Modeling tilt noise caused by atmospheric processes at long periods for several horizontal seismometers at BFO - a reprise

Author(s):  
W Zürn ◽  
T Forbriger ◽  
R Widmer-Schnidrig ◽  
P Duffner ◽  
A T Ringler

Summary Tilting of the ground due to loading by the variable atmosphere is known to corrupt very long-period horizontal seismic records (below 10 mHz) even at the quietest stations. At BFO (Black Forest Observatory, SW-Germany) the opportunity arose to study these disturbances on a variety of simultaneously operated state-of-the-art broadband sensors. A series of time windows with clear atmospherically caused effects was selected and attempts were made to model these “signals” in a deterministic way. This was done by simultaneously least squares fitting the locally recorded barometric pressure and its Hilbert transform to the ground accelerations in a bandpass between 100 and 3600 s periods. Variance reductions of up to 97 per cent were obtained. We show our results by combining the “specific pressure induced accelerations” for the two horizontal components of the same sensor as vectors on a horizontal plane, one for direct pressure and one for its Hilbert transform. It turned out that at BFO the direct pressure effects are large, strongly position dependent, and largely independent of atmospheric events for instruments installed on piers, while three posthole sensors are only slightly affected. The infamous “cavity effects” are invoked to be responsible for these large effects on the pier sensors. On the other hand, in the majority of cases all sensors showed very similar magnitudes and directions for the vectors obtained for the regression with the Hilbert transform, but highly variable from event to event especially in direction. Therefore this direction most certainly has to do with the gradient of the pressure field moving over the station which causes a larger scale deformation of the crust. The observations are very consistent with these two fundamental mechanisms of how fluctuations of atmospheric surface pressure causes tilt noise. The results provide a sound basis for further improvements of the models for these mechanisms. The methods used here can already help to reduce atmospherically induced noise in long period horizontal seismic records .

2020 ◽  
Vol 223 (1) ◽  
pp. 676-691
Author(s):  
A C B Alejandro ◽  
A T Ringler ◽  
D C Wilson ◽  
R E Anthony ◽  
S V Moore

SUMMARY Variations in atmospheric pressure have long been known to introduce noise in long-period (>10 s) seismic records. This noise can overwhelm signals of interest such as normal modes and surface waves. Generally, this noise is most pronounced on the horizontal components where it arises due to tilting of the seismometer in response to changes in atmospheric pressure. Several studies have suggested methodologies for correcting unwanted pressure-induced noise using collocated microbarograph records. However, how applicable these corrections are to varying geologic settings and installation types (e.g. vault versus post-hole) is unclear. Using coefficients obtained by solving for the residuals of these corrections, we can empirically determine the sensitivity of instruments in a specific location to the influences of pressure. To better understand how long-period, pressure-induced noise changes with time and emplacement, we examine horizontal seismic records along with barometric pressure at five different Global Seismographic Network stations, all with multiple broadband seismometers. We also analyse three Streckeisen STS-2 broadband seismometers, which are collocated with a microbarograph, at the Albuquerque Seismological Laboratory. We observe periods of high magnitude-squared-coherence (γ2-coherence; γ2 > 0.8) between the seismic and pressure signals which fluctuate through time, frequency, and even between seismic instruments in the same vault. These observations suggest that these tilt-generated signals are highly sensitive to very local (<10 m) site effects. However, we find that in cases where instruments are not located at a large depth (<100 m), the pressure-induced noise is polarized in a nearly constant direction that is consistent with local topographic features or the geometry of the vault. We also find that borehole instruments at a large depth (>100 m) appear to be unaffected by pressure-loading mechanisms outlined by Sorrells (1971) but possibly by Newtonian attraction. Correlating the induced-noise polarization direction with times of high coherence, we work to identify sensors that are ultimately limited by pressure-induced horizontal noise as well as period bands that can benefit from pressure corrections. We find that while the situation is complex, each sensor appears to have its own unique response to pressure. Our findings suggest that we can determine empirical relationships between pressure and induced tilt on a case by case basis.


2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.


Author(s):  
Jiapeng Liu ◽  
Ting Hei Wan ◽  
Francesco Ciucci

<p>Electrochemical impedance spectroscopy (EIS) is one of the most widely used experimental tools in electrochemistry and has applications ranging from energy storage and power generation to medicine. Considering the broad applicability of the EIS technique, it is critical to validate the EIS data against the Hilbert transform (HT) or, equivalently, the Kramers–Kronig relations. These mathematical relations allow one to assess the self-consistency of obtained spectra. However, the use of validation tests is still uncommon. In the present article, we aim at bridging this gap by reformulating the HT under a Bayesian framework. In particular, we developed the Bayesian Hilbert transform (BHT) method that interprets the HT probabilistic. Leveraging the BHT, we proposed several scores that provide quick metrics for the evaluation of the EIS data quality.<br></p>


Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 65
Author(s):  
Benjamin Akers ◽  
Tony Liu ◽  
Jonah Reeger

A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on R, the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, simulation costs, convergence rates, and generalizations of this method are all discussed.


2015 ◽  
Vol 2015 ◽  
pp. 1-3 ◽  
Author(s):  
Ming-Chi Lu ◽  
Hsing-Chung Ho ◽  
Chen-An Chan ◽  
Chia-Ju Liu ◽  
Jiann-Shing Lih ◽  
...  

We investigate the interplay between phase synchronization and amplitude synchronization in nonlinear dynamical systems. It is numerically found that phase synchronization intends to be established earlier than amplitude synchronization. Nevertheless, amplitude synchronization (or the state with large correlation between the amplitudes) is crucial for the maintenance of a high correlation between two time series. A breakdown of high correlation in amplitudes will lead to a desynchronization of two time series. It is shown that these unique features are caused essentially by the Hilbert transform. This leads to a deep concern and criticism on the current usage of phase synchronization.


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