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THE OCEAN AS AN ACOUSTIC SYSTEM By Frank Press and Maurice Ewing Columbia University Introduction—A cursory examination of the voluminous writing on the subject indicates that there is almost as much disagreement on the observational data of microseisms as there is on the question of their origin. Progress toward a solution of the problem can only be made by first deciding what are the data to be explained. We begin our discussion with a list of what we believe are basic facts derived primarily from data of east coast stations. The list pretends to be neither complete, nor generally applicable to other localities. It is our belief, however, that a successful theory of the origin of microseisms must satisfactorily explain these data (Donn, 1951a, 1951b, 1952a, 1952b) in addition to the observations from other localities. We realize that some of the data disagree with other observations re- ported at this meeting. However we are con- vinced that observations on this coast forces one to these conclusions. 1. Frontal microseisms are generated very soon (often abruptly) after a cold front passes seaward from land, with no obvious correlation to prior wind and sea conditions. 2. A relatively narrow spectrum of periods appears to be generated by a front, cyclone, or hurricane at a given time when the disturbance is over an area of uniform water depth. Char- acteristic periods of microseisms can be related to generating areas in the ocean. 3. As a front recedes from shore, the spec- trum gradually shifts to longer periods, and becomes fairly constant after deep water is reached. 4. Cold fronts and air masses following them can generate microseisms whereas warm air masses preceding the cold fronts fail to generate microseisms even when strong on- shore winds are present. 5. In many cases there are no obvious cor- relations between swell and surf conditions and microseisms. 6. Microseism energy is dissipated by a profound crustal discontinuity at the edge of the continental shelf. Hurricanes crossing the edge suddenly generate larger microseisms. It is our opinion that no published theory of microseisms satisfactorily explains all of these observed data. The authors' theory (Press and Ewing 1948) advanced some years ago utilizing the Airy phase associated with stationary values of group velocity re- quires long, homogeneous, propagation paths. The work of Donn and others shows that this is not the case for many microseism storms. The work of Longuet-Higgins, and others on stationary gravity waves appears to explain satisfactorily how pressure fluctuations of suffi- cient magnitude to account for microseisms may be communicated to the sea floor. That stationary waves capable of generating micro- seisms occur in the open ocean has not been demonstrated to the satisfaction of many in- vestigators and cannot be reconciled with many of the observations of Donn and others. Many difficulties are found with the theory of surf pounding. The authors have at present no theory which can account for amplitudes and periods of microseisms but feel that the data requires one in which the properties of the ocean-rock acoustic system under the generat- ing area are significant in determining micro- seism periods. A theory should also account for the observation that only certain air mas- ses appear capable of generating microseisms. The Ocean as an Acoustic System— Seismic re- fraction measurements and earthquake surface wave studies (Ewing et al, 1950, Ewing and Press 1950, Ewing et al, 1952, Ewing and Press in press, Officer et al, 1952) indicate that the ocean basins are underlain by about 1 km of mud with acoustic properties much closer to those of sea water than the underlying crys- talline rock. The mud velocity is about 5500 ft/sec with density about 1.5 gm/cm whereas the crystalline rock velocity is about 22,000 ft/sec with density 3.0 gm/cm (Donn 1952 b). This is to be compared with a velocity of 5000 ft/sec and unit density for sea water. It is seen that a great impedance contrast exists be- tween the water-mud layer and the crystalline floor. A single set of acoustic parameters can be used to specify the unique properties of the ocean-crystalline basement system over a large area of the ocean basin. In many cases, how- ever, microseisms are generated on the conti- nental shelf or near the continental edge and the paths do not cross this excellent acoustic system. 109

