Analysis of Time Series and Spatial Data Homepage

2008 Student Abstracts

Julien Chaput (11/12 a)

Temporal variability of body wave Green’s functions obtained through cross-correlation of eruption coda on Mount Erebus volcano

The recovery of a medium’s reflection profile, or Green’s function, is one of the most fundamental problems in seismology, and as such there exist various methods for attacking it. One such method in its relative infancy consists of cross-correlating seismic noise, either ambient or coda related, in order to directly recover the green’s function between two spatial points. More robust even is the autocorrelation of waveforms at a single spatial point, which yields the vertical reflection profile beneath that point, given adequate source locations. As this method requires a diffuse seismic wavefield, heavily scattering media are likely to yield better results since the short mean free path means that high frequencies are not attenuated before the wavefield reaches modal equipartition. In this paper I will demonstrate the usefulness of the aptly named seismic interferometry in recovering time varying body wave Green’s functions on Mount Erebus volcano, Antarctica.

Omar Marcillo (11/19 a)

System identification of canopy in response to an infrasonic wave.

An infrasonic wave passing through canopy will be studied to determine the frequency response of the wave to the canopy. The multiple and variable dimensions of canopy (e.g.: leaves, branches) would create a mechanical filter. This study aims to characterize this effect based on pressure measurements. By the use of infrasonic sensors, measurements of pressure will be taken inside and right outside of the canopy to prove this concept. The EMRTC blasts will be used as shock wave source. A comparison of the frequency content of the input and output signal will help us to characterize the system. Depending on the quality of the data,
deconvolution will be performed to calculate the transfer function of this system. This paper will also give a brief introduction on system identification and modeling.

Alisa Shtromberg (11/21 a)

PID Tuning on MROI’s Fringe Tracker Beam Combiner Modulators

The Magdalena Ridge Observatory Interferometer (MROI) will be a 10-element optical interferometer. The Fringe Tracker (FT) will be one of its beam combiner instruments that will be used to track combined beams as fringes are formed and feed back to MROI’s delay line to adjust its position. A set of mirrors that are part of the FT beam combiner will need to be modulated in order to acquire, measure, and track fringes. These modulators will use a piezo controller. Lab testing has been ongoing for the past few months in order to calibrate and test for specifications. This is necessary to meet the FT’s stringent requirements for accuracy and repeatability. A critically damped step response is desired from the modulator impulse signal. Proportional–integral–derivative (PID) tuning is necessary to correct the error between the measured and desired values by calculating and outputting a correction that can adjust the process as necessary. A transfer function of the PID control system is used to optimize the coefficient parameters for the desired response. The frequency domain representation is important for determining the system stability and coefficient tuning. Several existing techniques for PID tuning are explored and results are presented.

Jessica Elias (11/21 b)

Astronomical interferometry: Application and technique of aperture synthesis

Interferometry is an astronomical technique by which the signals from several instruments are combined to simulate an aperture-masked larger telescope. The signal from such an array is then deduced from studying the interference patters from the superposition of the combined waves. The signal is best expressed as a function that can be transformed into the Fourier domain and allows for the deduction of the signal phases. These transformed signals can then be correlated and by scanning through the signal to create an entire picture consisting of these transformed points. The inverse Fourier transform of this signal then restores this image, completing the process of aperture synthesis. I will briefly go over the optical physics of such a process, as well as demonstrate and explain in depth this type of data analysis on a real image.

Kevin Lenth (11/24 a)

The discrete wavelet transform and applications

In many fields that traditionally have made heavy use of discrete Fourier theory, the discrete wavelet transform (DWT) is rapidly replacing or augmenting the DFT as an analysis tool. This is largely because the DFT assumes a signal is periodic, and hence cannot give any information of how it changes over time; in contrast, the DWT provides some idea of the signal's time-evolution. We present a broad view of the DWT and some examples of its applications.

D. Bradly Christensen (11/24 b)

Tau-p transforms and the menacing multiples

The presentation of Tau-p and the Menacing Multiples will focus on my research on the island of Montserrat. Current data processing of the seismic data collected in December 2007 has revealed multiples within the gathers. Because volcanic rocks are difficult to work with, advanced processing will be necessary to pull out the proper reflectors. Deconvolution and f-k filtering have not been successful in the removal of multiples within the data. Because of this a more advanced transform may be needed to remove the menacing multiples from the volcanic data. The presentation will focus on the practical applications of the Tau-p transform and how it is used to remove multiples. The preparation for this presentation will be beneficial to me in understanding how the Tau-p transform works and why it needs to be used when multiples appear and are not easily moved using conventional deconvolution and f-k filtering. Examples will be presented from the SEA-CALIPSO experiment, Dec 2007, showing the effects of the Tau-p transform on multiples.

