Sensor density or sensor sensitivity?

Sensor density or sensor sensitivity? Xander Campman1, Phil Behn2, and Kees Faber2 Abstract

It is widely recognized that image quality can be improved by acquiring seismic data with long offsets, wide azimuths, low frequencies, and dense source and receiver sampling. To achieve this in an affordable way, we see a trend toward single-sensor recording in high-productivity land seismic surveys. Moving away from field arrays has a material effect on requirements for sensors and channels and for the way their performance is specified and displayed. While increased sampling density can compensate for the lack of sampling and noise reduction achieved by field arrays, there is a trade-off in the resultant sensitivity change of the sensor compared to the array and the preamplifier gain setting. Higher sensitivity geophones should be selected and lower preamplifier gain considered for single-sensor surveys. Two measures are introduced to help in finding a balance between adequate sampling and sensor/recorder channel performance at the acquisition design stage. The amplitude spectral density (ASD) expressed in ground-motion units is proposed as a frequency-dependent alternative for root-mean-square (rms) values to evaluate noise properties of the sensor/recorder channel combination. The operating range diagram (ORD) is adopted to offer a more meaningful dynamic-range measure than the instantaneous dynamic range by honoring the differing mathematical properties of signal and noise. The ORD compares fullscale rms values at a range of frequencies with narrowband noise values centered at the same frequencies.

Introduction

This paper follows up on the Advances in Seismic Sensors workshop held at the 2015 SEG Annual Meeting in New Orleans. Due to space limitations, we cannot discuss all the sensor technologies and applications reviewed during the workshop. Instead, we choose to focus on one discussion that arose during the workshop about the trade-off between the perceived need to improve the performance of sensors versus reducing the cost and deploying significantly more sensors in active-source land seismic surveys. Several representatives from oil companies and contractors alike supported this latter point of view. The past decade has seen some fundamental changes in land seismic acquisition. Dean (2012) describes an array of innovations related to surveying, positioning, sources, fleet management, sensors, and channels that have been incrementally implemented on land seismic crews, leading to, in his words, a “quiet revolution.” Driven by the need for more efficiency and higher-quality data, the revolution described by Dean actually enabled a change in the underlying philosophy of seismic acquisition. It is widely recognized now that, in most cases, image quality can be significantly improved and more information can be extracted from it when data is acquired with wide azimuths, long offsets, lower frequencies, and dense source and receiver sampling. To achieve this in an affordable way, the channel count should increase while the operational and equipment cost-per-channel 1 2

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should decrease substantially. This, in turn, leads to a growing interest in reducing the number of deployed sensors per channel. Thus we see a trend toward smaller arrays, to the limit of no arrays. This is commonly referred to as single-sensor recording. In summary, we see a shift from an emphasis on microgeometry (i.e., field arrays) to macrogeometry (i.e., the source- and receiver-line density) and the station interval. The shift in thinking about seismic sampling and the emphasis on low frequencies has a material effect on requirements for sensors and the associated channels, the systems that host the channels, and for the way we specify and display the sensor and recorder channel performance. In this paper, we first discuss the implications of abandoning arrays in favor of single sensors per channel and associated considerations on the required changes in acquisition-geometry and performance of the sensor/recording channel. We then review the basic properties and specifications of recording channels, geophones, and microelectromechanical system (MEMS) sensors in the context of their roles in the acquisition system. After we have discussed the sensors and recording channel, we propose a way to view and inspect, in one glance, the effective operational range of a sensor/channel combination.

High-channel-count seismic acquisition

We consider the impact of the use of high-channel-count systems on the acquisition geometry and required sensor/recording channel performance. High-channel-count systems are often associated with single-sensor acquisition, so let’s first look at the impact of abandoning arrays altogether. Arrays actually serve many purposes in seismic acquisition. When the number of channels in the field is limited, arrays are necessary to increase the sensor-coverage area. • First, approximately 90% of the energy of an active shot goes into surface waves (ground roll), which have overwhelming amplitudes and high wavenumbers. The seismic wavefield is sampled at a basic interval determined by the highest wavenumbers, usually associated with surface waves, expected in the data. • Next, the signals from several geophones in a pattern are summed, boosting the signal-to-uncorrelated-noise ratio by the square root of the sum of the number of sensors. The summation suppresses the overwhelming ground roll, reduces the peak signal level, and reduces the risk for channel overscale. The array also acts as a spatial anti-alias filter, which is necessary because the station interval is coarser than the basic sampling interval. • Finally, the total sensitivity of the array to the desired reflection signal is increased, effectively lowering the system noise floor. Seen in this light, it is a wonder that we would even consider discussing replacing groups with single sensors. However, this is http://dx.doi.org/10.1190/tle35070936.1.

