For many years the geophysical industry has spent considerable time and effort on improving the high-frequency content of recorded seismic data in the pursuit of higher resolution. However, in the last two decades we have seen an increased interest in extending the bandwidth of our data toward lower frequencies as well.
In this series of two articles, I will address the reasons we need low-frequency information, the issues related to its acquisition for onshore projects and discuss the equipment and methods being used.
Obviously, in order to be able to record low-frequency reflections, we need to be able to generate adequate signal strength in the desired low frequency range. This should be such that, after transmission through the Earth, we still have sufficient energy to be able to record signals that are not completely buried in noise – either ambient noise or the electronic noise from the recording sensors and instruments. The sensors themselves need to have adequate sensitivity in the frequency range needed.
An extremely important factor to note when discussing the bandwidth of seismic data is that we need to think in terms of octaves rather than in terms of hertz (or cycles per second, as we used to call them). When asked what low frequencies are wanted, many geologists or geophysicists will say “Oh, 1 or 2 hertz.” If we think in terms of hertz, this does not seem to be a very significant difference, but 1 to 2 hertz is a complete octave. There is often a substantial increase in data acquisition cost that results from acquiring this additional octave.
In this first article, we will review the reasons we need low frequencies, the signal transmission, the sensors used to receive the reflected signals and the recording instruments themselves. In next month’s article we will assess the differences between using explosives versus vibrators and the advantages and disadvantages of each.
Discussion
There are four primary reasons commonly stated for acquiring lower frequency data. The first is that it will provide higher resolution and more “character” to the processed seismic images. The second is that when low frequencies are missing, any form of seismic inversion is less stable than when they are present. The third is that they are extremely important in the development of accurate velocity/depth models needed for modern high accuracy pre-stack depth migration algorithms. The last is that in regions with sub-coal, sub-salt or sub-basalt reservoirs, the low frequencies are necessary to provide the penetration required through the strong acoustic impedance contrasts.
Figure 1 shows four different signal wavelets with different octave ranges, and therefore different frequency ranges. The uppermost wavelet has 2 octaves and it is apparent that the level of the sidelobes of the wavelet are quite high relative to the central peak. The second image shows the addition of 1 octave of higher frequencies. The central lobe is clearly much narrower, as is expected, and will directly provide higher resolution in the data. However, the sidelobes are still quite high and will overlap and interfere with primary reflections from closely-bedded formations. The third and fourth images from the top show the result of adding 2 additional octaves of lower frequencies to the first and second wavelets, respectively. These clearly show the reduction of the sidelobe amplitudes.
Figure 2 shows a “wedge” model and the result of filtering that model with each of the wavelets shown in figure 1. The reduction in the sidelobe amplitudes by the addition of the 2 low-frequency octaves is clearly visible in the comparison between the upper 2 and lower 2 filtered panels. The improvement in the vertical resolution is also obvious when comparing the panels with the additional high-frequency octave. On these, the Rayleigh criterion of being able to identify two separate peaks as the wedge thickens is visible at 8 milliseconds reflector separation on the wavelets with an upper frequency of 96 hertz versus 14 milliseconds for the wavelets with an upper frequency of 48 hertz.
What is not as obvious at this display scale is the distortion of the reflector wavelets caused by the interference of the sidelobes from the nearby reflectors. Figure 3 shows zooms of the wedge model filtered by the 2 octave and 5 octave wavelets. In the 2 octave image in figure 3a, the peaks of the reflection wavelets do not align with the model spikes. At the location of the green arrow to the left the spike separation is 14 milliseconds while the peaks of the wavelets are separated by just over 18 milliseconds. At the right edge of the model, the actual model separation is 30 milliseconds whereas the apparent thickness is approximately 2 milliseconds less. In figure 3b, the broader wavelet bandwidth reduces the sidelobe interference and the signal peaks are more closely, but still not perfectly, aligned with the model spikes.
Improvement in Geophones
For many years the geophysical industry has perhaps been more focused in extending the recording bandwidth to the upper frequencies in the pursuit of higher resolution. By far the most common geophones used today have a natural frequency of 10 hertz providing a flat response proportional to ground velocity above this frequency, and a response falling at 12 decibels per octave, below. See figure 4a. Over time, improvements have been made in such geophones to tighten parameters and reduce distortion yielding the range of high specification geophones that most seismic recording crews use today. Improvements in digital filtering in our recording systems have allowed for steeper-sloped anti-alias filters pushing the -3 decibel point toward 80-percent Nyquist. As most data is now recorded at 2 milliseconds with anti-alias starting at about 200 hertz, this has led to geophones with higher spurious frequencies pushed up into the rejection band near Nyquist. All this technology improvement has gone into what manufacturers term the “industry standard”: a 10-hertz geophone.
