in good agreement.
文摘There are so many Isolated Islands (inhabited islands) in the world, including Japan. However, at present islanders, there have been faced with the decline of industries, serious concerns of rapid aging and very low birthrate without children and water scarcity issues etc. It can be said that these situations are under the environment which shows a microcosm of Japanese and/or world survival society in the near future. In this paper, the experimental data on the reduction of the mixed water (seawater & rainwater) salinity by the sound wave when changing the volume ratio were first shown, taking into the characteristics of the Isolated Islands. Next, the main analysis result on the water qualities of mixed water with which sound wave was irradiated was shown and the consideration mainly based on the WHO drinking water quality standards was carried out. Finally, through a simple water quality improvement apparatus using small hydroelectric power, a consideration regarding a possibility of the purification of the water (to be a drinking water) based on the solar circulation energy (regenerative type’s natural energy) such as small hydropower utilization, natural sunlight utilization, natural gravity utilization, natural oscillation utilization has been described in the paper.
基金supported by GOES-R Algorithm Working Group Program and GOES-R High Impact Weather Project (Grant No NA10NES4400013)supported by the Korea Meteorological Administration Research and Development Program under Grant CATER 2006-2103the BK21 Project of the Korean Government
文摘This study investigates the use of dynamic a priori error information according to atmospheric moistness and the use of quality controls in temperature and water vapor profile retrievals from hyperspectral infrared (IR) sounders. Temperature and water vapor profiles are retrieved from Atmospheric InfraRed Sounder (AIRS) radiance measurements by applying a physical iterative method using regression retrieval as the first guess. Based on the dependency of first-guess errors on the degree of atmospheric moistness, the a priori first-guess errors classified by total precipitable water (TPW) are applied in the AIRS physical retrieval procedure. Compared to the retrieval results from a fixed a priori error, boundary layer moisture retrievals appear to be improved via TPW classification of a priori first-guess errors. Six quality control (QC) tests, which check non-converged or bad retrievals, large residuals, high terrain and desert areas, and large temperature and moisture deviations from the first guess regression retrieval, are also applied in the AIRS physical retrievals. Significantly large errors are found for the retrievals rejected by these six QCs, and the retrieval errors are substantially reduced via QC over land, which suggest the usefulness and high impact of the QCs, especially over land. In conclusion, the use of dynamic a priori error information according to atmospheric moistness, and the use of appropriate QCs dealing with the geographical information and the deviation from the first-guess as well as the conventional inverse performance are suggested to improve temperature and moisture retrievals and their applications.
基金This work is supported by National Natural Science Foundation of China
文摘By using the expressions for the maximum absorption per wavelength (αλ),and the relaxation frequency fr of the boric acid relaxation derived previously by the author and employing the related oceanographic literatures, the effects of pressure, temperature, pH and salinity on (αλ)r and ∫r of the boric acid relaxation in sea water have been estimated. Results show that ( αλ), not only increases with pH but also increases approximately linearly with pressure and temperature, and is nearly proportional to the 1. 35 power of salinity. However, pressure, pH and salinity have negligible effect on ∫r; therefore, ∫r, can be approximately expressed as a function of temperature only. Comparisons of the predicted with the measured ( αλ)r and ∫r in different ocean areas are given.
文摘This study was aimed at mapping the subsurface extent of saline water intrusions into aquifers at the eastern part of Dahomey basin, Nigeria. The study adopted geoelectric sounding methods. 108 vertical electrical soundings (VES) and 9 induced polarization soundings (IPS) data were acquired using Schlumberger array technique. Three aquifer units were delineated across the study area. The resistivity of the first, second and third aquifer layers varies from 0.2 to 1569 ohm-m, 0.5 to 904 ohm-m and 0.4 to 665 ohm-m respectively, while depth to the top of first, second and third aquifer varies respectively from 0.7 to 151.5 m, 1.4 to 305.5 m and 12.9 to 452.9 m. The depth to the first aquifer layer is shallow (less than 5 m) in the coastal area which makes this area to be highly vulnerable to anthropogenic pollution while their proximity to Atlantic Ocean makes them susceptible to saline water intrusion. In all the three aquifer units, the coastal area, Agbabu and other few locations in the mainland are characterized by low resistivity values (below 60 ohm-m) indicating possible presence of brackish or saline water. IP sounding results showed that all the low resistive layers in the mainland are characterized by clayey materials. The integration of VES and IPS results enabled the delineation of the saline water lateral extent across the study area. There is a strong direct correlation (r2 = 0.8564) between location distance from the saline water source and depth to saline water in the study area. This can therefore serve as a predictive model to determine depth to saline water at any location within the saline water zone in the study area.
文摘Cognitive-inspired computational systems play a crucial role in designing intelligent health monitoring systems which help both patients and hospitals.It also helps in early and consistent decision-making for various health issues including human psychological health.Water fountains built in parks and public spaces are used as decorative instruments which not only give appealing visuals but also provide a relaxing environment to the visitors.These natural sounds have a direct effect on the psychological health of visitors.Very few research works are reported on developing the relationship between water sounds and their corresponding psychological impact.This assessment needs trained manpower and a lot of experimental time which is costly and may not be always available.In this paper,to access the from the pleasantness from human health-friendly water fountain sounds,a perceptually weighted functional link artificial neural network(P-FLANN)model is developed.To reduce the computational complexity of training and for faster convergence,swam intelligence-based optimization algorithm is used for updating the weights.It is observed from the comparative simulation results that the proposed P-FLANN model can effectively perform prediction tasks which is not only cost-effective but also 95%accurate and can play a crucial role in designing human health-friendly water fountains in smart cities.