Special Section: New advances in seismic sensors

happening now operationally. It is becoming more efficient to deploy more stations with only one sensor per station rather than fewer stations with arrays, while maintaining or improving the final image quality. How do we ensure that the equivalent single-sensor survey maintains an adequate signal-to-noise (S/N) ratio? Use of the array addresses various types of noise: (1) electronic noise, (2) ambient seismic noise not synchronized with our sources, and (3) source-generated noise (direct and scattered ground roll). In the absence of arrays, each of these noises must now be addressed by reconsidering the macrogeometry parameters. Imaging, in particular 3D migration, is a very powerful uncorrelated noise attenuation tool. The increase in S/N ratio due to 3D migration is roughly proportional to the square root of the area of the first Fresnel zone and the fold, and inversely proportional to the square root of the bin size. Hence, there are essentially two ways to increase S/N ratio using the macrogeometry: one is to decrease the group interval, and the other is to decrease line spacing, which increases fold. System channel noise is uncorrelated between sensors and is reduced by a factor of square root of N compared to the signal when summed in an array or stacked in processing. However, we should note that arrays of standard geophones with a few elements in series have higher sensitivity than a single standard element sensor. High-sensitivity geophones should be selected when changing from arrays to single geophone sensors. In the absence of the array response suppressing ground roll, the system gain selection may need adjustment to a higher full-scale setting (less gain) to record the unfiltered ground roll. The change to a higher full-scale setting will potentially raise the referred-to-input channel noise, but this higher noise may well be benign and a suitable trade-off to the concurrent increase in fold from the higher channel count. Ambient seismic noise is usually uncorrelated at high frequencies and therefore is suppressed by migration substituting for summing in an array. The equivalent fold for single-sensor acquisition required to achieve the same signal-to-uncorrelated noise ratio can be estimated in the acquisition design stage given the sensor/recorder channel specifications and an estimate of ambient seismic noise levels. Changing the group interval and line spacing also has benefits for coherent noise suppression. Direct ground roll can be mitigated relatively easily in single-sensor surveys by choosing the station interval wisely. Advances in ground-roll-modeling and -removal algorithms allow mild aliasing such that the single-sensor interval does not have to be as small as the basic sampling interval in array recording. Correlated noise is best mitigated by increasing the density of point sampling (e.g., Regone et al., 2015). Tighter line spacing may also contribute to the suppression of other coherent noise types, such as multiples. Utilizing high source-productivity methods enables decreasing source-point interval and promotes sufficient crossline sampling. Scattered ground roll, however, presents an issue in crossspread geometries, typical to high-productivity land surveys, as it cannot be removed entirely by filtering. Instead, migration suppresses the remaining scattered ground roll. This typically requires tight line spacing to minimize scattered ground roll leaking through the stack. Ambient noise is often coherent at low

Special Section: New advances in seismic sensors

frequencies. It is suppressed in the same way as direct or scattered ground roll, depending on its origin. In summary, increases in available system channel counts are enabling the operational flexibility to substitute more channels with point receivers in place of fewer channels with sensor arrays. The obvious trade-off is the increase in fold from the increased density of receivers; the not-so-obvious trade-off is the importance to review the resultant sensitivity change of the sensor compared to the array, and the preamplifier gain setting. In the following sections, we will review some key properties of the system channels and sensors to assure that sensor sensitivities can be properly selected.