As we have seen above, extending the bandwidth to lower frequencies also improves resolution. If we wish to record signal with good signal-to-noise ratio down to 3 hertz or 2 hertz or even down to 1 hertz, we need to consider the receivers and recording systems to be used. Fortunately, this is not really an issue with modern recording systems. These systems generally have DC response. This means they can record a constant level, so have nothing “built-in” that limits their low-frequency response. Our high specification 10-hertz geophones however will show a falling response at low frequencies. A 10-hertz geophone with 70-percent damping is already -3 decibels at 10 hertz and will be an additional -24 decibels at 2.5 hertz and -36 decibels at 1.25 hertz. Although high quality low-frequency geophones are manufactured, these are generally not as common on seismic crews as 10-hertz geophones.
Another important factor to consider is that geophone signal output at the lower frequencies also suffers significant phase rotation. See figure 4b. The -12 decibels per octave roll-off and the associated phase rotation inherent in geophone design can be corrected by inverse filtering. This process flattens the geophone response below the natural frequency and applies the appropriate frequency-dependent phase rotation. It works well so long as there is adequate signal-to-(system) noise ratio. Typically, with reasonable signal strength, we can flatten the geophone response to about 2 octaves below the natural frequency, so for a 10-hertz geophone, we can get down to about 2.5 hertz. By using geophones with lower natural frequencies, we can maintain sensitivity to lower frequencies and then inverse filter to very low frequencies.
Controlling for Noise
The electronics in the recording system also produce noise, thermal or Johnson noise. This noise is a function of temperature but is also frequency dependent. Typically, electronics will exhibit an effect roughly proportional to the inverse of the frequency, or 1/f, which means that the random electronic noise will increase as frequency reduces. This effect raises the noise floor at low frequencies, so the lower frequency we record the higher the random noise contribution from the electronics themselves. This thermal or Johnson noise is random in nature and so will attenuate through summing. The electronics can also show DC offset. This offset is frequently introduced in the A/D converter and biases the data positive or negative. The offset can be removed by computing an average value over a record and then subtracting that value from all samples. Modern systems do this as part of the acquisition process. If very long recordings are made, this offset can change over time, causing a drift effect that might look like a very low frequency, usually of period much greater than 1 second. The low frequency drift can be removed by low-cut filtering.
Another sensor type that has been available for a number of years is the MEMS sensor. MEMS (micro-electromechanical-systems) digital sensors are accelerometers and so have a lesser (-6 decibels per octave, re. particle velocity) roll-off to low frequencies (see figure 4a, green line). Additionally, they have a response to DC, which makes them good candidates for low frequency recording. However, because there is a similar 1/f, effect in MEMS sensors, the noise floor of early generations of these sensors was higher than that of geophone/analog input recording systems and therefore was a limitation for recording low amplitude low frequency signals. In conditions with extremely low ambient noise, the internal noise of the sensors could potentially become the dominant noise source. A new generation of MEMS sensors has now been released that has overcome the noise issues but, because of the large number of high performance 10-hertz geophones already in use, it might take some time before they see routine usage.
It should be noted that the self-noise of an analogue geophone is extremely low since this is caused by the thermal or Brownian motion of the air molecules surrounding the moving mass. Because the geophone low frequency roll-off is a mechanical effect, it reduces both the signal and the ambient noise to the same degree, preserving signal-to-(ambient) noise ratio. However, under some conditions, typically low signal strength, the amplitude of the signal from the geophone might fall below the noise floor or the recording system, and then the signal-to-total noise ratio becomes compromised. A significant benefit of analogue geophones in such cases with very low levels of signal is that their output may be summed in arrays to improve the signal-to-noise (both ambient and system) ratio.
Earth unrest should also be considered. In the normal seismic band, Earth tide and other low frequency motions are well below the surface ambient noise and so do not trouble us. As we go to lower frequencies these earth noises become stronger, again following a 1/f relation (Peterson model) and might need to be considered.
Figure 5 shows a test comparison of standard high-performance 10-hertz geophones in comparison with high-sensitivity 5-hertz geophones and the latest generation of MEMS accelerometers. The geophones have all been inverse-filtered to remove the low frequency roll-off and the corresponding phase effects. The MEMS accelerometers have been integrated to velocity. Thus, all displays are of ground velocity. In this comparison, it is clear that the MEMS sensor has the strongest low frequency signal, the 5-hertz high-sensitivity geophone is next, and the 10-hertz geophone is last.
Conclusions
Given today’s seismic technologies and the current availability of equipment, there does not appear to be a universal solution to the challenges of low-frequency recording. There are many variables to consider in choosing the most appropriate equipment. In many areas, we will probably see continued use of 10-hertz geophones because of their availability. In addition, if the signal levels are low, they can be used in arrays to improve the signal to the ambient, and recording system, noise ratio. We might continue to see use of 5-hertz geophones in areas where they are already being deployed, but the future seems to be with using low-noise MEMS because of the improved signal-to-noise over a wider bandwidth than with conventional moving-coil geophones.
Acknowledgements
The author would like to thank Sercel for permission to use the data set in figure 5.