Abstract
It is now established that the primary microseism, the secondary microseisms, and the hum are the three main components of seismic noise in the frequency band from about 0.003 Hz to 1.0 Hz. Monthly averages of seismic noise are dominated by these signals in seismic noise. There are, however, some temporary additional signals in the same frequency band, such as signals from tropical cyclones (hurricanes and typhoons) in the ocean and on land, stormquakes, weather bombs, tornadoes, and wind-related atmospheric pressure loading. We review these effects, lasting only from a few hours to a week but are significant signals. We also attempt to classify all seismic noise. We point out that there are two broad types of seismic noise, the propagating seismic waves and the quasi-static deformations. The latter type is observed only for surface pressure changes at close distances. It has been known since about 1970 but has not been emphasized in recent literature. Recent data based on co-located pressure and seismic instruments clearly show its existence. Because the number of phenomena in the first type is large, we propose to classify all seismic noise into three categories: (1) propagating seismic waves from ocean sources, (2) propagating seismic waves from on-land sources, and (3) quasi-static deformation at ocean bottom and on land. The microseisms and the hum are in the first category although there are differences in the detailed processes of their excitation mechanisms. We will also classify temporary signals by these categories.
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1 Introduction
The study of seismic noise started shortly after mechanical seismic instruments were developed in the late nineteenth century to the early twentieth century (e.g., Wiechert 1904; Gutenberg 1912; Omori 1918; Bernard 1990). It was noted that the microseisms were the dominant signals in the absence of earthquake signals, even in these early seismic instruments. The cause of excitation was not clear but early postulates included the excitation by surf breaking on coasts (Wiechert 1904) and ocean swell (Omori 1918), which we now know to be correct for some microseism sources. However, it took almost a half-century before the basic mechanisms for the microseisms were sorted out by Hasselmann (1963). This was mainly because the cause of the secondary microseism was not properly understood until the work of Longuet-Higgins (1950). Gutenberg, who wrote a doctoral thesis in Göttingen on seismic noise (Gutenberg 1912), stated twenty-four years later (Gutenberg 1936) “while for most of the types of microseisms the cause is known, there is still no agreement among seismologists on the cause of the most common type, namely, the more or less regular microseisms with periods of from 4 to 10 s.” The double-frequency mechanism for the secondary microseism in which the interactions between ocean waves generate seismic noise was the missing element for many decades in the early twentieth century. Clarification of this process due to the nonlinear interactions among ocean waves was finally published by Longuet-Higgins (1950). This paper also referred to an earlier, equivalent work by Miche (1944) which was written in French. This led to a summary of excitation mechanisms for seismic noise by Hasselmann (1963).
Based on Hasselmann’s (1963) analysis, it has been stated (e.g., Ardhuin et al. 2015) that the two main mechanisms of excitation of microseisms, the direct interactions between ocean waves and solid Earth near the coast, and the interactions among the ocean waves can explain the excitation of the microseisms. Verification of these mechanisms was not straightforward in the 1960s and 1970s, however, because the widely analyzed seismic data during these decades came from the World Wide Standardized Seismograph Network (WWSSN) stations, which had two different sensors, covering the short periods (targeted at about 1 s) and the long periods (target at about 15 s) separately. These sensors were precisely designed to avoid the large microseism noise between these periods and prevented further analysis of seismic noise. This situation changed, however, when the digital, continuous recordings of broadband instruments became common in the mid-1980s, especially with the formation of the Incorporated Research Institutions of Seismology (IRIS Science Plan 1984).
In this paper, we limit our discussion to seismic noise in the low-frequency band from about 0.003 Hz to 1.0 Hz. We have learned from the past few decades that the dominant causes of seismic noise between about 0.003 Hz and 1.0 Hz are the processes in the oceans (e.g., Nishida 2017). Below 0.003 Hz, seismic noise is primarily controlled by atmospheric processes (e.g., Warburton and Goodkind 1977; Zürn and Widmer 1995; Beauduin et al. 1996; Tanimoto 1999; Roult and Crawford 2000; Tanimoto et al. 2015a, b). Therefore, seismic noise below about 1 Hz is primarily caused by nature rather than anthropological processes.
Above 1.0 Hz, there is noise generated by nature such as winds and ocean processes, but various forms of human activities contribute greatly. Examples include the resonant frequencies of buildings (except for the true high-rises) that are typically above 1 Hz and the noise from trains, automobiles (highways), factories, and other human activities. The high-rise buildings that have ~ 100 stories have resonant periods of the order of 10 s and are an exception to this statement, but such buildings are still quite rare.
