seismic signal processing

seismic signal processing For many years, seismograms consisted only of a paper record of the trace drawn by a pen or light-beam. This trace was an analogue record of the motion of the Earth at that point. That total motion consisted of more than the seismic signals which were of interest, but little could be done to separate interfering motions (i. e. noise) from the signal. As the computer revolution unfolded, seismology experienced a digital revolution. As a result, voltage variations from the seismometer that represent the ground motion could be fed into an electronic device called an analogue to digital converter, and the seismogram became a sequence of numbers which represented the amplitude of the ground motion sampled at some constant time interval, often a few milliseconds. This digital record, the signal, is a time series and is ideally suited for mathematical procedures which improve its utility. These procedures are generally known as signal processing, or conditioning, and are quite varied and sometimes complex. The digital revolution occurred first in the seismic reflection industry, which focuses on the exploration for hydrocarbons. Later, earthquake seismographs were developed that recorded digitally, and today virtually all modern seismic recordings are digital and thus involve some sort of signal processing. A simple example of seismic signal processing occurs in engineering and environmental applications when a hammer is used as a seismic source. An individual impact of the hammer is too weak to provide a signal strong enough to be useful. However, a usable record can be obtained by a simple signal processing scheme, which begins by storing the digital signal from the first impact in the memory of the computer which is part of the recording system. The digital record that represents each subsequent impact is first summed with the record in the memory, and the sum is then stored as the new record. The instrument operator examines each sum, and the process continues until a suitable record is obtained. At the other end of the spectrum of complexity, there are three-dimensional seismic reflection surveys where each seismic trace in the resulting ultimate image represents tens of thousands of individual seismic signals which have been summed in a variety of complex processes. The signal processing effort required to produce a good three-dimensional image in fact rivals the intensive field effort required to collect the actual data.

The most basic goal of seismic signal processing can be expressed simply as increasing the signal to noise (S/N) ratio. Noise is simply any ground motion which is not of interest. In digital terms, S/N is just the ratio of the number representing the amplitude of the signal to the number representing the amplitude of the noise. Another basic goal of signal processing is to increase resolution, which is the ability to recognize individual reflected or refracted seismic waves (see seismic exploration methods) as distinct arrivals or wavelets. Processing techniques that address this issue try to make the individual wavelets as compact as possible and to remove interfering waves which have travelled from the source to the receiver (seismograph) along any indirect path. In seismic reflection studies, a process called migration is usually the most complex processing step. Here the goal is to unravel the effects of complex subsurface structures and, in essence, sharpen the focus of the image which is the ultimate product of the processing effort.

Seismic signal processing is a complex subject, and processing of modern seismic reflection surveys is one of the most sophisticated and intensive computer applications that exists. However, a relatively small number of basic principles form the basis of most processing operations. Perhaps the most basic consideration is the application of Fourier analysis (named after J. B. J. Fourier, a prominent French mathematician). This common mathematical tool is very useful in seismic signal processing and has been the driving force behind many advances in this field. When viewed as a relationship between amplitude and time, a seismogram is a well-behaved mathematical function. Thus, a seismogram can be represented as the sum of a series of time-shifted sine waves with varying frequencies and amplitudes. If one chooses enough different sine waves (frequencies), their sum approximates the seismogram to an arbitrary degree of precision. When one views the seismogram in terms of the relative amplitudes (amplitude spectra) and time shifts (phase spectra) as a function of frequency (Fig. 1), one is analysing the frequency domain representation of the signal. This representation is obtained through a mathematical process called the Fourier transform, and it is a very intuitive way of representing the signal for many applications. For example, frequency filtering becomes simply a process wherein the desired frequencies are retained (i. e. multiplied by 1 in the frequency domain) and the undesired frequencies are multiplied by zero. After doing these multiplications, an inverse Fourier transform provides the seismogram with the undesired frequencies removed (Fig. 1).

When high frequencies are undesired, one employs a low-pass filter. A high-pass filter attenuates low frequencies, and a range of frequencies is passed by a band-pass filter. Modern seismic studies usually place a premium on obtaining broad-band data, which refers to the frequency domain where the desired signal would contain a broad range of frequencies. A broad-band signal has numerous advantages, including superior resolution. This fact can be illustrated by looking at the opposite extreme, which is a single sine wave containing, by definition, only one frequency and which is thus narrow band. A sine wave travelling through the Earth would be reflected and refracted, producing a sinusoidal seismogram on which no distinct arrivals could be recognized. This lack of resolution is the opposite of what is desired.

Another basic principal of signal processing is that of the linear system. Once the seismic wave has been generated at the source, a linear system allows one to model mathematically the processes that represent modifications of the wave as simple operations called convolutions. The main processes are the effects of travel through the Earth and the effects of the response of the seismograph system. These operations are independent of the order in which they are applied in both the frequency domain or the time domain. Often the goal of the seismologist is to model the response of the Earth by calculating seismograms that match those observed (see synthetic seismograms). By using the linear system concept, the seismic source and the response of the recording system can be separated from the response of the Earth so that it can be modelled.

A final basic concept is the stacking (summing) of seismograms to produce a result in which the S/N ratio is improved. The idea is that a signal of a given amplitude can be obtained by recording one big seismic source or many smaller ones and summing the results. The simple summing of a series of weak signals from a single source location at one receiver location is one example. Another is common mid-point (CMP) stacking, which was invented by the seismic reflection industry in the 1960s and is illustrated in Fig. 2. Here, seismic reflections travelling along different ray paths but sharing a common mid-point between a series of sources and receivers are analysed. These arrivals are not aligned in time initially. They can be aligned after making time shifts based on determining an average velocity of the material above the reflector. When then summed, a great improvement in data quality (better S/N) is attained. In modern reflection surveys, it is not uncommon to obtain over 200 seismograms that share the same CMP. The S/N ratio improves with approximately the square root of the number of traces. For example, 16 traces must be summed to obtain a fourfold increase in S/N.

The seismic signal processing procedures employed by the seismic reflection industry are by far the most complex of any seismological technique. However, two of the basic steps are common in most applications. The first is simply bookkeeping, in which computer files representing seismograms must be organized so that it is clear when and where they were recorded. Getting the data into a standard format that is easily recognized is also part of this procedure. This step is not as trivial as it seems when one realizes that hundreds of seismographs and seismic sources spread over large distances may be involved. The second step is harder to generalize, but would include some basic filtering, a first look at the data in some organized form, and perhaps some stacking of the seismograms. The last step entails sophisticated operations that apply to seismic reflection techniques and their goal is producing an image of the subsurface.

G. R. Keller

Bibliography

Telford, W. M.,, Geldart, L. P.,, and and Sheriff, R. E. (1990) Applied geophysics. Cambridge University Press.
Yilmaz, O. (1987) Seismic data processing. Society of Exploration Geophysicists, Tulsa.