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Harmonic tremor

Harmonic tremor is a distinctive type of volcanic seismicity characterized by a sustained, continuous seismic signal with a narrow-band spectrum featuring a fundamental frequency and its harmonics, typically ranging from 0.1 to 7 Hz, resulting from resonance or oscillatory fluid movement—such as magma or gas—in a volcano's conduit system.^[1]^[2] This phenomenon differs from discrete earthquakes by its emergent onset and prolonged duration, often lasting minutes to days or longer, and is commonly detected through seismic networks as low-amplitude ground vibrations that can sometimes be felt by humans near eruption sites.^[3]^[1] Observed since the early 20th century, harmonic tremor has been documented at diverse volcanoes worldwide, including Kīlauea in Hawaii, Mount St. Helens in the U.S., and Santiaguito in Guatemala, where it frequently precedes or accompanies eruptive activity by hours to days.^[1] Its wavefield properties typically include dominant Rayleigh and Love surface waves at shallow depths, with the signal's monochromatic nature—exhibiting sharp spectral peaks—distinguishing it from broadband volcanic tremor.^[1] Proposed source mechanisms emphasize fluid dynamics, such as resonance in fluid-filled cracks, gas slug ascent, or pressure perturbations in plugged conduits, which generate standing waves as magma advances.^[2]^[1] In volcanic monitoring, harmonic tremor serves as a critical indicator of subsurface magma migration and eruption onset, enabling short-term forecasting when integrated with geodetic and gas emission data; for instance, during the 2018 eruption of Mount Veniaminof, Alaska, it correlated directly with lava effusion and explosive phases.^[2] While its exact excitation can vary by volcanic setting—ranging from basaltic Hawaiian-style eruptions to more silicic systems—harmonic tremor underscores the role of multiphase fluid interactions in driving unrest, informing hazard assessments at observatories like the U.S. Geological Survey's Hawaiian Volcano Observatory.^[1]^[3]

Definition and Characteristics

Definition

Harmonic tremor is a type of volcanic seismicity defined as a sustained, continuous release of seismic energy, often lasting from minutes to months, that is primarily associated with the underground movement of magma or fluids in volcanic systems.^[4]^[5] This form of tremor contrasts with discrete earthquakes by its prolonged, rhythmic nature, representing a persistent vibration rather than impulsive energy release. Unlike broadband or stochastic nonharmonic tremor, which exhibits a relatively flat or irregular power spectrum, harmonic tremor is distinguished by its spectral signature: a prominent fundamental frequency accompanied by multiple evenly spaced overtones at integer multiples of that fundamental.^[6] The fundamental frequency typically ranges from 0.1 to 7 Hz, producing a narrowband signal that can sometimes extend into acoustic or infrasonic domains.^[1] Such signals are typically recorded beneath active volcanoes during periods of magma ascent or fluid migration through the crust, serving as an indicator of subsurface unrest.^[4] Although predominantly a volcanic phenomenon, rare instances of similar harmonic signals have been documented in non-volcanic tectonic environments.^[7]

Spectral Properties

Harmonic tremor signals in the frequency domain are characterized by a power spectrum featuring narrowband peaks at a fundamental frequency f and its integer multiples (harmonics such as $2f, $3f, and higher overtones), distinguishing them from broadband tremor. These peaks typically exhibit decreasing amplitudes with increasing harmonic order, reflecting the attenuation of higher-frequency components in the source excitation or propagation path. For instance, at Popocatépetl volcano, spectra showed a fundamental at 1.93 Hz with harmonics at 3.86 Hz and 5.79 Hz, where higher overtones had progressively lower power.^[6]^[8] A notable variant, gliding harmonic tremor, displays a progressive shift in the fundamental frequency over time while maintaining the harmonic structure, often associated with dynamic changes in the subsurface fluid system. Frequency glides can be upward or downward; for example, during dike intrusions at Kīlauea volcano in 2011, the fundamental shifted upward from ≤1.2 Hz to ≥5.6 Hz over 5 hours before reversing downward to 0.6 Hz over 10 hours. Similar glides from 0.90 Hz to 0.98 Hz were observed in deep tremor beneath Hakone volcano, spanning minutes to hours.^[9]^[10] Amplitude characteristics of harmonic tremor vary with intensity and proximity to the source, starting at low levels akin to microseisms before potentially escalating during heightened activity. Initial amplitudes are often subtle, but intense episodes can produce signals detectable up to 90 km from the volcano, as recorded at Hakone. In strong cases, the tremor may manifest as perceptible ground vibrations near the source, particularly when amplitudes exceed typical seismic noise thresholds.^[10]^[11] Superimposed on the harmonic carrier, harmonic tremor often exhibits quasi-periodic amplitude variations, known as envelope modulation, which can produce beating effects in the signal. These modulations appear as rhythmic fluctuations in the overall signal strength, observed in tremors at Mount Erebus where envelope cross-correlations revealed periodic amplitude changes across stations. Such features highlight the non-stationary nature of the source process.^[12]