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110 SYMPOSIUM ON MICROSEISMS Seismic refraction measurements on the submerged continental shelf off the eastern U. S. reveal that a wedge of sediments, thicken- ing seaward, overlies the crystalline basement rock. The details of the variation of sedimen- tary thickness with distance from the shore vary along the coast. An upper sedimentary layer with acoustic properties similar to those of water and a lower layer acoustically inter- mediate between sea water and the crystalline rock below are the major constituents of the sedimentary wedge. That these acoustically unique features of oceans are significant has been demonstrated from dispersion studies of earthquake Rayleigh waves in the period range 16-40 seconds. The coherent, sinusoidal oscillations showing a sim- ple, orderly dispersion point up the excellence of the acoustic system for these periods. A simple theory can account for the entire se- quence arrivals of first mode Rayleigh waves having oceanic paths in terms of normal mode propagation over long distances in the water- crystalline rock system. Predictions of the wa- ter and sediment thickness as well as the nature of the crystalline rock underlying ocean basins have been verified by seismic refraction meas- urements (Ewing and Press 1850, Ewing and Press in press, Officer et al. 1952). J. E. Oliver has been studying shorter pe- riod surface waves which propagate across the oceans with periods 7-12 seconds. These oscil- lations appear on transverse as well as radial and vertical components, and are best recorded on islands. Preliminary results suggest that they consist of bothLovewaves and second mode Rayleigh waves which are strongly refracted and almost entirely absorbed at the continental margins. This is in accord with the great dis- continuity known to exist at the continental margin. The dependence of the degree of ab- sorption and refraction on period can be demon- strated from surface wave studies. Investiga- tion of Mantle Rayleigh waves with periods greater than 60 seconds (Ewing and Press 1953) indicates that negligible absorption and refraction occurs. Comparison of absorption of first and second mode Rayleigh waves from the same tremor indicates that the shorter waves are much more strongly attenuated by the discontinuity. Evernden (1952) has shown that Rayleigh waves with periods less than about 35 seconds are significantly re- fracted by the continental margin. It seems probable from these results that these effects are even more pronounced for the shorter peri- od microseisms. It is not surprising that re- fraction effects and barriers are among the most significant features noted by those study- ing the data of tripartite stations in view of the length and irregularity of the continental mar- gin. It seems significant that the shortest period surface waves from earthquakes in the Atlantic Ocean are above the periods generally observed for microseisms. That this is not primarily due to the spectrum of the source is suggested by the fact that body waves occur with micro- seism periods, and the T-phase often present, appears with even shorter periods. Atmosphere-Ocean Coupling — ROSCHKE (1952) in a recent paper reports that micro- oscillations in the atmosphere of periods less than one minute reach their maximum ampli- tudes in the post-cold front interval and that streams of cold air are more efficient producers of microoscillations than warm air. Data from Columbia microbarographs are in agreement. In view of the previous observation that the type of air mass over the ocean is a significant factor in microseism generation these results strongly suggest that pressure fluctuations in the atmosphere may provide energy for micro- seisms in a manner as yet unknown to us. More data is needed on the areal extent of these oscillations as well as their oceanic amplitudes. It has been suggested that vertical os- cillations of the water column analogous to "organ pipe" vibrations may well be a signifi- cant feature of the ocean-rock acoustic sys- tem. Use of this concept to explain micro- seisms is not new (Banerji 1935). On a seismic prospect in shallow water (Burg et al. . 1951) where the bottom was composed of smooth hard rock, the predominant signal ob- scuring all other waves on short spread seismo- grams consisted of a repetitive pattern of the "organ pipe" modes of vibration of the water layer. In some cases all the modes but one could be filtered revealing a long train of si- nusoidal oscillations with the proper frequency for that mode and water depth. Another as- pect of vertical compressional oscillations of the water column is revealed by a simple cal- culation of the vertical displacements on the ocean floor originating from steady vertical oscillations applied to the surface. The results show, as might be expected from the general theory of transmission through plates, that the ocean is an extremely sharp filter for trans- mission of compressional waves from the sur- face to the bottom — the sharpness originating in the high impedance contrast between the water and mud and the crystalline basement. The peak periods, T, for waves transmitted to the crystalline basement are given by » = 1, 2, 3 Where H is the water-unconsolidated sediment thickness, v is about 5000 ft/sec. Calcula- tions by Dr. Jardetzky have shown (as one might expect from the general theory of fil- ters) that a transient impulse applied to the sea surface appears at the bottom as trains of damped sinusoidal waves having periods cor- responding to the "organ pipe" modes. Al- though these waves can explain microseism pe- riods they cannot be propagated horizontally to

