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Seismic Arrays

Applications of seismological arrays in the study of the interior of the earth enabled detection of weak seismic signals, which are otherwise below the detection threshold of single seismographs. Though arrays were basically developed for, and funded by, programs for monitoring underground nuclear explosions for developing seismic, these have greatly contributed towards the detailed studies of the seismic velocity structure, particularly in studying the velocity gradients in the earth’s interior. Arrays consist of a number of seismographs distributed over an area, from which seismic signals are recorded along with a common time base. The records from the different seismographs are then combined together to obtain a processed record, in which the signal to noise ratio is higher than in any of the single seismographs.

Signal to noise ratio improvement in the processed output of an array results from the fact that when the outputs from all the sensors (seismometers) of the array are added, with proper time shifts, the signal is added in phase whereas the noise is added out of phase. The improvement in the signal to noise ratio depends on the propagation characteristics of the noise as well as the signal across the array. The basic objective in array processing is, thus, to determine the time shifts that produce the desired improvement in the signal to noise ratio, and then to apply these to the various sensor outputs to produce the maximum signal to noise ratio. In the process sensors of the array are also assigned weights so that better quality records are given greater importance. The process of adding the array outputs with proper time shifts (and weights) is  called beam forming[1],[2].  For a monochromatic signal traveling across an array with an apparent velocity V_a the phase shift at a sensor location characterized by the coordinates (R_m, a_m) – where R_m   is its radial distance from the origin of the coordinate system and a_m is its angle from the initial line – may be written as:

b_m  = 2pR_mCos(q-a_m)/lV_a

Here l is the apparent wavelength of the signal and q is the azimuth (angle measured anticlockwise from north) of its source. The relative arrival times of the signal at the m^th sensor are, then, given by:

t_m = R_m. k₀/f

In this f is the frequency of the signal and k₀ is a vector pointing in the direction of the incoming signal wave front. The arrival of a seismic signal wave front and the location of the sensor characterized by (R_m,a_m)  is illustrated in the figure below. The phased output of the array at the nth point, in a digitized set of N seismic signals is given by:

O(n) =S I_m (n + j_m)   ,  m=1,2,3,…..N

In this I_m is the digitized seismic signal at the ith sensor and t_m=jm.Dt, Dt being the sampling interval for digitization of the signal traces.  The results of array processing are illustrated in the following pages in tabular and graphic forms. The computer program, which contains the basic array processing subroutines and generates synthetic data, is given in Appendix-1. In array processing dt/dD is quite often referred to as slowness – measured in seconds per degree (thus, inverse of velocity). Azimuth is the angle which the direction of the incoming signal makes with the direction of the north with respect to the center point (origin) of the array.  

In this table the slowness varies from 13.0 seconds/degree to 9.1 seconds per degree in steps of 0.3 seconds/degree. The azimuth varies from 110.0 degrees to 130.0 degrees (from the top downwards). Each of the other entries in the table shows the summed array output (normalized to 100) for the block of data in which the signal is present. It can be seen that the array output shows two peaks (marked in bold face). These correspond to two signals at 120 degrees azimuth:  one with slowness of 11.5 seconds per degree and the other at slowness of 10.3 seconds per degree.

Birtill, J. W. and F. E. Whiteway (1965). The Applications of Phased Arrays to Analysis of Seismic Body Waves. Phil. Trans., A 258, 421-493.

Green, P.E. Jr., E. J.Kelly,Jr and M. J. Levin (1966). A comparison of Seismic Array Processing Methods. Geophys. J.R. Astr. Soc. Vol. 11, pp 67-84

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