Don W. Steeples
Kansas Geological Survey
Lawrence, Kan.
Reflection seismology is a method of conveying information about the interior of the earth to the surface of the earth. Most commonly the source and receivers are located at or near the surface. This paper is a conceptual discussion of how one may maximize the amount of information received from reflection paths between sources and receivers. Some of the basic tenets of information theory are discussed in simple terms below for illustration purposes.
To begin, let us assume we have a continuous, monofrequency vibratory source located some distance from a receiver. Certainly, some signal would be reflected from existing subsurface interfaces and return to the surface to be recorded. However, it is impossible for us to extract information from that signal because there would be no unpredictable change in the signal over time. If we are to convey information, our signal must change unpredictably over time. If the recorded signal varies in an unpredictable manner that we can interpret, it begins to convey meaning and information.
We can design a monofrequency information transmission system where each wave-peak amplitude value represents a different symbol. In such an amplitude-modulated system, the greater the range of observable variation in amplitude, the greater the number of symbols that can be represented and, therefore, the greater the information-carrying capacity of the system.
It would also be possible to operate many monofrequency communication systems simultaneously in parallel, and we could measure the resulting spectra. Systems with broadband spectra have a greater carrying capacity because more monofrequency channels can be operated simultaneously.
Fig. 1 shows two different idealized spectra that might be obtained from the simple communication system discussed in the previous paragraphs. The information carrying capacity of the system with the flat spectrum is greater than that for the system with the sloping spectrum because there are more possible permutations of symbolism at the higher frequencies when the amplitude spectrum is flat.
Of course, with seismic reflection energy sources such as explosives, we broadcast a more or less flat and continuous spectrum and the earth selectively attenuates the high frequencies resulting in a spectrum somewhat like Fig. 1's idealized spectrum without shaping at the geophone. We can use spectral shaping techniques, however, to flatten the spectrum before the data reach the analog to digital (A/D) converter and to extract more information from the resulting seismograms.
PRECONVERSION SHAPING
There are at least two good reasons for wanting to flatten the spectrum before A/D conversion. The first reason is illustrated schematically for an 8-bit converter in Fig. 2. In the illustration for error without lowcut filters, the seismic waves passing into the A/D converter are dominated by ground roll to the extent that only the least significant bit (LSB) contains reflection information. Seismograph specifications commonly list accuracy limits to be "plus or minus half the least significant bit," which as shown represents an amplitude error of 50%.
As shown in the illustration for error with lowcut filters, however, we can drop the reflection amplitude error caused by A/D conversion to about 6% if we can set at least 4 bits with reflection information. In many cases it is possible to use spectral shaping filters to increase the number of significant bits of reflection information. If we can set more than 4 bits, we can decrease the amplitude error even more. While this example is for a fixed-gain, 8-bit seismograph, the principle is the same for modern seismographs with floating-point amplifiers.
The second reason for flattening the spectrum before A/D conversion is to detect weaker reflections. Suppose that we do not shape the spectrum before A/D conversion, and that some reflecting horizon is represented with only the least significant bit in the digital word. Any weaker reflection will not set any bits at all and will go undetected, at least on that particular seismogram. Furthermore, the weaker reflectors cannot be brought out in processing because their signatures will never get into the computer to be enhanced.
On the other hand, if we can shape the spectrum before A/D conversion to make the stronger reflector from the previous paragraph set 4 bits, then we have the potential to detect reflectors at least 18 db weaker than the 4-bit reflector. While their amplitude accuracy will not be as good as that for the 4-bit reflector, at least the reflector's presence is known and can be enhanced during processing.
Each seismograph system has some minimum detectable level of amplitude change. To the extent that we can increase the reflection amplitudes above that lower limit, we can increase their accuracy. This is particularly important for applications where recovery of true reflection amplitude is needed. Likewise, to the extent that we can increase the amplitudes of the strong reflections, we are more likely to see subtle reflections that may be important in unraveling stratigraphy, geologic structure, or direct detection of hydrocarbons. Even if we don't see subtle reflections on final stacked sections, it is comforting to be confident that they are not there in the real world rather than to worry that they were missed during the A/D conversion process.
The rest of this paper is devoted to showing some relevant examples of spectrally shaped data and to further discussion of obtaining better resolution with seismic reflection data.
Fig. 3 compares the amplitude spectrum of data recorded with a preemphasis lowcut filter and data recorded with open passband. Note the data obtained with the narrow passband have a substantially broader and flatter spectrum than the data recorded with open passband. The source location and geophone plant were identical, so information received by the geophone was invariant. The data recorded with open passband are actually more narrow band than the data recorded with the preemphasis filter. There is little significant energy greater than 250 hz in the data recorded using the open passband. The lowfrequency components of the signal saturated the system, and the high-frequency components were insignificant by comparison. The preemphasis filter, on the other hand, attenuated the low frequencies sufficiently that the highfrequency components maintain a relative significance to frequencies greater than 400 hz.