Temporal Features

Harmonic tremor episodes exhibit a wide range of durations, typically spanning from minutes to hours during eruptive phases, but extending to days, weeks, or even months in cases of prolonged unrest. For instance, at Mount Spurr in 1992, individual tremor bursts lasted 3.5 hours, while a subsequent episode persisted for 6 days, and at Karkar volcano from 1978 to 1979, tremor activity continued intermittently over 6 months. These durations often feature waxing and waning intensity.^[13] Burst-like episodes of harmonic tremor are characterized by intermittent onsets and offsets, frequently occurring as discrete packets of activity that emerge and subside over short timescales. At Arenal volcano, such bursts last several hours daily, with sharp or smooth transitions marking their start and end, often embedded within broader seismic sequences. These bursts sometimes synchronize with other volcanic signals, such as long-period events, where the coda of a long-period event transitions directly into harmonic tremor, suggesting coupled fluid dynamics.^[14]^[15] The evolutionary patterns of harmonic tremor typically involve initial emergence during periods of volcanic unrest, followed by intensification as activity escalates toward eruption, and abrupt cessation shortly after the event.

Generation Mechanisms

Fluid Resonance Models

Fluid resonance models propose that harmonic tremor arises from the excitation and sustained oscillation of standing acoustic waves within fluid-filled structures in volcanic conduits or cracks, generating characteristic harmonic spectra observed in seismic records. These models treat the tremor source as a resonator where pressure perturbations in a low-viscosity magmatic fluid or gas slug propagate as compressional waves, coupling with the surrounding rock to produce seismic signals.^[16] The organ-pipe resonance model conceptualizes the volcanic conduit as a vertical, fluid-filled pipe open at the top and closed at the bottom, analogous to an organ pipe, where the fundamental frequency f of oscillation is given by f = \frac{c}{2L}, with c as the speed of sound in the fluid (typically 1000–3000 m/s for magma or gas mixtures) and L as the conduit length. For observed fundamental frequencies of 0.5–2 Hz at volcanoes like Kīlauea, this implies conduit lengths of approximately 1–5 km, with higher harmonics appearing as integer multiples if damping is low. This model was developed to explain sustained tremor episodes during the 1963 Kīlauea eruption, where repetitive pressure pulses from gas release or magma movement excite the fundamental mode, leading to observable overtones in the spectrum. In the Helmholtz resonator analogy, the conduit acts as a closed-bottom cavity with a narrow neck, where oscillations are driven by pressure fluctuations from ascending fluid slugs or bubbles collapsing or expanding periodically. The fundamental frequency emerges from the interaction between the cavity volume and the neck's geometry, producing harmonics through nonlinear effects in the fluid dynamics, though higher overtones are often attenuated. This configuration has been applied to interpret tremor at stratovolcanoes with complex plumbing systems, where the resonator volume is estimated from spectral peaks to constrain subsurface structure.^[16] These models share key assumptions, including a low-viscosity fluid (such as basaltic magma or exsolved gas) occupying a cylindrical crack or dike within the edifice, with viscous damping and wall compliance limiting the excitation of higher harmonics beyond the first few overtones. The resonance is passively sustained by intermittent pressure inputs from magma ascent, rather than continuous flow, distinguishing it from other mechanisms. Historically, fluid resonance models emerged in the 1970s–1980s from analyses of tremor data at Hawaiian volcanoes, particularly Kīlauea, where broadband seismic networks revealed consistent harmonic patterns linked to magmatic activity. Seminal work by Chouet in 1985 introduced the organ-pipe framework using pipe acoustics to fit observed frequencies, building on earlier fluid-driven crack ideas from the 1970s. These concepts were refined in the 1980s through theoretical extensions to three-dimensional cracks and supported by laboratory experiments simulating bubble-driven oscillations in fluid conduits, which replicated harmonic spectra under controlled decompression.^[17]