The importance of human-generated seismic noise for frequencies above 1 Hz became abundantly clear during the COVID-19 lockdown periods in the past few years (e.g., Lecocq et al. 2020; ** factors of the secondary microseismic wavefield. J Geophys Res 120:6241–6262" href="/article/10.1186/s40645-023-00587-7#ref-CR37" id="ref-link-section-d175109428e660">2015)
These waves, typically at periods of about 14 s but occasionally becoming longer periods of up to about 18 s, do not generate seismic waves while they are in deep oceans. This can be understood easily if we examine the wavelength and the depth extent of these waves. The dispersion relation of these ocean waves (in deep water meaning \(\mathrm{tanh}(kH)\approx 1\)) is given by \({\omega }^{2}=gk\) where \(\omega (=2\pi f)\) is the angular frequency (f is the frequency in Hz), \(g\left(=9.8\frac{m}{{s}^{2}}\right)\) is gravitational acceleration, \(k(=\frac{2\pi }{\lambda })\) is the wavenumber and \(\lambda\) is the wavelength. Rewriting this relation in terms of the wavelength, we can write it as \(\lambda =g/\left(2\pi \right)\times {T}^{2}\approx 1.56{T}^{2}\). Using a typical period \(T=14\) (s), \(\lambda =306\) (m), which is the horizontal wavelength. These waves are surface waves in the ocean and their amplitudes decay exponentially with depth. Therefore, the predominant oscillating parts of these waves may reach about 200 m but not beyond. Therefore, in open oceans where ocean depths are typically 3–4 km, they cannot possibly interact with the solid Earth. Consequently, no excitation of seismic waves can occur by those propagating waves in one direction (Longuet-Higgins 1950).
When the swells reach near the coasts, ocean depths become shallow enough for ocean-wave energy to interact with the seafloor. Figure 3c indicates a possible location of seismic waves near the coast, indicated by 1. If there is a continental shelf region near the coast, this interaction occurs within the shelf with ocean depths of less than about 200 m.
This process of direct interaction may also be viewed as the scattering of seismic waves. Propagating ocean waves are a particular mode of surface waves. If the Earth were layered and laterally homogeneous, it would maintain its mode types and remain orthogonal to other modes. But once their motions reach the ocean floor, either due to topography on the ocean floor or shallow and slo** coastal structure, some portions of their energy get converted to other types of seismic waves by the scattering process. This process can produce Rayleigh and Love waves as well as body waves such as P waves and S waves.
2.2.2 Excitation of the secondary microseism by the wave–wave interaction
2.2.2.1 The Longuet-Higgins pressure formula
The mechanism for the excitation of secondary microseism is entirely different and ocean waves do not need to directly interact with the solid Earth. In Fig. 3c we indicate a possible location as 2, but the excitation can occur anywhere in the ocean. The only condition is that two ocean waves that propagate in an opposite direction must meet (or collide). Then, through the nonlinear term in the Navier–Stokes equation, an equivalent vertical force results from this interaction; more explicitly, the origin of this effect is the second term on the lefthand side of the Navier–Stokes equation:
where \(\uprho\) is density, \(\mathbf{v}\) is velocity, P is pressure and g is gravitational acceleration. We drop the viscous term because it is not important in our discussion.
Longuet-Higgins (1950) showed that when two ocean waves that propagate in an opposite direction meet, it generates pressure given by
where \(\zeta\) is the ocean surface displacement and the bar indicates spatial averaging over a large region whose scale is much larger than the wavelength of ocean waves. For example, if we take a case of two cosine waves that propagate in opposite directions, we have
Substituting (3) in (2), we get.
where \(\mathrm{P}\) is proportional to \({a}_{1}{a}_{2}\) and has twice the frequency of ocean waves that collided. The depth extent of ocean waves may be confined to the upper 100–200 m from the ocean surface for the relevant frequency range of 0.05–0.07 Hz (ocean swell frequencies) but Eq. (4) shows that this pressure is associated with a standing wave and can exert pressure at any depth under the location where two waves meet. The important point is that this process can generate seismic waves in the ocean of any depth. This process is often termed the wave–wave interaction process.
