Ocean Acoustic Propagation by Finite Difference Methods

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Water waves travel faster on the surface of deep water than they do on shallow water. Examples include water waves, waves on strings or rope, light and other electromagnetic waves. Surface waves — In this type, the particles travel in a circular motion. A peak is a place where the water rises higher than when the water is still and a trough is a place where the water sinks lower than when the water is still.

One example of a transverse wave is a water wave where the water moves up and down as the wave passes through the ocean. A set of straight or 'plane' waves passes through a gap in a barrier. This applies to waves with wavelengths larger than a few centimeters. But as the wave gets to shallow water, the wave begins to drag on the bottom. On the previous pages, wave propagation was discussed as if a single sinusoidal wave was propagating through the material. Types of Electromagnetic waves include Visible Light, Microwaves etc.

Just add wind. This boundary behavior of water waves can be observed in a ripple tank if the tank is partitioned into a deep and a shallow section. Carr' and Marshall E. What's shallow In this lesson, you will see how the wavelength of a particular wave impacts the wave's speed in deep waters. As the waves grow larger with continued wind, Let's talk about wave characteristics. As a matter of fact, the ocean could be seen as a gigantic energy storehouse collector conveyed by the sun rays to the oceans, with the waves transporting the conveyed kinetic energy across the ocean surface.

The P wave can move through solid rock and fluids, like water or the liquid layers of the earth.


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Waves are generally generated by wind blowing over the ocean, although tsunamis can be generated by large water displacements such as those occurring during earthquakes or major landslides, we will however limit ourselves to the study of wind generated waves, as harnessing the power of tsunamis is beyond current technical reach. Waves transmit energy, not water, across the ocean and if not obstructed by anything, they have the potential to travel across an entire ocean basin.

A water wave is an example of a transverse wave. Mechanical transverse waves require a material medium and propogate by means of vibrations of the medium perpendicular to the direction of travel. Light waves are different from classical waves such as sound and water waves. For both of these cases, equations for waves can be easily approximated.

Since chop and swell are waves, they can interact and pass through each other. But because - [Voiceover] If two waves overlap in the same medium, we say that there's wave interference. These waves usually occur at interfaces. Surface water waves may be classified according to the period frequency of the wave, and the nature of the disturbing and restoring forces at different periods determines the characteristics of the wave.

The friction In science, a wave is defined as a transfer of energy. So this box here could represent a speaker and this could be the sound wave it generates or it could represent a laser and this would be the light wave it generates or it could be some sort of ripple tank generator and this is the water wave it generates. Now that the wave has friction, the wave starts to slow down. The water moves up and down while the wave travels over the surface of the water.

Waves are created by energy passing through water, causing it to move in a circular motion. In science, a wave is defined as a transfer of energy. Water utilities have a big vested interest in the water supply, of course, but not a lot of money to spend fixing the efficiency challenge. One wavelength equals the distance between two successive wave crests or troughs.

They are actually the energy, not the water as such, which moves across the ocean surface. Diffraction is often demonstrated with water waves in a ripple tank.

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A rising tide. S- waves are transverse waves; Ultraviolet waves travel as transverse waves. In the case of. To define the locations of points of constructive and destructive interference. Airy wave theory is strictly only applicable to conditions in which the wave height is small compared to the wavelength and the water depth. In fluid dynamics, wind waves, or wind-generated waves, are water surface waves that occur on the free surface of the oceans and other bodies like lakes, rivers, canals, puddles or ponds.

The waves plashed on the shore and told stories to the pebbles and the sands. Wave erosion is also known as coastal erosion and occurs not only in oceans, but also in other large bodies of water. Previous Water waves are mostly transverse. Sign up to view the full version. The motion of the water is forward as the peak of the wave passes, but backward as the trough of the wave passes, As the wind glides over the ocean surface, a fraction of the kinetic energy from the wind is shifted to the water beneath, resulting in waves. Problem setup 1. Longitudinal wave - A longitudinal wave is a wave in which the motion of the medium is parallel to the motion of the wave.

Definition, bifurcation and solitary waves A generalization of criticality - called secondary criticality - is introduced and applied to finite-amplitude Stokes waves. Champion big-wave surfer Richard Schmidt will have you walking on water in seven easy steps. The slower wave in the shallow The waves are whirling their boat past the rocks into the shallows. When waves meet, they add or cancel out, something called superposition. Plane waves travel in the direction perpendicular to the wavefronts.

The bottom creates drag that affects its orbital motion. The Refraction of Water Waves. Hence water waves are Describing Waves. This is known as the cycle of the wave. Water is therefore a dispersive medium with respect to deep water surface waves, in much the same way that it is a dispersive medium for light waves. The energy of a deep-water wave does not touch the bottom in the open water Fig. Water Sports. Variation of Elemental Manipulation and Liquid Manipulation.