Magma Flow Dynamics

In magma flow dynamics, harmonic tremor arises from the active movement of ascending magma or associated fluids within volcanic conduits, where shear stresses and turbulent eddies generate periodic pressure fluctuations that propagate as nonlinear seismic waves, producing harmonic spectral peaks.^[18] This mechanism contrasts with passive structural resonances by emphasizing the direct role of fluid instabilities in exciting the tremor.^[19] Turbulent flow in viscous magmas, such as andesites, creates eddies that shed at characteristic frequencies, leading to repetitive impulses on conduit walls and nonlinear wave steepening that forms overtones.^[20] The particle impact model posits that collisions between solid fragments, crystals, or bubbles entrained in the ascending magma produce rhythmic seismic energy through repeated wall strikes in the conduit.^[21] In this framework, the dominant frequency f relates to the magma flow velocity v and average particle spacing d via the relation v = f \cdot d, where impacts occur at intervals dictated by the flow regime.^[21] This process is particularly evident in explosive eruptions, where fragmented material enhances the periodicity, though it can persist in effusive settings with bubble clusters acting as effective "particles." Gliding effects in harmonic tremor manifest as accelerating frequency shifts, often upward, driven by increasing magma flow rates or conduit narrowing associated with degassing and crystallization.^[22] As exsolved volatiles reduce magma density and viscosity, ascent accelerates, shortening the effective wavelength of flow instabilities and raising the fundamental frequency from below 1 Hz to over 10 Hz in minutes.^[23] Conduit constriction from wall cooling or degassing-induced foaming further amplifies this glide by increasing shear and turbulence.^[9] Composite triggers involve interactions between ascending magma and geothermal fluids or gas slugs, which modulate tremor in composition-dependent ways across volcanic systems.^[19] In basaltic settings, low-viscosity magmas facilitate rapid gas slug formation and bursting, generating impulsive pressure waves that excite harmonics through conduit-wide oscillations.^[24] Conversely, in andesitic systems, higher viscosity promotes sustained interactions with hydrothermal fluids, where fluid-magma mingling sustains prolonged tremor via coupled buoyancy and shear instabilities.^[25] These dynamics intensify pre-eruptive signals by amplifying flow perturbations.^[26]

Detection and Monitoring

Instrumentation

The primary instruments for recording harmonic tremor are broadband seismometers, which capture low-frequency seismic signals essential for detecting sustained volcanic vibrations. Models such as the Streckeisen STS-2 and Nanometrics Trillium are widely deployed in volcano observatories due to their broad frequency response, typically ranging from 0.01 Hz to 50 Hz, allowing resolution of both long-period tremors and higher-frequency components.^[27]^[28] These sensors have become standard for volcanic monitoring since the mid-1990s, replacing earlier short-period instruments to better record the continuous, low-amplitude nature of harmonic tremor.^[29] Seismic networks are configured as dense arrays around active volcanoes, with station spacings of 3-10 km to ensure adequate coverage and triangulation of tremor sources within 20 km of the vent.^[30]^[31] These arrays often incorporate complementary sensors, such as tiltmeters to measure ground deformation and infrasound microphones to detect acoustic emissions, enabling correlation between seismic and other geophysical signals for improved tremor characterization.^[32]^[33] Real-time data transmission is facilitated by telemetry systems, including GOES satellite links for remote volcanoes, supporting continuous 24/7 monitoring that has been operational since the 1990s.^[30] Challenges in instrumentation include signal masking from environmental factors like wind-generated noise or cultural (human-induced) interference, which can obscure low-frequency tremor signals.^[34]^[35] To mitigate these, site-specific installations are employed, such as burying seismometers in vaults or boreholes 1-2 meters deep to couple sensors to stable bedrock and reduce surficial noise.^[30]^[36]

Analysis Methods

Spectral analysis forms the foundation for processing harmonic tremor signals, enabling the identification of characteristic frequency peaks and their temporal evolution. Short-time Fourier transforms (STFT) are commonly applied to generate spectrograms that reveal the harmonic structure, where fundamental frequencies and overtones appear as distinct ridges, allowing researchers to track phenomena such as gliding—gradual shifts in spectral content indicative of changing source conditions.^[37] Continuous wavelet transforms (CWT) offer an alternative with superior time-frequency resolution for non-stationary signals like tremor, preserving localization properties that STFT may smear due to fixed windowing, thus better resolving overlapping harmonics in broadband volcanic spectra.^[38] Open-source software packages such as ObsPy facilitate these transforms in Python environments, supporting efficient handling of large seismic datasets for real-time or post-processing analysis. Automated detection algorithms enhance the efficiency of identifying harmonic tremor amid continuous seismic recordings, reducing manual effort and enabling comprehensive catalogs. Pitch-detection methods, adapted from audio processing, scan spectrograms for stable harmonic series by estimating fundamental frequencies and checking for integer multiples, successfully applied to datasets from volcanoes like Redoubt, Alaska.^[6] Threshold-based approaches further refine detection by evaluating peak prominence, where overtones must exceed a prominence criterion—such as greater than 3 dB relative to noise—to confirm harmonic structure and distinguish from non-harmonic events like spasmodic tremor.^[6] Machine learning classifiers, including random forests or neural networks trained on spectral features, achieve high accuracy in categorizing harmonic versus non-harmonic seismicity, as demonstrated in deployments at Stromboli volcano using dense networks. Recent deep learning models, such as VOISS-Net, further enhance classification accuracy for harmonic tremor in operational monitoring settings as of 2025.^[39]^[40] Source location techniques leverage seismic arrays to pinpoint tremor origins, crucial for linking signals to subsurface structures. Beamforming methods compute signal coherence across array elements, maximizing output power to estimate azimuth and incidence angles, thereby deriving horizontal and vertical source positions from phase differences.^[41] Migration approaches extend this by back-propagating observed phases to a subsurface grid, identifying high-coherence points as sources, particularly effective for shallow tremors where phase delays indicate depths on the order of hundreds of meters.^[42] Tools like RETREAT implement these in real-time for array data, integrating beamforming with phase analysis to track migrating tremor sources during unrest episodes.^[41] Quantitative metrics derived from harmonic spectra provide insights into source properties, such as conduit geometry and fluid dynamics. The decay of amplitudes with increasing overtone number reflects attenuation mechanisms, including viscous damping in fluid-filled systems.^[43] These ratios, computed from observed peaks, allow inference of conduit radii or viscosities when calibrated against models, as validated in synthetic and field data from fluid resonance scenarios.^[44]