Such preconversion spectral balancing reduces the detrimental influences of the low-pass earth filter, improves the significance of the recorded data, and makes the recording of high-resolution data possible by attenuating to a manageable level the low-frequency signal that would saturate a flat-response recording system. The reader should note that resolution of seismic data depends on total bandwidth and on the presence of high frequencies.
THE IDEAL SOURCE
To put the need for spectral balancing into perspective, I will discuss the theoretical aspects of the ideal seismic source. One might expect the ideal-source spectrum to be flat from zero hz to infinity. That is not true, and one of the most important reasons for writing this paper is to get that point across. The ideal source would have a spectrum that increases at the high frequencies to exactly offset the low-pass nature of the earth with respect to seismic waves. In other words, we want our source to provide more high-frequency energy to make up for the earth's natural tendency to attenuate high frequencies. The result would be recorded data with a frequency spectrum that is flat from zero hz to infinity (actually to the Nyquist frequency). (It is interesting to note that because of differential attenuation of various frequencies, this ideal source would only be ideal for one raypath length from source to receiver.)
Naturally, our ideal source will need an infinitely variable and controllable output energy. We need only that amount of energy that gives an acceptable signal-to-noise ratio in our data. We also want our source to have a totally linear method of coupling its energy into the ground, because stressing large volumes of earth beyond the elastic limit has a deleterious effect on our seismic data. It also can cause environmental damage, and our ideal source must produce zero environmental damage. We also want our source to produce absolutely no air-coupled waves, since these waves often obscure waves that come through the ground. Our ideal source must also be repeatable. We want our source to be safe so nobody will ever be injured by it.
We would like our source to have a minimum phase wavelet to stabilize some of the processing steps. Wait a minute; what processing steps? If we had an ideal source, there would be little need for processing, since there would be no ringing of the source wavelet, there would be no need to filter, there would be no need to use common depth point methods. We might need to apply the normal moveout correction and to migrate the data to put things in their proper spatial perspective, but beyond that there would not need to be any processing done, and we could simply use either common offset methods or single-fold coverage.
SHAPING THE RECORDED DATA SPECTRUM
Since dreaming about sources is a marginally productive exercise, we must move on to practical methods of simulating ideal sources. One method is to use nonlinear Vibroseis sweeps to enhance the higher frequencies. Another method is to shape the recording spectrum to compensate for the earth's attenuation of high frequencies.
These two techniques complement each other and can be used together to improve resolution. Previously, we noted that frequency bandwidth has an effect on resolution. High frequencies may be present but not detected if the dynamic range of the recording system is insufficient to represent both the high-amplitude low frequencies and the low-amplitude high frequencies simultaneously.
SEISMOGRAPH CONSIDERATIONS
Seismic recording hardware used to shape the recording spectrum must be designed to extract and record high-resolution information with minimum distortion. This can be accomplished with properly designed analog filter circuits.
Progress in solid-state switching now allows variable slope on the shoulders of the filters. Classically, filters had a fixed number of poles that produced a constant filter slope of something like 12, 18, 24, or 36 db/octave rolloff. The slope was fixed because each filter was implemented by a manual switching mechanism that contributed a significant amount of noise to the signal as it passed through.
Modern solid-state switches add a very small amount of noise to the signal. Some new designs have multiple stages in the filters, which allow the operator to selectively shape the spectrum by varying the attenuation, corner frequencies, and slopes of the filters to meet the needs of a specific survey.
One commercial seismograph that uses this approach is the 1/0 System One, in which the filters are called "spectral-shaping filters."
An important factor in maximizing transmission of information is to shape the energy passband so the seismograph digitizes data having a spectrum that is as flat and broad as possible. This involves lowcut filtering and high-frequency boosting of the data before A/D conversion so the magnitude of the prevalent low-frequency noise does not swamp the high-frequency signal.
The objective is to permit boosting the amplitude of the high-frequency signals to fill a significant number of bits of the digital word. Judicious use of a lowcut filter is one element of this step, although geophone selection is also a factor because geophones have a - 12 db/octave velocity response at frequencies less than the resonant frequency of the spring-mass system.
Fig. 4 shows a seismic reflection from a depth of 2.6 m that was recorded as part of a high-resolution reflection survey near Great Bend, Kansas. Now notice that the pre-A/D lowcut filter used was 600 hz with 24 db/octave rolloff. Conventional wisdom of seismic data recording would predict that the reflection wavelets recorded under these parameters would ring. Note that the wavelet is not ringy, and in fact is a nearly perfect minimum-phase wavelet with a dominant frequency of 335 hz. This is due to the broad bandwidth (270 hz) of the data, which was obtained in spite of a recording passband that was only two thirds of an octave wide (600-1000 hz).