The radius of the circles decreases as the depth into the water increases. Mechanical wave. The user can create, shape and manipulate water, inorganic compound with liquid, gas steam, water vapor , and solid ice states, including changing them from one state to other. WAVE, n. Surfers use an extremely long board, while bodyboarders use a much smaller board. Transverse mechanical waves are able to be transmitted into solids and liquids. This forces the wave to grow upwards, so wave height increases. The bottom of deep-water waves doesn't affect its orbital motion.

Waves in water consist of moving peaks and troughs. The winds cause waves on the surface of the ocean and on lakes. These waves are of a higher frequency than surface waves. Transverse Waves Particles move perpendicular to the motion of the wave Water-level oscillations with periods or recurrence intervals larger than around 1 hour, such as astronomical tide and storm surge, are referred to as water-level variations.

Wind waves are generated by friction between the wind and the water that transfers energy to the water in the form of waves. As the waves spread, the straight front will retain its length, whereas the circular sides will grow in bigger and bigger circles, hence the impression that on a large body of water the waves end up being circular - they are not, but very close. All types of waves have some feature in common. Electromagnetic waves in unbounded free space are nondispersive as well as nondissipative and thus can propagate over astronomical distances.

In deep water only the surface is affected by a wave, but once they get to more shallow water, the waves start to drag on the bottom. KJV Dictionary Definition: wave wave. If you have observed water sloshing back and forth in a swimming pool, bathtub, or cup of water, you may have witnessed a small-scale seiche pronounced saysh.

Water waves, light How does the medium that supports a wave move? To me that makes sense because the energy of a dropped pebble will eventually go to nothing as it's wave spreads out across the lake. Wave Train. The change in speed of the wave will cause refraction as shown in the picture below. While waves can move over long distances, the movement of the medium of transmission—the material—is limited.

Surprisingly, water waves do not satisfy the standard wave equation we derived in previous chapters, except in some special limit cases. Theories of Wind Generated Waves. It is for this reason, that a wave is said to involve the movement of a disturbance without the movement of matter. The most obvious example is when, on the beach, we see waves approaching the beach nearly parallel to the shore when the wind creating the waves is along the coast.

The definition of a Spilling Wave. The audience wave is an example of transverse wave. Therefore, oscillating material does not move far from its initial equilibrium position. A seiche may occur in any semi- or fully-enclosed body of water. Plan your minute lesson in Science or Waves with helpful tips from Ellen Herman A wave is characterized by a propagation speed that depends on the environment. The procedure is extended by superposition to a breakwater with a gap. Definition of water wave. There are two main types of waves: mechanical and electromagnetic.

As a result, water with a free surface is generally considered to be a dispersive medium. It appears in a clustered trio reaching towards the heavens along a roadside in Missouri. Generated by the wind some distance away and now propagating freely across the ocean away from their area of generation, these waves can propagate in directions that differ from the direction of the wind, in contrast to a wind sea. Ocean waves are usually generated by wind on the ocean's surface. It is commonly referred to as linear or first order wave theory, because of the simplifying assumptions made in its derivation.

Ocean waves are called mechanical waves because they travel through a medium. Water waves travel faster on the surface of deep water. For those who suggested the depth of water had something to do with it: you were partly right in that the precise angle of the waves from the bow depends on the depth of water rather than on the speed of the boat. From the wave of sound words spattered out and up like spray. Ocean waves normally form when the wind blows across an open body of water, giving them the alternate title of wind waves or wind generated waves.

As the wave maker imparts When the stone hits the water, the energy is carried to water molecules nearby. Jurjen Battjes has long worked in the area of waves and has inspired the authors throughout their careers, we dedicate this paper to him. The space between the P wave and the R wave within the QRS complex is called the PR interval and normally lasts to milliseconds. Linear water waves are small amplitude waves for which we can linearise the equations of motion Linear and Second-Order Wave Theory.

It is gravity that helps the water stay in its place. Ocean waves are caused by wind moving across the surface of the water. Examples are water waves, ripples, seismic shear waves, and waves in stretched strings as above. Water Depth. Light Waves. The unit of Intensity will be W. Define water wave.

Waves are a repeating pattern of motion that transfers energy from place to place without overall displacement of matter. P Waves.


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One by one, each uttering the name of her beloved, leaped into the waves. Humans harness this power along the coastal regions of the United States, Canada, Scotland, and Australia. Light is an example of a transverse wave. Periodic waves. Sign up to access the rest of the document. These can be observed in a ripple tank. Wave speed does not change with depth, in other words, the phase speed of a deep water wave is independent of depth h. The Wavebrake provides a lasting resolution to these problem. Some simple definitions; Dispersion relation; Deep water waves; Wave Spectrum.

Gamma rays are another example. Figures 1 and 2 show the dispersion error curves of the traditional and the new staggered grid FD schemes for the homogeneous acoustic model in 2D. From Figures 1 and 2 , we get the conclusion that the new staggered grid FD scheme can also preserve the dispersion relation in a pretty wider range compared with the traditional staggered grid FD methods. However, the new staggered grid FD scheme saves wave equation simulation time because Eqs.

Dispersion error curves of the traditional staggered grid FD schemes.