Recorder channel

Understanding sensor performance and limitations requires a concurrent understanding of important characteristics of the channels of the recording system. We will discuss briefly several key attributes of high-performance channels: system gain, quantization range, dynamic range (DR), and noise. System gain is a term defining user-selected preamplification gain assigned in system operation. Most systems offer the user multiple gain settings from which to select system gain. The selection of system gain, in turn, defines the channel operating properties of quantization range, equivalent input noise (EIN), and DR. Selecting the system gain setting is important, as trade-offs are inherently made in this selection that can have unrecognized consequences in the acquired data. Quantization range defines the upper and lower limits of signal that can be quantized in a sample by the converter. The upper limit, sometimes referred to as full scale, defines the largest measureable signal, above which the signal will appear clipped and distorted. The lower limit is defined by the least significant bit (LSB) of the converter. In the absence of other noises, the LSB defines the smallest measurable signal. Abrams and Elder (2013) discuss channel DR and EIN, and provide useful definitions and illustrations of basic performance properties of modern 24-bit instrument channels. Abrams and Elder (2013) provide an example of coherent signal stacking, demonstrating that sufficient fold brings signal at or above the minimum quantization limit out of random noise. The industry measure of DR is defined by the ratio of the rms of a signal at maximum signal level to EIN, the rms of the time series of noise. Analysis of signals in the time domain by rms calculation depends on the assumption that the signal is observed with high S/N ratio in the time series and that noise is observed in the absence of a signal. Analysis by rms of time-domain signal or noise is not inherently diagnostic — it lacks spectral visibility, as it does not measure discrete frequencies. Furthermore, characterization of signal is different than that of noise. This is because of the differing mathematical properties of signal and noise when expressed spectrally. Signal is usually associated with an energy signal; it has bounded energy — it dies out at some finite time. Noise is considered a power signal; it has finite power but infinite energy because it lasts forever. For this reason, the two classes of signals have different spectral units. A bounded energy signal is analyzed easily by Fourier transform, resulting in energy spectral density (ESD), describing how the energy of the signal is distributed with frequency.

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Fourier transform does not analyze the infinite-duration noisepower signal as easily. The solution to evaluate a noise-power signal is to use a long interval of time, to split the power signal up into multiple finite-length time sequences, take the fast Fourier transform (FFT) of each time sequence, and then average the scaled magnitudes (scaled per Hz) of the FFTs of the sequences. The result is power spectral density (PSD), a different measure compared to ESD. PSD noise specifications often are converted to amplitude and presented as amplitude spectral density (ASD) — expressed in the unit of measure per root Hz and referred to input. Units of measure are commonly volts, if representing only the channel, or m/s or m/s2 or g, if representing channel and sensor. Recorder channel EIN specifications, presented as rms values, can be translated into spectral noise density given the specification of bandwidth. Recorder bandwidth specifications often exclude frequencies below 2 Hz. Translation of the EIN to spectral noise density requires the assumption that the noise density is flat. This frequency exclusion sometimes indicates that the PSD of the channel may not be flat below this frequency. Quantifying instantaneous dynamic range (IDR) with the intention to identify DR as a function of frequency — as the ratio of the full-scale rms over the spectral noise density — is problematic because the units of measure are different. We will address the solution to this problem later in this paper. Meunier (2011) discusses that when stacking fold is large enough to bring the S/N ratio significantly above one, signal that is below the LSB can be recovered. A necessary condition for this is that the channel-integrated noise is higher than the LSB, or stated differently, the channel noise density is higher than the quantization noise of the converter. With single-sensor recording, the critical parameter is the system gain. Although higher-sensitivity single geophones may not match the sensitivity of the arrays they replace, the absence of noise averaging by the array to the same ground motion means the single geophone may still have peak noise amplitudes that exceed array noise, requiring a lower gain setting with a higher full-scale tolerance.

turn is proportional to the ground acceleration. The MEMS resonance frequency is well above the sensor passband, enabling a flat passband response in the acceleration domain. The light green curve in Figure 1b illustrates the MEMS sensor response in acceleration, and the orange curve illustrates the MEMS sensor response in velocity. Sensing displacement, velocity, or acceleration in most applications will yield equivalent responses after integration or differentiation to the domain of choice. Subtle issues may exist that could influence the decision for which sensing domain is best. Each of the measurements can be translated to the other, but the results may vary based on the signal and/or dominant noise properties present in the data.

Geophone sensors

The geophone is a velocity transducer, characterized by basic attributes of sensitivity (in V/m/s), resonant frequency (in Hz), and damping. As a damped harmonic oscillator, the damping is a combination of the open-circuit damping property of the sensor, damping provided by a sensor termination resistor, and the damping provided by the input impedance of the recorder channel.