The wave–wave interaction can happen in the neighborhood of a low-pressure (weather) system in open oceans as the center of the low-pressure system moves. Teleseismic P-wave sources are now commonly identified near a tropical cyclone (hurricane and typhoon) which can be explained best by the wave–wave interaction. It can also occur near a coast because the incoming ocean waves can reflect from the coast and meet the incoming waves after their reflection. The latter near-coast case can be verified quantitatively by comparing the amplitudes of the primary microseism and those of the secondary microseism. Near the coast, the amplitude of a reflected wave may be written as \(\alpha A\), where \(\alpha\) is the reflection coefficient. Then the above pressure term becomes proportional to \(P\propto \alpha {A}^{2}\). It means that if the amplitude of the primary microseism is \(A\), the amplitude of the secondary microseism should be \(proportional\;to\;A^{2}\). This relation was verified in Nishida (2017) for stations near the coasts. However, for locations far away from the coast this relation becomes obscure. This is probably because propagation across the complex continental structures in the crust from the coast to an in-land seismic station can mask the distinct amplitude characteristics due to scattering during the propagation of waves.
2.2.2.2 Modal excitation theory and the effects of ocean depth
Longuet-Higgin’s (1950) derivation for pressure is relatively intuitive and is often used to explain the wave–wave interaction mechanism. Simply stated, the double-frequency standing waves are generated by colliding ocean waves and create pressure change at the seafloor. But we can also analyze this excitation problem as a modal excitation problem. The modal excitation by the nonlinear term in (1) was analyzed by Tanimoto (2007a), following the normal mode excitation theory (e.g., Gilbert 1970; Aki and Richards 2002; Dahlen and Tromp 1998). The results confirmed that a term equivalent to the above pressure term emerges through the analysis. However, the quantitative match required consideration of the frequency range and the ocean depth. For the frequency range 0.05–0.07 Hz, if the ocean depth were 1 km or less, Fig. 4 shows that Longuet-Higgin's pressure term and the modal excitation theory agree almost perfectly. But if the ocean were deeper, the modal excitation theory predicted a more efficient excitation than that predicted by the Longuet-Higgins formula. For an ocean depth of 5 km, an equivalent force was larger by a factor of five (Tanimoto 2007b).
The relative size of the excitation of Rayleigh waves between the normal mode theory and the Longuet-Higgins formula. The five lines are for different ocean depths from 1 to 5 km. At low frequencies, the ratio approaches 1 and shows quantitative agreement. At frequencies of the secondary microseism, they differ but that is because the formula (Eqs. 2 or 4 in the text) does not contain the depth resonance effects. Longuet-Higgins (1950) discussed this depth effect which was correctly used by Kedar et al. (2008) and Ardhuin et al. (2011)
But this is not a fair comparison as the effects from ocean depth are not included in (4). The effects from ocean depth are related to the resonant effects within the oceanic layer. Longuet-Higgins (1950, p. 34) stated that “the microseism amplitudes may be increased by a factor of order 5 owing to the greater response of the physical system for certain depths of water.” In other words, the excitation may be enhanced due to resonant effects if the ocean depth is close to ½(m − 1) + 1/4 of an acoustic wavelength in water, where m is an integer related to the number of reverberations in the ocean (Kedar et al. 2008). The modal excitation approach contains such effects automatically. The inclusion of ocean-depth effects with the above pressure term in (2) resolves this problem and in most applications such effects are taken into account (Kedar et al. 2008; Ardhuin and Herbers 2013; Ardhuin et al. 2011; Gualtieri et al. 2015).
2.3 Hum: background oscillations
2.3.1 Discovery
The frequency range of the hum is approximately from about 3 mHz to 15 mHz. An example of spectra, stacked from 15 global broadband stations (Tanimoto 2005), is shown in Fig. 5 (top). Spectral peaks of individual fundamental spheroidal modes are clear from about 3 mHz to 8 mHz but the broad background spectra that span in frequency from about 3 mHz to 15 mHz have a peak at about 9 mHz. An arrow is shown to indicate this broad peak. This peak had already been recognized by Peterson (1993, Fig. 1). The boxed part in the top figure is enlarged in the bottom panel and the spectra confirm that each peak is a fundamental spheroidal mode. The reason that each spheroidal mode peak cannot be seen above 8 mHz should be partly due to attenuation. It can also be because of contributions from smaller sources in which only minor-arc Rayleigh waves are observed. Observation of modal peaks in spectra requires not only minor-arc Rayleigh waves but also great-circling Rayleigh waves that circulated the Earth a few more times and constructively interfere with other great-circulating Rayleigh waves. Such constructive interference can only occur for a strong source; this implies there are many weaker sources responsible for this portion of the spectra. The lack of constructive interference among many minor-arc arrivals can produce a broad peak like the one in Fig. 5 (top).