Maya El Hariri (11/26 a)

Empirical Green’s function method applied to the 2006 Java tsunami earthquake

I will use the Empirical Green’s Function (EGF) method to calculate the source parameters of the 2006 Java tsunami earthquake using a smaller magnitude aftershock (EGF). An earthquake signal in the time domain is the convolution of the earthquake source function with the path traveled, the surface site effects and the instrument response. By deconvolving the EGF from the mainshock the site effects, propagation effects and instrument response are isolated. This yields the relative source time function (RSTF) of the mainshock, which reflects the source characteristics. Deconvolution will be performed by spectral division in the frequency domain by transforming the seismograms from the time to the frequency domain (by Fast Fourier transform) and performing spectral division to obtain the spectral ratios of the source. To obtain the RSTF, the seismograms will be transformed back to the time domain by applying the Inverse Fourier Transform. Using the RSTF several source parameters will be calculated.

Jon Brown (11/26 b)

Specic heat spectroscopy of a simple chain model simulation as a means to investigate the glass transition

Amorphous solid - glasses and polymers have complicated viscoelas tic properties. They have liquid-like and solid-like properties but never go through a thermodynamic state transition into a solid crystalline state. As temperature decreases, their viscosity simply diverges to infinity. The temperature where the material goes from a mostly-solid glassy state to a deformable or soft state is called the glass transition. To investigate this behavior molecular dynamics simulations were run on a simple chain model of a amorphous polymer, while forcing the temperature to vary sinusoidally, for a range of frequencies and mean temperatures. Assuming linear response, storage and loss moduli - measures of storage and dispersion of energy at a given frequency - were computed. The data were fit with standard models, and relaxation properties and glass transition
temperature were computed.

Guohui Wu (12/1 a)

Image processing using the FFT

In the real world, a two-dimensional image is considered to be a function of two real variables, for example, f(x,y) with f as the amplitude (e.g. brightness) of the image at the real coordinate position (x,y). Among many tools to process digital images, I will study image processing using Fast Fourier Transforms (FFTs). First of all, I will discuss thetwo-dimensional FFT followed by the introduction of two kinds of filters. They are lowpass filter and highpass filter. Then, comparisons will be made between lowpass and highpass filters when applied to image processing. Finally, I will write my own MATLAB code and present an example to illustrate the application of FFT in image processing.

Craig Nicholas (12/1 b)

Extracting sheet music from audio files

By an apparently arbitrary decision process, the sheet music corresponding to a musical piece may or may not be in the public domain, even though the information conveyed by the sheet music is, in principle, contained in any audio file of a performance of that work. Restricting our attention to piano music, we develop an algorithm that, within certain parameters, can determine what note(s) are being played at any given moment in a performance of a work for piano. In brief, our algorithm slices a wav file into small segments, performs a Fourier transform on each segment, and uses a modified Karhunen-Loève decomposition on the sequence of transformed slices to circumvent the difficulty associated with the overtones that appear in a straightforward FFT.

Benjamin Dickinson (12/3 a)

Stolt F-K migration; the fourier transform migration method for stacked 2D data

Reflection data can yield inaccurate positions of reflectors and subsurface targets who's precise locations are particularly important in the petroleum industry. The purpose of migration in exploration seismology is to correct distorted and dispersed signals returning from reflectors or diffracting points and develop accurate target locations and depth. The Stolt F-K migration technique offers a fast and effective way to address corrections in complex subsurfaces and dipping layer positions by utilizing the fourier transformation of the wave equation (frequency-domain migration). Within my presentation I plan to explain the fourier transform migration velocity method (Stolt F-K migration), the limitations of the process (constant velocity model) and present further work that can aid in the production of more realistic subsurface models.