Geophone and MEMS sensor responses

Geophones and MEMS sensors are inertial sensors. They are based on a mass-spring system wherein the ground motion moves the case and the inertial mass remains stationary. Geophones generate an output voltage proportional to geophone case velocity (which in the case of good coupling moves exactly with the ground). MEMS sensors develop an output proportional to case acceleration. Geophones and accelerometers have characteristic transfer functions (TF) for the ground motion; the TF amplitude and phase responses represent a filter effect relating the output to the respective ground motion. The characteristic TF of the geophone is flat above the resonance frequency while it rolls off 12 dB/oct below it. This roll-off essentially means that the geophone is a low-cut filter for ground velocity. The orange curve in Figure 1a illustrates the amplitude spectrum in velocity domain for the geophone. The light green curve illustrates the geophone response in acceleration domain. In MEMS capacitive accelerometers, the displacement of the proof mass is measured by a change in capacitance, which in

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Figure 1. (a) Typical geophone response in velocity (orange) and acceleration (green). (b) Typical MEMS sensor response in velocity (orange) and acceleration (green).

Special Section: New advances in seismic sensors

To observe the true case motion of the sensor at frequencies at and below the resonant frequency, it is necessary to compensate the response, which is to remove channel and geophone TFs from the sensor response. The channel TF represents all important filter functions such as input protection filters and possibly the analog-to-digital conversion (ADC) filter response. Dividing the sensor response by the combined elements of the geophone and channel TF forms the compensated response. The compensated response in the velocity domain will be a noise profile with a high, low-frequency noise content, falling off to higher frequencies and flat above the natural frequency. In the subsequent figures and discussion, we will also differentiate this geophone sensor response and present it in units of acceleration. After conversion, the geophone response appears as a V-shaped curve with the kneepoint at the natural frequency. The ability to recover the true ground motion from the measurement by geophone response compensation depends on its S/N ratio. Stienstra et al. (1993) provide a noise-density model that expresses noise in ground-motion units. Conventional passive geophones have two intrinsic noise sources: Johnson noise, which is electrical noise linearly proportional to coil resistance, and Brownian motion (or suspension) noise, which is mechanical noise inversely proportional to the moving coil mass. In studying the noise contributions, it is important to consider the sensor and recorder channel holistically. For example, geophone damping is always increased when connecting a string or single geophone to a recording system. The level of this increase depends on string configuration and the input impedance (often 20 kΩ) of the recorder. A noise evaluation should always include the referred-to-input preamplifier noise expressed in units of ground motion by scaling by the sensor sensitivity. It is important to note that increasing the preamplifier gain results in a lower recorder channel-noise contribution, but also reduces the available full-scale headroom and reduces the overall DR.

MEMS sensors

The MEMS sensor is an acceleration transducer. An important difference is that the mass is a fraction of a gram with mechanical support springs. With MEMS sensors, a companion mixed-signal application-specific integrated circuit (ASIC) exists to operate the sensor in a closed-loop force-feedback mode. Transducer sensitivity is expressed differently with MEMS sensors than with geophones. The geophone transducer output is by electrical signal with sensitivity of V/m/s and is paired with the recorder channel sensitivity of V/bit. Velocity motion sensitivity, in m/s/bit, is determined by dividing the digitized voltage by the transducer sensitivity. The MEMS sensor is paired with the companion ASIC and delivers a digital output with 24-bit quantization. MEMS sensor sensitivity is expressed directly in m/s2/ bit. The directional relationship of transducer sensitivity of MEMS to geophone that quantizes a smaller signal is inverted — increasing the geophone transducer sensitivity and decreasing the MEMS sensitivity enables smaller signals to be quantized. The MEMS sensor has Brownian motion noise, and must be packaged in a vacuum to minimize this noise. The ASIC has a similar instrument-noise property to a recorder channel used with

Special Section: New advances in seismic sensors

Figure 2. Example of modeled noise density contributions of a 70.7% damped, 10 Hz geophone and channel at room temperature, scaled in acceleration units. The light green line is Brownian motion noise; the dark green line is the Johnson noise; and the dark blue line is the composite noise of both. The yellow line is the referred-to-input channel noise at high gain, scaled by the sensor sensitivity. The brown line is the total geophone and channel noise. Note that the noise is dominated by the recorder, even at high gain.

a geophone. Noise specification comparison is easier, as MEMS sensor manufacturers are expressing sensor noise in acceleration units (e.g., noise density and rms). The noise-density profile can be included in plots similar to Figure 2. A preferred presentation is a direct plot of measured noise density (see Lainé and Mougenot, 2014). With MEMS sensors, the flat-line noise-density assumption derived from an rms channel noise specification may not adequately describe the sensor noise floor. Since the introduction of INOVA’s SVSM (VectorSeis) in the last decade, the noise floor of MEMS sensors has been progressively lowered.

