Seismic Interferometry Using Persistent Noise Sources for Temporal Subsurface Monitoring

Abstract

In passive source seismology, seismic interferometry typically refers to the cross correlation of ambient noise to construct an estimate of the Green's function between sensors. The presence of persistent natural and/or anthropogenic sources can bias or prevent the retrieval of these estimated Green's functions. Here we show how these strong persistent sources can be used to measure small changes in the medium between a source and either (or both) source-sensor pairs. The method relies on localizing the sources and using this information to identify and select cross-correlation functions for each source of interest. We illustrate this method by monitoring growth of a block cave at an underground mine using three nearly continuously operating ore crushers which dominate the wavefield. This technique should work equally well in natural environments using sources such as volcanic tremor, hydrothermal bubble cavitation, and microseisms.

Key Points

• Persistent seismic sources can be used to perform temporal monitoring of a medium
• This involves making measurements from cross-correlation functions selected to isolate each source
• We demonstrate this technique by inferring cave growth using ore crushers at a block caving mine

1 Introduction

1.1 Seismic Interferometry

First proposed by Claerbout (1968), seismic interferometry typically refers to the cross correlation and summation of seismograms to create virtual events or to the deconvolution of a controlled active source in seismic exploration projects. It has since been demonstrated that the cross correlation of ambient seismic noise can be used to construct estimates of the Green's function between sensor pairs, effectively turning each sensor into a virtual source (Campillo, 2006; Sabra et al., 2005; Shapiro & Campillo, 2004; Roux & Kuperman, 2004) and allowing for very sensitive monitoring of temporal velocity changes in the medium between sensor pairs (Brenguier et al., 2008; Sens-Schonfelder & Wegler, 2006). One of the primary limitations of this method is the reliance on either a fully diffuse wavefield (i.e., equipartition of modes) or a homogeneous distribution of spectrally white noise sources (Lobkis & Weaver, 2001; Weaver & Lobkis, 2004), although these conditions can be relaxed slightly in the presence of scatterers which act as secondary sources (Snieder, 2004).

Changes in the noise source distribution induce greater errors in the reconstruction of the direct waves in the seismic Green's function than in the coda (Froment et al., 2010; Hadziioannou et al., 2009). As a result, most studies using ambient noise cross correlation to measure changes in seismic velocity have been done in the coda waves of the reconstructed Green's function (e.g., Brenguier et al., 2014; Donaldson et al., 2017; Olivier et al., 2017). However, when the sensor distribution is sparse, it may be useful to use the direct waves to get an estimate of the location of the measured changes. Also, if large changes in medium are expected, the coda of the cross-correlation functions (CCFs) may become incoherent over time and prohibit its use coda to measure changes in the medium.

Mathematically, the cross correlation (⊗) of ground velocity in a spectrally white and diffuse noise field u(t) recorded at sensors A and B estimates the Green's function G_AB(t) of the sensor pair, convolved (∗) with the autocorrelation of the noise N(t), according to:

(1)

In environments such as underground mines, where few strong sources produce anisotropic and directional wavefields, conditions are generally not suitable to estimate seismic Green's functions (Olivier, Brenguier, Campillo, Lynch, et al., 2015). For example, by cross-correlating time periods when a single persistent stationary source C dominates the wavefield, we are estimating the following function:

(2)

where n(t) is the source time function of the persistent source. This equation can be described as the cross correlation of the Green's functions for the two source-sensor pairs convolved with the source time function of the persistent source. In the case where G_CA and n(t) remain stable, any change in u_A(t) ⊗ u_B(t) must be due to changes in G_CB. The seismic Green's function G_CB is primarily influenced by the direct arrivals, which are a coupling between the geometry of the least-time raypath (between source C and sensor B) and the medium along this path (described by a sensitivity kernel). Therefore, if this raypath passes through or near volumes where we expect changes in the medium, we can monitor these changes through u_A(t) ⊗ u_B(t) (Dales et al., 2017).

Although the use of active sources to perform temporal monitoring is not a novel technique (e.g., Grêt et al., 2006), here we are dealing with multiple persistent and uncontrolled sources. We define an uncontrolled seismic source as a source for which we cannot control the location and/or source time function. This problem is frequently encountered in applications of ambient noise interferometry where few persistent sources often dominate the CCFs, resulting in arrivals at nonphysical lag times (with respect to interstation propagating seismic waves). We would like to highlight that once located, these typically contaminating sources can be exploited to perform temporal monitoring. Using uncontrolled sources to perform temporal monitoring has not been used routinely in seismology, but equivalent methods have been used for many years in radio astronomy (e.g., Rogers et al., 1983). Very long baseline interferometry (VLBI) involves the detection of an uncontrolled astronomical source (such as a quasar) in multiple radio telescopes on Earth. These signals are then cross correlated between different radio telescope pairs. By looking at changes in the arrival times in the cross-correlation function, the distance between the radio telescopes can be measured to within millimeters to show the movement of tectonic plates. In our case we use cross correlations of time periods where an ore crusher is active to monitor the growth of a block cave.