Christine Ruhl (12/3 b)

Maximizing the signal-to-noise ratio: Matched filtering

In seismic studies where the source is faint or noisy, it is beneficial to use simultaneous multichannel correlations to reduce the signal-to-noise ratio and bring out repeating signals. The technique of matched filtering involves exploiting the similarities of the unknown, weak signals and known stronger signals in the same area. Beneath Shikoku, Japan, non-volcanic tremor associated with the Nankai trough subducting slab causes low-frequency earthquakes which are ideal for applying matched filtering. This presentation will explore the techniques of matched filtering and use the Nankai trough as an example of an appropriate situation to have used it.

Sonja Behnke (12/5 a)

An analysis of electric field changes during the 2008 eruption of Chaiten, Chile

In May of 2008, the Chilean volcano Chaiten erupted, producing a brilliant display of lightning in the volcanic plume and near the vent. In response, a small Lightning Mapping Array (LMA) and one slow antenna were deployed around Chaiten with hopes of capturing similar electrical activity. The slow antenna, which records the change in electric field, can provide insight into the polarity of a lightning flash. However, there exists 50 Hz noise and associated harmonics in the data, which prevents accurate assessment of the field change. This periodic noise will be removed using an appropriate notch filter implemented in MATLAB. The effects of this on the amplitude and timing of the field changes will be discussed. The field changes in the slow antenna data will then be compared with VHF signals from discharges near the vent as recorded by the LMA to provide a characterization of the type of lightning occurring near the vent.

Michael Jew (12/5 b)

Kalman filters: A method for estimating position

Particularly in robotics, accurate knowledge of the position, velocity, orientation, and other aspects of the robot relative to a known position and direction is very important. Without knowing where the robot is located and where it is going, any sort of autonomous control system will not be able to function. The GPS system is an useful tool that can give position and velocity information. However, the GPS system is only as accurate as the 1 second updates from the satellites. The infrequency of the GPS updates leds to the robot's control system be unable to quickly respond to changing conditions. To solve this problem, an inertial system that gives more frequency data is included. By applying a Kalman filter to the inertial system, the robot can then predict its position and velocity often enough for a control alogrithm to make corrections.

Kyle Jones (12/8 a)

The effects of filtering on cross-correlation and infrasound event location

Local to regional arrival times from infrasonic sources are a good way to determine where volcanic events are occurring. Infrasound locations can be far more accurate and precise than seismic locations because the Green’s functions (impulse responses) for waves traveling through the atmosphere are typically much simpler than for waves traveling through the solid Earth and because the acoustic velocities are relatively slow. However, a big problem with some infrasound data arises from uncorrelated wind noise. This noise can make it very difficult to accurately locate event sources.
I will generate synthetic infrasound signals and add noise (white, red, etc). I will use different filters to try to bring out the signal again. Once the signal is isolated I will cross-correlate signals to obtain relative lag times that I can then use to estimate event locations and associated errors. Which filter is chosen will affect the location estimate. This occurs because the filter affects the correlation of the noisy data, and thus affects the arrival time and location estimate. I would like to use this as a sensitivity study to be included in my thesis so that I understand critical effects of filtering that I will be doing on my data and thus make sure that my locations are as accurate or justifiable as possible.

Amanda North (12/8 b)

Name that sound

Television is continuously bombarding society with programs that take the everyday police work and show how it evolves leaps and bounds scientically. Reality shows give the "Average Joe" a slight insight into how the most complicated of cases can be solved by using simple lab techniques to catch a criminal. One technique that is used by many government organizations to catch criminals before they commit a crime, is to use sound identication and pinpoint a suspect based upon audio. This is better known as voice recognition. In my project I will set up a database of sounds, or English phonemes, and create a training set with which to compare other speakers. I write a MATLAB program that will digitally process each phoneme, take the fast Fourier transform of the signal, and use a power density spectrum to plot and store the coefficients of the training set. The next step is to record several other people saying the training set of sounds, and see if the program can predict what sound is being said by comparing the coefficients from the original training set to those of the speaker. This predictive code has potential in many areas and will incorporate several concepts that have been presented in the Time Series course material.