Noise evaluation

The ambient ground-motion noise response, viewed in the acceleration domain and compared to Peterson’s new high- and new low-noise models (NHNM, NLNM) (Bormann, 1998), provides our reference point for evaluating the sensor/recorder channel-noise performance. In the earlier geophone discussion, passive geophones were shown to have negligible noise contributions because the recorder channel dominates sensor noise. This is demonstrated with actual field data in Figure 3. It shows the noise ASD’s from an experiment in Oman. The red curves are a collection of noise density traces recorded with 10 Hz geophones in the active spread. The traces have been compensated with the geophone response as previously described. The blue curve is the ASD from a recorder channel noise test (i.e. without a geophone attached), compensated with the theoretical 10 Hz geophone response. We see that from about 2 Hz and below, the noise traces from the spread follow exactly the recorder noise except for a small hump around 0.4 Hz, which may be attributed to the secondary microseism in the global noise spectrum. This means that below 2 Hz, we cannot see the true ambient groundmotion seismic noise apart from the small peak at 0.4 Hz.

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Figure 3. Noise density plots from an Oman experiment. (a) Active-spread noise-density traces in red, resistive-terminated measured recorder channel compensated with a 10 Hz geophone string response in blue, and the Peterson NLNM and NHNM in dark blue. (b) Resistive-terminated recorder channel in blue, and calculated white noise model from system total noise specification compensated using the same 10 Hz geophone string response in light green. (c) Same as (b), but included in orange is the resistive-terminated measured recorder channel in blue compensated with a single 5 Hz, high-sensitivity geophone response.

Figure 4. Operating range diagram of a state-of-the-art sensor/recorder channel combination. The blue line is the mechanical clip limit of the geophones. The red line is the recorder full scale. The yellow line is the combined lower bound of each. The dark blue line is the resistive-terminated measured recorder channel compensated with a 10 Hz geophone string response and integrated over 1/3 octaves centered on each frequency bin. The light green line is the calculated white noise model from system total noise specification compensated using the same 10 Hz geophone string response and integrated over 1/3 octaves centered on each bin.

Figure 3c illustrates the low-frequency improvement gained by using a 5 Hz geophone with slightly smaller sensitivity, instead of a 10 Hz geophone string, both compensated with their theoretical responses. The lowest point of the noise-density curve moves to a lower frequency, and reveals a beneficial gain of about 5 dB in motion sensitivity at 1 Hz while losing the same amount around 20 Hz. The noise floor determines to what extent we can recover the ground velocity at low frequency from the recorded trace. This is important, in particular at low frequencies where the geophones have reduced sensitivity to ground motion.

Operating range diagram

In an earlier section, we identified the problem of relating the full-scale rms to the spectral noise density. Is there a way to compare these two quantities? The operating range diagram (ORD) from Evans et al. (2010) is adopted to define the relationship. The ORD provides, in one glance, the time-domain comparative performance of a sensor/ recorder combination in a frequency dependent way.

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The ORD is inspired by scientists from the U. S. Geological Survey (USGS) who use it to compare seismometer and recorder systems. With the increasing interest in recording low-frequency information, it is particularly important to understand the sensor and ADC behaviors at low frequencies. The ORD should become a standard specification for integrated seismic systems. Consider Figure 3b, which displays the theoretical and measured noise density of a recorder channel in high gain, scaled by the sensitivity response of a string of 10 Hz geophones. How can we compare this to the full scale of the recorder channel? We are faced with the problem that full scale is an rms value, a measure of signal in the time domain, while noise is characterized by spectral density. We can overcome this difficulty by calculating an integrated noise value (rms) from the noise-density curve over a sliding 1/3-octave frequency band. The blue curve in Figure 4 is the resultant ORD illustrating the profile of integrated noise values. The ORD also includes the profile of full-scale rms values shown in yellow. A new dynamic-range property of the sensor system is revealed by comparing differences in rms value of the full scale to the (narrowband) rms noise as a function of frequency. This dynamic-range property is very similar to, but not the same as, IDR and is better suited to fulfill the IDR intention. The ORD noise term can be considered the rms of the noise trace filtered with a very narrow band-pass filter at the frequency of interest. The ORD enables a comparison of calculated narrowband rms noise to the rms of a just-not-clipping sine wave at the frequency of interest.