An example of the hum signals, obtained from stacking of 15 global seismic stations. Peterson's (1993) low noise model, NLNM, is shown by dots in the top panel. A small box in the top panel is enlarged in the bottom panel. Vertical lines in the bottom panels show the eigenfrequencies of fundamental spheroidal modes of PREM. There are individual peaks of spheroidal modes between about 2 mHz and 8 mHz but the entire spectral bump from 2 to 15 mHz is the hum, mostly consisting of globally circulating Rayleigh waves
The hum was initially discovered as the background oscillations of the Earth around the year 1998 (Nawa et al. 1998; Suda et al. 1998; Kobayashi and Nishida 1998; Tanimoto et al. 1998; Kanamori 1998). It was recognized then that there were small oscillations that exactly matched the frequencies of fundamental spheroidal modes (Fig. 5, bottom), even in the absence of earthquakes with a moment magnitude of about 5.5. The amplitudes for these oscillations were shown to be equivalent to earthquakes with a moment magnitude of about 6 (Tanimoto and Um 1999) despite the fact there was no occurrence of such earthquakes. This discovery was about 100 years later than the discovery of the microseisms because their amplitudes were much smaller. Furthermore, the frequency band of the hum required high-quality broadband sensors that are sensitive at about 0.01 Hz.
Using the fact that spheroidal fundamental modes are equivalent to traveling great-circling Rayleigh waves, Ekström (2001) showed that there existed background great-circling Rayleigh waves in vertical component seismograms through the autocorrelation approach. This work also detected a large six-month periodicity in amplitudes that agreed with the modal study by Tanimoto and Um (1999). The maximum amplitudes were found in January and July. Ekström (2001) also reported that the amplitudes of the hum were equivalent to an earthquake of about magnitude 5.8 which was a more precise estimate than Tanimoto and Um (1999). Detection of seasonality finally made it clear that the cause of excitation was not of tectonic origin such as small earthquakes or slow slips on faults; the cause must be in the atmosphere or the oceans. This was reviewed in Tanimoto (2001) but a more recent, up-to-date review of the hum can be found in Nishida (2013).
2.3.2 Excitation mechanism
The initial hypothesis for the cause of the hum was the atmospheric excitation or pressure changes on Earth’s surface. Random pressure changes on Earth’s surface were assumed to excite the resonant vibration modes of the Earth (Kobayashi and Nishida 1998; Tanimoto and Um 1999; Fukao et al. 2002; Nishida et al. 2002). For such randomly distributed surface forces to excite normal modes, the crucial parameter turned out to be the lateral correlation length of surface pressure (Kobayashi and Nishida 1998). In hindsight, this hypothesis was untenable because the required correlation length of pressure to explain the observed modal amplitudes was 1–10 km. Such a long correlation length is incompatible with pressure observations. The observed pressure correlation length varies temporarily and spatially but is in the 10–100 m range most of the time.
Intuitively, the choice of ocean waves as the cause of excitation seems far more reasonable than the atmospheric hypothesis. This is because pressure perturbations in the oceans are much larger than pressure perturbations in the atmosphere; for example, the largest pressure changes in the atmosphere occur when tropical cyclones develop but the pressure difference between the lowest pressure at their center (~ 900 hPa) and the average pressure outside (~ 1000 hPa) is at most 10% (100 hPa). In the oceans, ocean waves with amplitudes of about 10 m can be found quite commonly in winter of the northern hemisphere or the southern hemisphere. Pressure perturbations in such a situation can be as large as 1000 hPa, therefore the pressure perturbations could reach about 100%.
An oceanic excitation hypothesis was discussed earlier when the atmospheric excitation hypothesis was first proposed (Watada and Masters 2001), but it took a few years until the oceanic excitation hypothesis was seriously considered. In an observational study, Rhie and Romanowicz (2004, 2006) showed that the excitation sources of the hum were in the ocean by using broadband seismic arrays in Japan and California. This result suggested that ocean waves with frequencies of about 10 mHz were somehow generated (often called oceanic infragravity waves) and led to the excitation of solid Earth modes. Tanimoto (2005) also presented various supporting evidence for the oceanic excitation hypothesis from the analysis of seismic data from the IRIS global network data and the satellite significant-wave-height data (SWH). Specifically, the SWH data showed high-amplitude ocean-wave activities in January and July that matched the seasonal, maximum amplitudes of the hum. Further studies that improved the locations of the excitation sources and understanding of the excitation mechanisms were published by Nishida and Fukao (2007), Bromirski and Gerstoft (2009), Fukao et al. (2010), and Harmon et al. (2012). In general, the excitation sources in the oceans were found close to the coasts but were spatially spread out (Bromirski and Gerstoft 2009; Traer et al. 2012; Nishida 2017).