文摘It is complicated to model the acoustic field in stratified ocean for airborne aircraft,due to high speed of the source and air-to-water sound transmission.To our knowledge,there are very few papers in the open literature dealing with this complicated problem;but,in our opinion,they all require great amount of computation.We now propose a different method that requires much less computation.We improve the wavenumber integration method to model the received temporal signal for a moving source in stratified ocean and sum up in a concise form the core of our paper as follows:(A) Eq.(11) can be calculated by means of fast Chirp Z transform and the signals at all N time points are generated simultaneously;(B) direct numerical evaluation of the wavenumber integral in Eq.(4) produces large numerical errors;so it is necessary to shift the integration slightly below the real axis;(C) we compare the computation cost of direct calculation method with that of our fast calculation method;from the results presented in table 1,we can see that the fast calculation method consumes much less computation time,particularly for long duration signals;(D) for an airborne rapidly moving source,we compute the Doppler-shifted signals in shallow water and analyze their short-time Fourier transform;from Fig.1b,we can see that the received signals have multiple frequency components for a tonal source due to source motion and that each component corresponds to an arrival path.
文摘To unlearn the meaning of a sustainable water resource conservation is now an essential issue in using of sustained, sound, and high-quality water in the world. In this paper, a water quality purification by the Schumann frequencies was first considered through the murmuring sound of upper reach at the mountain stream (Kyoto Pref., Japan) regarding the conservation of water resources. Second, water is changing freely and easily accepting the wavelength of all the sounds. We therefore referred to a flow and dynamic equilibrium to realize and understand the water quality purification process. Finally, a “consciousness only Buddhist philosophy” of water quality as an analogical approach was introduced to realize and understand the water purification process. As a result, we have confirmed the water purification capability by Schmann frequencies in an experiment on water quality. And through the experiment, we have realized the importance/significance to find the meaning for a person’s primary meaningless such as 1) meaning connection among life, environment, and economics as a condition of human life, 2) energy, entropy and fluctuation under law of thermodynamics, 3) a metaphor between water quality and mutual possession of the ten worlds based on conscious-only theory, and 4) sense of wonder through the water purification process.
文摘Authors have conducted an experiment of irradiation using sound waves (frequency) including ultrasonic waves into water such as drinking water, sea water and forest water and wastewater so far. As a result, almost the same effect of improvement of water quality was confirmed for each sound wave. Then, an environmental anthropological study of watershed management based on the sound was carried out assuming that a water quality management using the sound could be possible. The Goulburn River basin in the southern part of Australia in which indigenous peoples (Yorta Yorta) have been concerned with the management for a long time so far was selected as an objective drainage basin this time. As a result, a couple of environmental anthropological perspectives on watershed management were proposed.
文摘The current research focuses on the detection of sea water intrusion in Rashid area which is located about 75 km east to Alexandria, Egypt. For this purpose, geoelectrical survey was carried out using the Schlumberger Vertical Electric Sounding (VES) to identify freshwater thickness, sea water intrusion and estimate subsurface lithology. Seventeen VES stations were measured with current electrode separation (AB/2) ranging from 1.5 m to 100 m. Then, the VES data was interpreted using 1-D and 2-D inversion schemes of DC resistivity data based on least squares method with smoothness constrains. The inverted resistivity distribution at relatively shallow depth shows an important low resistivity zone that probably reflects salt water alteration zone (northern parts). Depth to the freshwater bearing layer reaches its maximum at the south and decreases towards the north. From quantitative interpretation, invasion of salt water started at depth about 10 m at north in the thickness of freshwater bearing layer ranging from 15 to 25 m, while at depth of about 120 m all the layers were saturated with salt water.
文摘There is a new method of calculating the trajectory of sound waves (rays) in layered stratified speed of sound in ocean without dispersion. A sound wave in the fluid is considered as a vector. The amplitudes occurring at the boundary layers of the reflected and refracted waves are calculated according to the law of addition of vectors and using the law of conservation of energy, as well as the laws that determine the angles of reflection and refraction. It is shown that in calculating the trajectories, the reflected wave must be taken into account. The reflecting wave’s value may be about 1 at certain angles of the initial wave output from the sours. Reflecting wave forms the so-called water rays, which do not touch the bottom and the surface of the ocean. The conditions of occurrence of the water rays are following. The sum of the angles of the incident and refracted waves (rays) should be a right angle, and the tangent of the angle of inclination of the incident wave is equal to the refractive index. Under these conditions, the refracted wave amplitude vanishes. All sound energy is converted into the reflected beam, and total internal reflection occurs. In this paper, the calculation of the amplitudes and beam trajectories is conducted for the canonical type of waveguide, in which the speed of sound is asymmetric parabola. The sound source is placed at the depth of the center of the parabola. Total internal reflection occurs in a narrow range of angles of exit beams from the source 43° - 45°. Within this range of angles, the water rays form and not touch the bottom and surface of ocean. Outside this range, the bulk of the beam spreads, touching the bottom and the surface of the ocean. When exit corners, equal and greater than 77°, at some distance the beam becomes horizontal and extends along the layer, without leaving it. Calculation of the wave amplitudes excludes absorption factor. Note that the formula for amplitudes of the sound waves applies to light waves.