Conclusions

The use of field arrays mitigates various types of noise in seismic surveys. In the absence of arrays, sampling for noise with single-sensor channels has to be achieved by selecting new parameters for the macrogeometry (i.e., line intervals and pointsampling intervals). Increased sampling density is a main contributor to the quality of seismic images in single-sensor recording: both correlated and uncorrelated noises are more effectively suppressed with higher sampling density. In the remainder of this article, the focus has been on the implications of abandoning arrays on the required sensitivity, DR, and noise floor of sensors and recorder channels — all characteristics of sensors and recording channels that most influence acquisition success.

Special Section: New advances in seismic sensors

The sensor and recorder channel should always be evaluated together and in the context of the entire acquisition system. The ASD, a frequency-dependent measure of noise density expressed in ground motion units-per-square-root Hz, is recommended for this. The ASD can be integrated over a specified bandwidth to yield the more familiar rms noise levels. The sensor/recorder channel noise should always be compared to expected ambient noise levels (see also Kimman and Vermeer, 2015) and Peterson’s noise models. The operating range diagram provides a new method yielding narrowband rms noise values that provide a more meaningful evaluation of sensor-recorder channel noise and comparison to full scale. The inclusion of full scale is relevant in singlesensor acquisition, as the often-overwhelming ground roll is no longer suppressed. The S/N ratio and full-scale properties of the sensor-recorder combination should be taken into account at the acquisition design stage. The use of the ground-motion ASD and the ORD should help in balancing the performance of sensor and recorder channel with the required acquisition effort to achieve an adequate S/N ratio. Current state-of-the-art sensors and recording channels appear to be quite adequate for high-density high-channel-count seismic acquisition if the geometry properly accounts for the lack of arrays. When possible, improvements in channels should be directed to increasing IDR by lowering the noise floor (lower geophone/ channel noise floor) and sensors by improving low-frequency sensitivity. Improvements to MEMS should be directed to reducing motion sensitivity per bit and achieving a flatter noise floor.

Acknowledgment

The authors are grateful to Petroleum Development of Oman and the Oman Ministry of Oil and Gas for permission to use the data shown in the examples. We thank Shell Global

Special Section: New advances in seismic sensors

Solutions International B.V. and ION for permission to publish this work, and Kees Hornman (Shell) for his comments on the manuscript. Corresponding author: [email protected]

References

Abrams, M. L., and A. K. Elder, 2013, Dynamic range in a seismic channel: First Break, 31, no. 1, 79–87. Bormann, P., 1998, Conversion and comparability of data presentations on seismic background noise: Journal of Seismology, 2, no. 1, 37–45, http://dx.doi.org/10.1023/A:1009780205669. Dean, T., 2012, Land seismic: the ‘quiet’ revolution: Preview, 157, 38–41. Evans, J. R., F. Followill, C. R. Hutt, R. P. Kromer, R. L. Nigbor, A. T. Ringler, J. M. Steim, and E. Wielandt, 2010, Method for calculating self-noise spectra and operating ranges for seismographic inertial sensors and recorders: Seismological Research Letters, 81, no. 4, 640–646, http://dx.doi.org/10.1785/gssrl.81.4.640. Kimman, W. P., and P. L. Vermeer, 2015, Use of low and high noise models for land surface-seismic data: 77th Conference and Exhibition, EAGE, Extended Abstracts, http://d x.doi. org/10.3997/2214-4609.201412594. Lainé, J., and D. Mougenot, 2014, A high-sensitivity MEMS-based accelerometer: The Leading Edge, 33, no. 11, 1234–1242, http:// dx.doi.org/10.1190/tle33111234.1. Meunier, J., 2011, Seismic acquisition from yesterday to tomorrow: SEG/EAGE, Distinguished Instructor Short Course No. 14. Regone, C., M. Fry, and J. Etgen, 2015, Dense sources vs. dense receivers in the presence of coherent noise: A land modeling study: 85th Annual International Meeting, SEG, Expanded Abstracts, 12–16, http://dx.doi.org/10.1190/segam2015-5833924.1. Stienstra, A., A. S. Badger, and P. W. Maxwell, 1993, Intrinsic noise in geophones: 55th Conference and Technical Exhibition, EAEG, Extended Abstracts, A039, http://dx.doi.org/10.3997/22144609.201411481.

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