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THE OCEAN AS AN ACOUSTIC SYSTEM 111 any significant distances due to downward leak- age of energy out of the system as body waves. Recently it has been shown that under cer- tain circumstances a resonant transfer of ener- gy from the atmosphere to the earth's surface can occur despite the tremendous impedance mismatch between the two media ( H a s k e 11 1951). This phenomenon has now been ob- served for coupling between compressional waves in the atmosphere and Rayleigh waves on the earth's surface (Press and Ewing 1951a), flexural waves on floating ice and tsunami (Press et al. 1951b, Press and Ewing 1951c). When viewed from the ele- mentary standpoint of the theory of travelling disturbances, resonant coupling occurs when a disturbance travels along the surface of a me- dium at a velocity close to that of a free wave in the medium. If the free wave is dispersive the energy from the disturbance goes into those waves whose periods are such that the phase velocity is close to the velocity of the disturb- ance. The resonance is especially sharp for large density contrasts between the two media as is the case with the atmosphere and the earth. The possible connection between this mode of coupling of atmosphere to ocean and microseisms is being investigated. One obvi- ous feature is that pressure oscillations in the atmosphere striking the sea surface at an al- most vertical angle and maintaining coherence over a large area do not fully satisfy the con- ditions for resonant coupling since "organ pipe" oscillations in the sea column are not free due to the small leakage at each boundary. REFERENCES BANERJI, S. K., Proc. Ind. Acad. Sci. I, 727-53, 1935. For a discussion see F. J. W. Whipple and A. W. Lee, "Notes on the Theory of Microseisms," Mon. No. Roy. Astron. Soc. Geophys. Suppl., 3, 287-297, 1936. BURG, K. E., EWING, M., PRESS, F., and STULKEN, E. J., "A Seismic Wave Guide Phenomenon," Geophysics, 16, 594-612, 1951. DONN, W. L., "Cyclonic Microseisms Generated in the Western North Atlantic Ocean," Jowrn. Met. 9. 61-71, 1952a. "Frontal Microseisms Generated in the Western North Atlantic Ocean," Journ. Met. 8, 406- 415, 1951a. "An Investigation of Swell and Micro- seisms from the Hurricane of Sept. 13-16, 1946" Trans. Amer. Geophys. Union 33, 341-344, 1952a. "A Comparison of Microseisms and Ocean Waves Recorded in Southern New England" Col. Univ. Techn. Report on Seismology No. 21, 1951b. EVERNDEN, J. F., "Direction of Approach of Rayleigh Waves and Related Problems," Abstr. 1952 Pro- gram Geol. Soc. Amer. Cordill Sect. mtg. EWING, M., WORZEL, J. L., STEENLAND, N. C., and PRESS, F., "Geophysical Investigations in the Emerged and Submerged Atlantic Coastal Plain" Bull. Geol. Soc. Amer. 61, 877-892, 1960. EWING, M., WORZEL, J. L., HERSEY, J. B., PRESS, F., and HAMILTON, G. R., "Seismic Refraction Meas- urements in the Atlantic Ocean Basin," Bull. Seism. Soc. Amer. 4, 233-242, 1952. EWING, M., and PRESS, F., "Crustal Structure and Sur- face Wave Dispersion," Bull. Seism. Soc. Amer., 40, 271-280, 1950. "Crustal Structure and Surface Wave Dis- persion," Part II, Bull. Seism. Soc. Amer., in press. EWING, M., and PRESS, F., "An Investigation of Mantle Rayleigh Waves," in press, Bull. Seism. Soc. Amer., 1953. HASKKI.I,, N. A., "A Note on Air Coupled Surface Waves," Bull. Seism. Soc. Amer., 41, 295-300, 1951. OFFICER, C. B., EWING, M., and WUENSCHEL, P. C., "Seismic Refraction Measurements in the Atlantic Ocean," Part IV, Geol. Soc. Amer. Bull., 63, 777- 808, 1952. PRESS, F., and EWING, M., "A Theory of Microseisms with Geologic Applications," Trans. Amer. Geophys. Union, 29, 163-174, 1948. PRESS, F., and EWING, M., "Ground Roll Coupling to Atmospheric Compressional Waves," Geophysics, 16, 416-430, 1951a. PRESS, F., CRARY, A. P., OLIVER, J., and KATZ, S., "Air Coupled Flexural Waves in Floating Ice," Trans. Amer. Geophys. Union, 32, 166-172, 1951b. PRESS, F., «nd EWING, M., "Theory of Air Coupled Flexural Waves," Journ. Appl. Phys., 22, 892-899, 1951c. ROSCHKE, W. H., JR., "The Relation Between Air Pres- sure Micro Oscillations and Concurrent Synoptic Patterns," Journ. Met., 9, 213-219, 1952. Discussion N. A. HASKELL Air Force Cambridge Research Center I have tried to make a crude order of mag- nitude estimate of the amplitudes to be ex- pected from the generation of microseisms via excitation of the "organ pipe" modes in the ocean by atmospheric pressure oscillations. The results seem to me to indicate that this mech- anism is of questionable quantitative signifi- cance. In Roschke's (1952) study of at- mospheric pressure oscillations he classifies os- cillations of periods less than 1 minute as "large" when the double amplitude is greater than about 2 dynes/cm'. In the illustrations he gives of typical high microbarometric activ- ity immediately following the passage of a cold front the double amplitude appear to run around 6 dynes/cm1. The same order of magnitude has been quoted for pressure fluctua- tions having periods in the neighborhood of 5 sec. observed at the Signal Corps Engineering Laboratories (Daniels. 1952). Now if the ocean is excited in one of the vertical "organ pipe" compressional modes by a pressure oscillation of amplitude P0 at the