Special order items

Dispersion error curves of the new staggered grid FD schemes. Let the left part of Eq. From dispersion relation Eq. Then, the stability condition of the new staggered grid FD scheme is from Eq. Figure 3 shows the stability condition of the traditional and the new staggered grid FD scheme in 2D.

We can see that the stability condition becomes stricter with the increase of the FD operator length. Stability condition in 2D. The two roots give the following dispersion relation [ 11 ]:. Usually, Eq. For the first-order staggered grid FD scheme, the following dispersion relation can be obtained from Eq. Different with previous staggered grid FD scheme for the first-order elastic wave equation, the simplest centered second-order staggered grid FD operator can be used for the spatial derivatives in Eqs.

It will be demonstrated later that the staggered grid FD scheme in Eqs. Then, the new dispersion relation can be obtained from Eq. We first consider a layered velocity model. A Ricker wavelet with the main frequency as The seismic source position is denoted as a asterisk, and the receivers A and B are denoted as a circle and a diamond from top to bottom, respectively. The space grid interval is 20m, the FD operator length M is 7 and the time step is 1. The staggered grid FD coefficients used in Figure 4 are shown in Table 1.

In the first row is the traditional staggered grid FD coefficient obtained from Table 3 of Chu and Stoffa [ 17 ]; in the second row is the least squares staggered grid FD coefficient obtained from Table 3 of Liu [ 35 ]; and in the last rows are the staggered grid FD coefficients used for Eq. The seismograms recorded at positions A and B by different methods are presented in Figure 5. Figure 5 a is obtained with the traditional staggered grid FD scheme with the FD coefficient obtained in the space domain by Taylor expansion method [ 17 ].

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The grid dispersion is obvious. Figure 5 b is obtained with the traditional staggered grid FD scheme with the coefficient obtained in the space domain by the least squares method [ 35 ]. The staggered grid FD coefficient provided by Liu is one of the best staggered grid FD coefficient provided in recent years [ 35 ]. Figure 5 c is obtained with the new staggered grid FD scheme with the coefficient determined in the time-space domain by the linear method. Figure 5 d is obtained with the pseudo-spectrum method with the second-order acoustic wave equation.

We observe that the grid dispersion in Figure 5 b and c is similar to each other and is close to the nearly analytic results obtained with the pseudo-spectrum method in Figure 5 d. However, the required simulation time is reduced by using the new staggered grid FD scheme because Eqs. Seismograms recorded by different simulation methods. The seismic source function is the same as the previous example. The pseudo-spectrum method is used for the second-order acoustic wave equation as shown Figure 7 d. Seismic records obtained with different methods.

Figure 7 a is obtained the with the traditional staggered grid FD scheme with the coefficient obtained in the space domain by Taylor expansion method. Figure 7 b is obtained with the traditional staggered grid FD scheme with the coefficient obtained in the time-space domain by the least squares method [ 27 ]. Most of the grid dispersion is suppressed. Figure 7 c is obtained the with the new staggered grid FD scheme with the coefficient obtained in the time-space domain by the linear method. The grid dispersion in Figure 7 c is very similar to the grid dispersion in Figure 7 b.

However, the simulation time to get Figure 7 c is reduced compared with the simulation time to get Figure 7 b. Both seismic records in Figure 7 b and c are close to seismic record in Figure 7 d. We want to mention that the linear method is faster than the LS method to determine the FD coefficients. It is also observed that with the coefficient obtained in the space domain by Taylor expansion method, the grid dispersion is serious in the simulation result. The simulation results are almost overlapped for the traditional staggered grid FD scheme and new staggered grid FD scheme with optimized FD coefficient.

The grid dispersion in Figure 9 c is very similar to the grid dispersion in Figure 9 b. It demonstrated that the new staggered grid FD scheme is accurate for the particle velocities in Eqs. Particle velocity snapshots vx obtained with different methods. We first consider a homogeneous model.

The seismic source position is at the center of the model. The snapshots of the horizontal component obtained by different staggered grid FD methods are presented in Figure 10 a — c. Figure 10 a is obtained with the traditional staggered grid FD scheme with the traditional FD coefficient. Figure 10 b is obtained with the traditional staggered grid FD scheme with the new FD coefficient. Compared with Figure 10 a , the grid dispersion is suppressed.

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Figure 10 c is obtained with the new staggered grid FD scheme. The grid dispersion curves in Figure 10 b and c are very similar, which is further demonstrated in Figure 10 d. Figure 11 shows the salt model from Society of Exploration of geophysicists. The S wave velocity is obtained from the P wave velocity. When you read an eBook on VitalSource Bookshelf, enjoy such features as: Access online or offline, on mobile or desktop devices Bookmarks, highlights and notes sync across all your devices Smart study tools such as note sharing and subscription, review mode, and Microsoft OneNote integration Search and navigate content across your entire Bookshelf library Interactive notebook and read-aloud functionality Look up additional information online by highlighting a word or phrase.

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Finite‐difference modeling of wave propagation in a fluid–solid configuration

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