A theory of spectral analysis based on the characteristic property of a linear dynamic system

Kumazawa, Mineo; Imanishi, Yuichi; Fukao, Yoshio; Furumoto, Muneyoshi; Yamamoto, Akihiko

doi:10.1111/j.1365-246x.1990.tb05574.x

Cited by 91 publications

(69 citation statements)

References 19 publications

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“…In addition, analysis of the complex frequencies of selected LP events is consistent with a steam-filled crack. We applied the Sompi method [Kumazawa et al, 1990] to the source time function of our model crack and found growth rates for our dominant frequency that are consistent with low Q values of 10 -20. Such high attenuation can be attributed to bubbly magma, bubbly water, or steam [e.g., Kumagai and Chouet, 2000;Kumagai et al, 2005].…”

Section: Source Processmentioning

confidence: 99%

Eruption dynamics at Mount St. Helens imaged from broadband seismic waveforms: Interaction of the shallow magmatic and hydrothermal systems

2008

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[1] The current eruption at Mount St. Helens is characterized by dome building and shallow, repetitive, long-period (LP) earthquakes. Waveform cross-correlation reveals remarkable similarity for a majority of the earthquakes over periods of several weeks. Stacked spectra of these events display multiple peaks between 0.5 and 2 Hz that are common to most stations. Lower-amplitude very-long-period (VLP) events commonly accompany the LP events. We model the source mechanisms of LP and VLP events in the 0.5-4 s and 8-40 s bands, respectively, using data recorded in July 2005 with a 19-station temporary broadband network. The source mechanism of the LP events includes: 1) a volumetric component modeled as resonance of a gently NNW-dipping, steam-filled crack located directly beneath the actively extruding part of the new dome and within 100 m of the crater floor and 2) a vertical single force attributed to movement of the overlying dome. The VLP source, which also includes volumetric and single-force components, is 250 m deeper and NNW of the LP source, at the SW edge of the 1980s lava dome. The volumetric component points to the compression and expansion of a shallow, magmafilled sill, which is subparallel to the hydrothermal crack imaged at the LP source, coupled with a smaller component of expansion and compression of a dike. The single-force components are due to mass advection in the magma conduit. The location, geometry and timing of the sources suggest the VLP and LP events are caused by perturbations of a common crack system.

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Section: Source Processmentioning

confidence: 99%

Eruption dynamics at Mount St. Helens imaged from broadband seismic waveforms: Interaction of the shallow magmatic and hydrothermal systems

2008

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“…(64) with observed noise can be reduced to an autoregressive (AR)-type model of the extended Prony method or Sompi method (Kay and Marple, 1981;Kumazawa et al, 1990). These methods are useful in decomposing the transfer function with weak decay, such as in Fig.…”

Section: Discussionmentioning

confidence: 99%

Transfer function measured by electromagnetic sounding with an accurately controlled signal

Yokoyama¹,

Kumazawa²,

Nakajima³

2014

Earth Planet Sp

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We present the fundamentals of an electromagnetic sounding with an accurately controlled source signal. In this method, the tensor transfer function between transmitted and received vector electromagnetic fields is measured. We formulated the transfer function by introducing a ray model that describes the propagation of the general electromagnetic field in the whole frequency region. The transfer function includes information of the underground structure: electromagnetic parameters, propagation distance, and boundary planes. The information of the electromagnetic parameters and the propagation distance is commonly described in all the tensor elements. It is in a form of complex functions of frequency. The information concerning the boundary planes is described as real coefficients of the complex functions. The coefficients are different for each of the tensor elements. When we use an accurately controlled signal, we can estimate the information as a linear inversion problem. A profile of the transfer function varies with the frequency region: it decays rapidly in the low-frequency region and oscillates in the high-frequency region. Such a profile can be explained by the approximate form of the transfer function: a sum of complex exponential functions in a narrow frequency band. The approximate form also provides a good model for data decomposition.

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“…The coefficients of the AR filter are obtained by solving the modified YuleWalker equation (Marple, 1987) and the coefficients of the MA filter can be estimated using the Durbin method (Kay, 1981;Mars et al, 2004). Alternatively, in the Sompi method, the AR coefficients are obtained by an eigen decomposition of the autocorrelation matrix (Fukao and Suda, 1989;Hori et al, 1989;Kumazawa et al, 1990). The filters obtained from the autocorrelation are minimum phase.…”

Section: Methodsmentioning

confidence: 99%

Automatic estimation of optimal autoregressive filters for the analysis of volcanic seismic activity

Lesage

2008

Nat. Hazards Earth Syst. Sci.

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Abstract. Long-period (LP) events observed on volcanoes provide important information for volcano monitoring and for studying the physical processes in magmatic and hydrothermal systems. Of all the methods used to analyse this kind of seismicity, autoregressive (AR) modelling is particularly valuable, as it produces precise estimations of the frequencies and quality factors of the spectral peaks that are generated by resonance effects at seismic sources and, via deconvolution of the observed record, it allows the excitation function of the resonator to be determined. However, with AR modelling methods it is difficult to determine the order of the AR filter that will yield the best model of the signal. This note presents an algorithm to overcome this problem, together with some examples of applications. The approach described uses the kurtosis (fourth order cumulant) of the deconvolved signal to provide an objective criterion for selecting the filter order. This approach allows the partial automation of the AR analysis and thus provides interesting possibilities for improving volcano monitoring methods.

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A theory of spectral analysis based on the characteristic property of a linear dynamic system

Cited by 91 publications

References 19 publications

Eruption dynamics at Mount St. Helens imaged from broadband seismic waveforms: Interaction of the shallow magmatic and hydrothermal systems

Eruption dynamics at Mount St. Helens imaged from broadband seismic waveforms: Interaction of the shallow magmatic and hydrothermal systems

Transfer function measured by electromagnetic sounding with an accurately controlled signal

Automatic estimation of optimal autoregressive filters for the analysis of volcanic seismic activity

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