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112 SYMPOSIUM ON MICROSEISMS surface, the pressure amplitude at the bottom is greater than P0 in the ratio Pbcb/ wcw where gb and gw are the densities and Cb and Cw are the compressional wave velocities in the bottom and water respectively. If we take Q, = 1, QO= 3, c. = 5000 ft/sec, cb= 22,000 ft/ sec, this ratio is 13.2, giving about 80 dynes/ cm" at the bottom for a 6 dyne/cm" amplitude at the surface. The displacement amplitude at the bottom for an oscillation of period T will be of the order of TPb/27ipbcb = TP0/2rc which is about 0.3 micron for T = 5 sec and the other quantities having the values assumed. This should be a value characteristic of the immediate area of generation and the ampli- tude at a seismic station at some distance should be considerably less, yet the amplitudes of microseisms attributed to the passage of cold fronts over deep water may run to more than 2 microns. There seems to be a discrep- ancy by a factor of 10 or more. I rather doubt that the idea of resonant coupling between elastic waves in>two different media due to coincidence between the phase ve- locities of different wave types will turn out to have a great deal to do with the coupling of atmospheric pressure oscillations to the ocean bed. Where it has been possible to cor- relate wave forms of microbarometric waves across a tripartite array, the apparent phase velocity has usually come out to be very much less than sound velocity and comparable with the wind velocity at some moderate altitude. Gravity surface waves on the ocean also have phase velocities of the same order as wind ve- locities, so that if microbarometric oscillations are coupled with anything in the ocean it is presumably with gravity rather than compres- sional waves. Gravity waves only 1 meter high would give pressure oscillations of the order of 10" dynes/cm" near the surface and bottom pres- sures exceeding the 80 dynes/cm2 estimated for the direct excitation of the "organ pipe" modes for all water depths less than 1.25 wave lengths, or about 160 feet for waves of 5 sec. period. So far as pressures go, surface waves in shal- low water seem to be adequate to generate observable microseisms. However, there seems to be a good deal of statistical evidence that at least some micro- seismic activity, and perhaps most of it in some areas, has a deep water origin. Whipple and Lee (1935), investigating Banerji's (1930) suggestion that gravity waves should generate compressional waves that were not attenuated exponentially with depth, showed that the compressional wave travelling with the velocity of gravity surface waves would neces- sarily have an exponential attenuation rather than a sinusoidal variation with depth. If therefore appears to me that neither the direct action of atmospheric pressure oscilla- tions nor indirect coupling via gravity waves in the first order linear approximation are ade- quate to explain the generation of microseisms in deep water, and the second order term in the expression for the bottom pressure as discussed by Longuet-Higgins (1950) is the only mecha- nism that has been proposed so far that looks quantitatively adequate. The failure of some observers to verify the two-to-one ratio between the periods of ocean waves and of mi- croseisms as deduced from this theory may in- dicate nothing more than that the wave peri- ods observed on a swell recorder in shallow wa- ter near the coast are not necessarily the same as the periods of the interfering wave systems that produce microseisms in the storm area. A deep-water bottom pressure recorder should throw a great deal of light on this question. REFERENCES BANERJI, S. K., Microseisme Associated with Disturbed Weather in the Indian Seas. Phil. Trans. Royal Soc. A., 229, 287 (1930). DANIELS, F. B., Acoustical Energy Generated by the Ocean Waves. Journ. Acoust. Soc. Amer., 24, 83 (1952). LONGUET-HIGGINS, M. S., A Theory of the Origin of Microseisms. Phil. Trans. Royal Soc., A., 242 (1950). ROSCHKE, W. H., JR., The Relationship Between Air Pressure Micro-Oscillations and Concurrent Synop- tic Patterns. Journ. Met., 9, 213 (1952). WHIPPLE, F. J. W., and LEE, A. W., Notes on the Theory of Microseisme. Mthly. Notes Royal Astrom. Soc., Geo., Suppl, 3, 287 (1935). Discussion from the Floor Lynch. Since the purpose of this conference is to reconcile contradictory views on micro- seisms as far as possible, I should like to call attention to a contradiction or at least an ap- parent contradiction presented by the opening part of Dr. Press' paper. He states, on the basis of Dr. Wm. Donn's work that micro- seismic activity on the East Coast begins only when the cold front enters the Atlantic. The speaker in a paper yesterday states that he and his colleagues feel positive that microseis- mic activity on the East Coast from cold fronts originates in the Great Lakes. Here then we have an apparent contradiction—one author claims the activity originates in the Great Lakes, another author claims the activity origi- nates in the Atlantic—to the casual listener surely a contradiction! This, however, is one contradiction that we can easily reconcile. I should like to point out that the time taken for a microseismic wave to reach New York from the Great Lakes is a matter of minutes. I should like to point out