In theory, the hum could be excited in deep oceans because the long-period oceanic infragravity waves that are the cause of excitation have amplitudes that reach the ocean floor even in the open oceans (3–4 km). Examples of the eigenfunctions of ocean waves for the frequency band of the hum, about 10 mHz, are shown to reach the ocean bottom (Fig. 6). This is the case for the Preliminary Reference Earth Model (Dziewonski and Anderson 1981) which has an ocean depth of 3 km. The eigenfunctions only marginally reach the seafloor at 20 mHz (Fig. 6, right) but they have significant amplitudes on the seafloor at 10 mHz. These features in eigenfunctions suggest that the hum at 10 mHz may be excited by the direct interactions between ocean waves and the solid Earth in the open ocean, although the hum at 20 mHz can only be excited in shallower ocean areas. Therefore, in theory, the excitation of the hum could occur anywhere in the oceans (Tanimoto 2005). However, observational studies for the excitation sources of the hum seem to indicate the potential source areas are close to the coasts (Bromirski and Gerstoft 2009; Ermert et al. 2017; Harmon et al. 2012). It is generally thought that the generation of low-frequency ocean infragravity waves preferentially occur in shallow oceans close to the coasts but we still do not have a clear understanding of this process (Ardhuin et al. 2014; Aucan and Ardhuin 2013; Dolenc et al. 2008; Herbers et al. 1995; Uchiyama and McWilliams 2008; Rawat et al. 2014).
Eigenfunctions of ocean-wave modes for PREM. U is the vertical function and V is the horizontal function of modes. At 0.02 Hz (20.05 mHz), U and V are equal, showing the typical circular particle motion of ocean gravity waves. At 0.003 Hz (left) and 0.010 Hz (middle), they have non-zero values at the ocean bottom. Any topographic deviation from a layered medium can cause scattering and generate Rayleigh waves at the same frequencies. Solid lines are for PREM (elastic model) and dashed lines are for the rigid ocean bottom model
Based on these developments, the cause of the hum is now generally considered to be in the ocean. However, there may be an exception at low frequencies, especially below 5 mHz (Nishida 2017). First of all, even though we stated that the low-frequency end of the hum is 3 mHz, the background noise, caused by atmospheric processes, increases toward lower frequency (Fig. 1) and precludes its definitive determination. This feature may be masking the background oscillation signals (Fig. 5) and if so, the lower frequency limit of 3 mHz is not certain. We note that Nawa et al. (1998) reported very low-frequency modes in their analysis for the background oscillations (hum). Although it seems to be the only paper to show such results, if their observations were true, the atmospheric process seems to be a serious candidate for the excitation of such a low-frequency part of the hum, because there is much more background energy in the atmosphere than in the oceans at low frequencies.
2.4 A unified view for the excitation of the microseisms and the hum
Ardhuin et al. (2015) claimed, following Hasselmann (1963), that there are two types of seismic-noise excitation by ocean waves. One is by the direct interaction between ocean waves and the solid Earth and the other is by the wave–wave interaction among ocean waves. The hum and the primary microseism are examples of the direct interaction and the secondary microseism is an example of the wave–wave interaction. Similar arguments were essentially made by Nishida and Fukao (2007), Nishida et al. (2008), Fukao et al. (2010), and Saito (2010). They also discussed the excitation mechanism of Love waves in the hum, caused by the interactions between propagating oceanic infragravity waves and the solid Earth through the ocean-floor topography. Both the excitation of Rayleigh and Love waves may be explained by this process.
An alternative excitation mechanism for the hum similar to the wave–wave interaction was proposed by Webb (2008) and was also analyzed by Tanimoto (2010). The reason that this process was proposed was that the excitation due to a collision of low-frequency ocean waves could become large for frequencies below 5 mHz. At such low frequencies, horizontal components of ocean-wave eigenfunctions become like that of Tsunami waves (modes) and have large amplitudes from the surface to the ocean floor. But this mechanism should create at least two spectral peaks, one corresponding to the frequency of ocean waves and the other being its double-frequency peak, as this process is a low-frequency version of the wave–wave interaction. Such a double-frequency feature has not been identified in observed data for the hum. It appears that the direct interaction is a better mechanism to explain the excitation of the hum, especially because it can also explain the excitation of Love waves that have been observed (Kurrle and Widmer-Schnidrig 2008).