Richard Sanderson (12/10 a)

Comparing absolute times of the onsets of different signal phases

Seismic signals generated at volcanoes often contain a range of frequencies which vary depending on the type of source process generating them. The seismic signals generated by explosive processes at Santiaguito volcano, Guatemala, contain both long-period (LP) frequency components> (0.125 – 5 Hz) as well as very-long-period components (0.05-0.125 Hz). In order to identify changes in explosive source processes one can compare the onset times of the LP and VLP signals. However, the application of band-pass filters to isolate these frequency bands can introduce> undesired artifacts into the signals which make the comparison of absolute onset times more challenging. Such artifacts may include amongst others, large transients, precursory “ringing”, phase delays and group delays. Other complicating factors include a low signal to noise ratio. This work will focus on finding the optimal way to compare the absolute onsets of VLP and LP components of seismic signals at Santiaguito by investigating the effects of different IIR and FIR filtering techniques performable with MATLAB while considering both stability and computational efficiency.

Pamela Moyer (12/10 b)

From coda envelopes to apparent stress: processing seismic data for source spectra analysis

Using coda waves to determine seismic source spectra is a complex but widely used process for making consistent and reliable magnitude estimations. Coda waves are manipulated to obtain frequency envelopes that calculate and average energy dissipated by an event. Once corrections are made for site and path effects as well as the instrument transfer function, the corner frequencies and seismic moment of an event may be determined. Using data from stations that were deployed to Costa Rica during the Fall of 1999, the process of coda wave manipulation for source spectra analysis, and the steps leading up to an apparent stress calculation from the seismic moment, are discussed.

Sandra Saldana (12/12 a)

What exactly is vibroseis correlation?

Vibroseis sources have been used by industry for many years. This non-impulsive seismic source utilizes a metal plate coupled to the ground to input a sweep of pre-programmed frequencies into the ground. The response is then detected by seismometers set out at regular intervals from the source. What is detected, however, is not actually usuable data but must be correlated in order extract the frequency response of the Earth. The process of correlation is called vibroseis correlation and is key to using vibroseis data. The process of vibroseis correlation and why it works is disected and presented in order understand how digital signal processing can be used to reduce noise and improve signal to noise in order to produce clear seismic reflection cross-sections of the Earth.

The first balloon-borne slow antenna capable of measuring all three vector components of field change
was launched from Langmuir Laboratory during the summer of 2004. The high frequency noise involved in the sounding
data significantly prevents the accurate acquisition of field change, which is essential for the estimation of charge
transferred to the ground by individual strokes, as well as the source locations. After the Fourier analysis of the noise
and recorded data associated with lightning strokes, the low pass filter function in MATLAB is applied to reduce the influence of
noise, and the intrinsic defect of this procedure is analyzed. The positions of charge sources inferred from the optimized field
data are compared with LMA mapping observation results.

Solution of deconvolution via Tikhonov regularization

By deconvolution we mean the solution of a linear first-kind integral
equation with a convolution-type kernel, i.e., a kernel that depends only
on the difference between the two independent variables. Beacuase
deconvolution is sensitive to noise and subject to instabilities, its
treatment often requires the use of regularization methods. The aid of
this presetation is to show how to use a Tikhonov regularization method to
solve the develution problem.

There are times when it is necessary to compare seismic records from
different instruments. In order to do this comparison it is necessary to
simulate the other instrument. I will explore the methods used to make on
instrument look like another, as well as the problems associated with such
a simulation.

Normally, sampling of an analog signal must be done at sufficient speed to
avoid aliasing. Due to the effects of the interstellar medium (ISM) on
radio pulsar signals, intentionally aliased signals can be used to obtain
wider bandwidth signals than the sampling speed can allow. I will give
background on pulsars, particularly on the ISM propogation effects, and
discuss a method for removing the aliasing effects from the recorded
signal.

Techniques on reconstruction of non-uniformly sampled data'.

Due to the economical and other restrains on seismic data acquisition, the
resulting data is incomplete and aliased. There are several algorithms on
how to optimize these data sets, such as the Gulunay's algorithm,
non-uniform DFT, non-unifort FFT and the FRSI algorithm. However, some of
these algorithms have large drawbacks. For example, the Gulunay's method
does not work on non-uniformly sampled data, and the Fourier transforms
have problems with aliasing. It seems optimal to combine some of these
algorithms together to get results without gaps and aliasing.

Seismic arrays can be used to suppress noise. In this project, I am going to introduce the feature of recordings from such stations,
which is that they allow weak signals to be enhanced above noise. Then how this aids in the interpretaion of seismograms and studies of
source mechanisms particularly for test ban seismology in distinguishing between earthquakes and explosions will be concerned.

Analysis of Time Series and Spatial Data (Geophysics 505/Math 587)