One of the least understood but most important concepts in instrumentation is that of dynamic range. "Dynamic range" was defined by Sheriff1 as "the ratio of the largest recoverable signal (for a given distortion level) to smallest recoverable signal." The effectiveness of a seismograph system in recording accurate seismic reflection data is determined largely by the instantaneous dynamic recording range of the system, which is the ratio in decibels between the largest signal and the smallest signal that can be recorded simultaneously. For high-resolution seismic reflection surveys, instantaneous dynamic recording range is of special significance because we are trying often to extract a very small high-frequency seismic-reflection-signal voltage from a very large voltage that is commonly dominated by ground roll.
Boosting high frequency in preamp can prevent reflections from being swamped by ground roll at the instant of A/D conversion. Further increase in frequency response can be obtained by sophisticated lowcut filters that selectively attenuate low frequencies instead of eliminating them altogether. These two techniques would serve to provide the best frequency response and instantaneous dynamic range. Such improvements are, however, predicated on noise levels in preamp filter sections being very low.
In the practical sense, reflection seismologists often deal with blackened wavelets on white paper. The dynamic range of the human eye is such that under suitable conditions, wave amplitudes in the range from 0.1 mm to about 1 cm can be transmitted simultaneously to the brain. This represents a dynamic range of 40 db.
Consider a seismograph that uses 15-bit A/D conversion, not including sign. Such a system potentially has a dynamic range of 90 db. Because its dynamic range is better than that of the human eye, it is possible that seismic reflections may be present on field seismograms in the data that are invisible to the eye.
For example, consider Figs. 5 and 6. Fig. 5 shows a seismogram recorded in the back yard of the Kansas Geological Survey and a seismogram from the same locality after preemphasis filtering with a 340 hz lowcut filter. Notice that a reflection at about 48 ms is present on the seismogram with filtering that is not even hinted at on the other. We used this test site for 8 years with many combinations of sources, geophones, offsets, and filters but did not see any reflections at all until we used the 340 hz lowcut filters for the first time.
Fig. 6 shows two seismograms recorded without and with spectral shaping filters, with all other recording parameters held constant. Note that in the seismogram with spectral shaping there are reflections between 1.0 and 1.1 sec that are not even hinted at on the seismogram without shaping.
The degree of care required in designing the filter response depends in part on the resolution of the recording instrument. The merits of a recording system include its precision (number of bits digitized), its noise level, and its dynamic range at all preamplifier gains. The objective is to maximize the significance of all desired frequencies recorded within the signal band-pass. This means the total response of all components combined should be high-pass to counterbalance the low-pass filter characteristic of the earth. Hence, rather than requiring a flat instrument response, a high-pass instrument response that increases gain with increasing frequency is required.
CONCLUSIONS
To improve resolution, application of lowcut filters prior to A/D conversion is often critical, for several reasons. Most elements of the seismic reflection system are working against the generation, transmission, and recording of high-frequency data. The high frequencies received at the geophone can be of such small magnitude compared to the low frequencies that they do not register in the A/D conversion. They are lost in the system noise, or they are smaller than the voltage value represented by the least significant bit of the A/D converter.
Even if the high frequencies do register on one or two least significant bits, they are subject to large errors. To reduce the significance of the recording errors, it is necessary to fill several bits of the A/D converter with high-frequency reflection information. Applying a lowcut filter can improve this situation by attenuating the low frequencies to a level where their magnitude is comparable to the magnitude of the high frequencies. This technique then allows one to emphasize the high frequencies by increasing the gain applied in the amplifiers.
If we can set more significant bits with the stronger reflectors, then there is a possibility of seeing weaker reflectors that would not show up without spectral shaping. It is better to be confident that subtle reflectors are not present in the geology than to worry that they were missed because of inadequate field recording techniques.
There are times when use of spectral shaping is not appropriate. There are some localities where any degree of filtering of the low frequencies causes the data to ring unacceptably. If the dominant reflection frequency is near the natural frequency of the geophones, it may be necessary to pass more low frequencies. Some localities have a very broad natural spectrum of reflectors that can be degraded by spectral shaping.
The techniques used in shallow, high-resolution reflection applications can easily be scaled to deeper petroleum exploration surveys. As noted in the introduction, spectral shaping prior to A/D conversion can often move the upper band-edge of the spectrum upward by 10-30%, depending on the specific site geology. This can often be done without losing more than an equivalent percentage of the lower band-edge, which effectively broadens the bandwidth and improves the associated resolution limits.
As a typical petroleum exploration example, assume that the data were relatively flat from 10 hz to 60 hz. If we can move both the upper and lower band edges upward by 20% by spectral shaping, we can broaden our spectrum to 12 hz to 72 hz, which will improve resolution. Generally, spectral shaping can improve resolution more in good-data areas than in bad-data areas.
REFERENCES
- Sheriff, R. E. (1973), Encyclopedic dictionary of exploration geophysics: Soc. of Explor. Geophys.
- Knapp, R.W., and Steeples, D.W. (1986), "High-resolution common depth point seismic reflection profiling, instrumentation," Geophysics, 51, 276-282.
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