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THE OCEAN AS AN ACOUSTIC SYSTEM 113 also that the position of Cold Fronts on weath- er maps is only a rough geographical location —and good only within a period of a few hours. It is therefore impossible to state within min- utes just when a cold front first enters the Atlantic. That pronounced microseismic ac- tivity is recorded when a cold front enters the Atlantic we most heartily agree. One state- ment of yesterday therefore in no way contra- dicts those of Dr. Press. We do state, how- ever, that a matter of hours before this (the precise number of hours depending on how fast the cold front is advancing) we record microseismic activity caused by the front as it passes over the Great Lakes. We record this in a matter of minutes after the front has reached the Lakes—giving the seismograph a definite warning value in the case of fronts. In a sentence, the contradiction is ex- plained by pointing out that we are recording waves from the frontal activity over the Lakes, whereas Press and Bonn are referring to waves from the frontal activity over the Atlantic. I merely wish to emphasize that we are all in agreement on the microseismic activity as the front passes over the Atlantic. Longuet-Higgins. (1) The response curve for the movement of the ground shown in Figure 1 is considerably sharper than that shown in my paper (Figure 7). The reason is probably as follows: the first curve is the re- sponse to a horizontal plane oscillation of in- finite extent, which causes energy to be propa- gated vertically downwards into the ground; the other is the response to a pressure distribu- tion of finite extent from which the waves are propagated outwards horizontally. The first waves are relatively difficult to generate, being subject to less constraint. (2) Dr. Press has pointed out the rather sudden onset of microseisms at the time that a cold front crosses the coast. I think that there is no difficulty at present in supposing that this is due to wave interference. As the weath- er maps show, there is then a very sharp change in the direction of the wind. It is not necessary that the wind should be exactly re- versed in direction, because a given wind will probably generate waves which, when analyzed, will be found to have some wave components travelling at a considerable angle to the mean direction. N. F. Barber has shown by an optical diffraction method that even a regular swell has components spread over an angle of 30°; for an irregular sea the angle would be greater. The rapidity with which the micro- seism amplitude is built up may be explained by the fact that, if once the original progres- sive system of waves is established (from which no microseisms would be expected), only a small amount of wave energy travelling in the reverse direction would be sufficient to produce the necessary pressure fluctuations. Data at present available for the rate of growth of waves under a wind refers to waves growing gradually under a following wind; it is quite conceivable that the rate of growth of waves travelling downwind, but in the presence of an opposing swell, is greater, on account of the roughness of the sea surface. Observations of the rate of growth should be obtained. Con- trolled experiments could also be made on a smaller scale, using a laboratory wave tank and an opposing artificial wind. (3) The amount of wave reflection from the New England coast is probably very small, since the shore in most places is not steep. The exact value of the reflection coefficient can- not be assumed to be the same as for laboratory experiments with a beach of the same slope, since the scaling, for waves of different period, is uncertain; also in the laboratory experiments the motion was laminar, while in the sea tur- bulence may play a part in the energy dissipa- tion. However, it may be possible actually to determine the extent of reflection from differ- ent parts of a coast by a comparative study of the spectra of pressure fluctuations on the bot- tom, just offshore. (Bath pointed out that on the Norway coast the effect is when the front crosses the coast and not the edge of the shelf. After Haskell's formal discussion, Melton asked if the sudden increase in microseisms and the Lon- guet-Higgins theory may not be consistent due to the reversal of winds. Longuet-Higgins pointed out the waves will then be short. Donn pointed out cases where the sea has been calm but there are microseisms. Byerly commented on the fact that at least one seismologist be- lieves microseisms result from winds against mountains. Gutenberg replied to this that be- cause of the location the wind may actually be on the shore. Press described a swell observed on the New England coast in instances of a large swell and no microseisms. Longuet-Hig- gins blamed this on a low reflection coefficient. Deacon inquired if during some of the swell described by Press, which was of eighteen sec- onds period, there were any nine second micro- seisms, and was told no.)