Role in Volcanology

Eruption Precursors

Harmonic tremor often emerges as a key pre-eruptive signal in volcanic systems, typically onsetting from days to weeks prior to explosive eruptions, with durations ranging from 1 to 30 days in many documented cases.^[45] This tremor is characterized by patterns of increasing amplitude, reflecting escalating fluid dynamics within the conduit, and frequency gliding—where spectral peaks shift upward or downward over minutes to hours—indicating acceleration toward eruption.^[22] Such gliding, often upward toward higher frequencies like 30 Hz, signals imminent pressure buildup and has been observed immediately preceding Vulcanian explosions.^[22] These tremor patterns frequently correlate with other geophysical indicators of unrest, such as ground deformation from magma intrusion and elevated gas emissions from degassing, providing a multifaceted view of subsurface changes.^[46] In integrated monitoring frameworks like the USGS Volcano Alert Level system, the detection of harmonic tremor alongside these signals can elevate alert levels from advisory to watch or warning, enhancing public safety measures during unrest phases.^[47] Harmonic tremor's forecasting utility stems from statistical models that link its intensity and duration to eruption magnitude, particularly for events classified as Volcanic Explosivity Index (VEI) 2-4, where tremor amplitude correlates with ejecta volume and explosivity.^[48] Process-based models further incorporate tremor data to predict eruption timing and style by simulating seismicity progression tied to magma ascent.^[49] However, limitations persist, including false positives during non-eruptive unrest episodes, where tremor may indicate fluid movement without leading to surface activity, thus requiring corroboration from multiple datasets to improve reliability.^[50] Since the 1980s, harmonic tremor has been integrated into global volcanic monitoring through programs like the Smithsonian Institution's Global Volcanism Program, which archives tremor observations in weekly reports to track worldwide unrest and refine eruption forecasting protocols.^[51] This long-term data compilation aids in identifying recurring pre-eruptive signatures across diverse volcanic settings.^[52]

Case Studies

During the 2009 eruption of Redoubt Volcano in Alaska, strongly gliding harmonic tremor was prominently observed prior to six nearly consecutive explosive eruptions in March, with the fundamental frequency gliding upward from approximately 2 Hz to 6 Hz over periods of several hours.^[53] This tremor was linked to processes involving partial conduit plugging by growing gas slugs or viscous magma plugs, consistent with resonance mechanisms.^[53] At Lascar Volcano in Chile, persistent low-frequency harmonic tremor with a fundamental frequency near 0.63 Hz and up to 30 overtones was recorded over an 18-hour interval in April 1994, modeled as resonance in fluid-filled cracks within the volcanic edifice.^[19] Similar harmonic tremor activity, characterized by narrow spectral peaks at a fundamental around 1 Hz, occurred intermittently from January to March 1993, preceding the major explosive eruption on 19 April 1993.^[54]^[19] In 2021, deep low-frequency earthquakes and associated tremor signals were detected beneath Hakone Volcano in Japan using data from the Hi-net seismic array, with sources relocated at depths of approximately 10-20 km and exhibiting spectral features indicative of overtones.^[55] These events were linked to magmatic fluid movement contributing to phreatic unrest in the region.^[55] During the 1980s at Kīlauea Volcano in Hawaii, sustained harmonic tremor accompanied episodes of summit inflation, particularly during repose periods between eruptive phases of the Puʻu ʻŌʻō eruption, with tremor amplitudes strong enough to be felt up to 5 km away from the source.^[56]^[57] For instance, in the January-August 1983 east rift eruptions, harmonic tremor persisted at low levels near the eruptive vents while the summit reinflated gradually after deflation events.^[57]

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