An Intelligent System for Seismic Source Localization Ramzi El-khater Computer Science University Of Nevada, Las Vegas
[email protected]
John Istle, Pamela Mandelbaum Computer Science University Of Nevada, Las Vegas
Evangelos Yfantis Computer Science University Of Nevada, Las Vegas
Barbara Luke Civil and Environmental Engineering University Of Nevada, Las Vegas
Abstract In a stationary sensor situation, locating signals arriving from different directions can be achieved by using multiple sensors placed at different locations. Different methods for locating seismic signals using an array of seismometers have been examined. Matched field processing is a method for source localization whereby model fields are calculated and compared to measured data.
1. INTRODUCTION The computer graphics and digital image processing laboratory at UNLV, is conducting research on the processing of seismic data. The data is recorded on three seismometers installed at the Yucca Mountain test site by the engineering and geophysics laboratory at UNLV. A new technique known as Matched Field Processing is being applied to determine the location of seismic events; this will establish the feasibility of remotely identifying rock fall events and other sources of seismic energy. Section 2 of this paper describes software developed at the computer graphics and image processing laboratory for processing seismic data recorded by the seismometers. Section 3 describes a robust method for source bearing estimation and section 4 describes two matched field algorithms that can be used for source localization.
2. BACKGROUND INFORMATION To aid us in our study of seismic signals we have developed an application for reading, graphing and processing seismic data, this section briefly describes this application. The software can read in two file formats, Society of Exploration Geophysicists Y format (SEGY) and Seismic Analysis Code (SAC). The SEGY format contains a 240 byte header followed by the data samples which are either 32-bit floating point, 32-bit integer or16-bit integer. There
are two types of SEGY formats, standard and PASSCAL. The only difference between the two is the arrangement of the 240 byte header. The software can read both and determine what information it needs depending on the type of SEGY file. The other format we use for reading in data is SAC. This format consists of a 632 byte header followed by the data samples in floating point format. It knows what values to expect from certain locations of the header. The software has mathematical tools for the study of the behavior of seismic signals. The data is plotted as a function of time with the time as the x-axis scale and amplitude as the y-axis scale. When a seismic data file is opened initially, the seismic data is plotted as function of time with each value taking up one pixel on the screen, our software gives the user the ability to zoom in and out of the graph in order to view certain parts of the entire file more closely. Also the software allows for graphs of multiple data files to be stacked one underneath another so that they can be easily compared and contrasted to each other. There are two methods for the user to center the data. One method is a very simple one that just subtracts the mean from every sample. Another method we used is similar to pulse code modulation. Each sample is subtracted from the previous sample. The FFT algorithm has been implemented and is used to obtain data in the frequency domain as well as to view the spectrum of a seismic event.
3. DIRECTION OF ARRIVAL DETECTION 3.1 Beamforming In classical beamforming a signal arriving from a certain known bearing θ is isolated from other signals in the presence of background noise. The signal impinges upon an array of sensors, forming the angle θ with the normal to the array. The output of the beam former is as follows: [6]
g(t) = ∑ wn fn(t-τn)
(1)
wn : real-valued amplitude weights for a given θ fn(t): is the signal received at sensor n at time t τn: time it takes for signal to be received at sensor n after being received at n-1 The lag τn between consecutive sensors can be found by: τn= (dn sinθ) / c
know the order in which the signal was picked up by the seismometers, we are able to estimate the angle θ, relative to the array, where the signal is coming from. One method to find θ, given an ordering of the seimometers, is to use Voronois theory. We know that the seismometer closest to the source will pick up the signal first. Voronois theory is illustrated with the following diagram:
(2)
where c is the propagation speed of the wave and dn is distance between two consecutive sensors. Another method of finding τn is by using the crosscorrelation to find the time lag between two sensors, the lag at which the cross-correlation is maximized can be taken to be τn.
a
b
figure - 1
3.2 The Cross-correlation method for finding the time delay
if we take the bisector of a line joining two points a & b, any point in the plane on the same side as point a is closer to a than to b.
The cross-correlation of two signals is given by:
The Voronois diagram for our three seismometers is shown in figure-2. According to Voronois theory any point in the region A is closer to S1 than S2 and closer to S2 than S3, therefore, a signal from region A will be received in the order S1, S2, S3. Also any point in region B is closer to S2 than to S1 and closer to S1 than to S3, so a signal from region B will be received in the order S2, S1, S3. Using a similar argument we can determine the order of seismometers for regions C, D, E and F.
r(i)= ∑N-i f1(t)f2(t+i) / N-I
(3)
f1(t): is data value at channel 1 at time t f2(t): is data value at channel 2 at time t N: is total number of samples i: is the lag value in samples It is well known that, the lag i at which r(i) is maximized can be taken as the time delay between two signals. So in-order to find the delay τn between two consecutive sensors, we perform the cross-correlations for a number of different candidate lag values, and take the lag that gives us the maximum r(i) as the true lag between two sensors. The time delay can be found from the sample delay by dividing by the Sampling Rate (S):
F
S1
A B
S2
τn= i / S
(4)
S: is the sampling rate (samples per second) i: is the lag in samples For our application we used the cross-correlation to find the time delays between our seismometers. The cross-correlation provides us with a more robust and environmentally tolerant method than using the method that relies on the propagation speed of the seismic waves.
E
L
S3
C D
figure – 2 (seismometer Voronois diagram)
3.3 Bearing Estimation
Using the GPS coordinates of our three seismometers we were able to calculate the angle range for θ relative to the bisector L of the line S3,S2 for regions A, B, …,F . The angles θ relative to the ordering of the seismometers are shown in table – 1.
Once we have found the time delays between the different seismometers, we are able to sort them with respect to the time each picks up the signal. Once we
Order of seismometers 1, 2, 3
Arrival Angle Range 0ο