1.2 Block Caving Mines

Block caving (see Figure 1, left) involves undercutting an ore body and allowing it to progressively collapse under its own weight and is an economical way to mine large volumes of low-grade ore (for more details, see Brown, 2007). To enable the collapse (which can take up to several years), trucks must continuously remove the broken ore from the extraction level to nearby conveyor belts which feed the ore crushers. Monitoring the progressing cave has important implications for both production and safety but limited access to the cave front makes this a difficult task. In terms of production, tracking the cave front is important to ensure that the cave continues to advance on schedule and is not drifting away from the target ore body. In terms of safety, it is important to identify periods when the cave has stopped advancing, as continuing to extract material widens the air gap between the cave front and the yielded material. This creates the potential for a powerful and deadly air blast if a large volume of rock yields at once and compresses air into any connecting tunnels.

Figure 1

(left) Cartoon example of a block cave. After initial blasting the cave front should naturally propagate to the surface as material is drawn from below. Microearthquakes concentrate in the highly stressed rock above the cave known as the seismogenic zone. (right) Mine plans for a block caving mine showing estimated cave shape in beige and ore crushers as blue, green, and red, respectively. Geophones shown as black triangles with respective sensor names as labels.

During this progressive collapse, tracking of the cave front is primarily accomplished using a combination of boreholes (drilled to intersect the cave) and passive microseismic monitoring. Although boreholes allow for direct access to the cave front, drilling is expensive and periodically lowering instrumentation (e.g., cameras) down the holes is labor intensive. In contrast, microseismic monitoring is relatively cheap and easily automated. This involves using information on the location and rate of seismicity, as microearthquakes typically concentrate in the stressed rock immediately above the cave-front fracture zone (Dales et al., 2017; Mendecki, 1996; Mercier et al., 2015). Drawbacks of microseismic monitoring are that cave growth can still occur without generating any detectable events, and there is little constraint on lateral growth as few events occur around the sides of the cave.

Although existing cave tracking methods are unlikely to be replaced, there is a need for new complementary and cost-effective monitoring techniques. Our proposed technique has the advantage of using existing mine infrastructure and being easily automated.

2 Data and Methods

Our data set consists of 40 days of continuous seismic recordings from an operational block cave mine for which the estimated cave outline can be seen in Figure 1, right. The seismic wavefield at this mine is dominated by three nearly continuously operating ore crushers (at least one is active at all times) and hundreds of microearthquakes per day. An example of the signal generated by an ore crusher and recorded at a nearby sensor can be seen in Figure S1 in the supporting information. Operation of an ore crusher alternates between a loading phase, where ore from the conveyor belt fills the gyratory crusher, and an active phase where the ore is ground. Each of these phases typically lasts between 2 and 10 min with maximum energy emitted during the active crushing phase where the source time function is determined by the nature of the material being crushed. Although the locations of the ore crushers are known and fixed, in practice we do not control their locations or operational scheduling.

The seismic system at this mine consists of over 60 triaxial geophones; however, to illustrate our technique, we use only vertical component data from a subset of six sensors. The sensor nearest the blue ore crusher (S1) serves as the reference station (as we expect minimal change in the medium between this sensor and the ore crusher) whose signal is cross correlated with recordings from the five other sensors (S2 to S6) surrounding the cave.

The goal of the data preprocessing is to maximize the contribution the persistent sources make to each cross-correlation function. To achieve this, the raw recordings are bandpass filtered between 50 and 500 Hz, where the crusher is most energetic, spectrally whitened to reduce the effect of electrical noise and one-bit time domain normalized to remove the contribution from microearthquakes (see Bensen et al., 2007). A cross-correlation window length of 10 s is used with the resulting waveforms selectively stacked (based on crusher activity) into 10 min long blocks. The result is 5,760 CCFs for each sensor pair over the 40 day period.

When the persistent sources operate intermittently in time (such as the ore crushers), selective stacking of the individual CCFs can greatly simplify the process of interpreting and making measurements from the final stacked CCFs through isolation of the contribution from a specific source. Selective stacking is accomplished using a template matching approach where the templates are created from a cross-correlation function for a single sensor pair. Since the crusher locations are known, we can identify lag time windows where each respective S × S contribution in the template CCF should appear based on the difference between the two crusher-sensor travel times. Note that in cases where the source distribution is unknown, it can easily be determined by beamforming using the CCFs themselves (see Dales et al., 2017). These windowed signals, which represent the characteristic waveforms for each crusher, are used as the templates and are then correlated with their respective portions of each CCF in a semicontinuous fashion, results for which can be seen in Figure 2 (right). We associate high correlation value with active crushing to selectively stack periods where each crusher is active. To demonstrate the cave front tracking technique, we restrict ourselves to only using CCFs from periods when the blue crusher is active.

Figure 2

Individual cross-correlation functions (10 s window length) computed for a single sensor pair over a (bottom left) 35 min period and (top left) stacked. Since crusher locations are known, we build three templates (color coded for each crusher, respectively) from the stack. (right) The result of correlating the templates with their respective portions of each individual CCF. These values serve as a proxy for relative crusher activity at any given time. Reproduced from Dales et al. (2017).

The next step is to measure temporal changes in the CCFs for each sensor pair over the 40 day period. We expect crusher-sensor travel times to increase for those rays which are nearby or intersect the growing cave. Travel time changes are measured using a simple marching method which follows an initially selected local minimum or maximum in the CCF over time. We found this type of method to be robust (compared to correlation based methods) when dealing with waveforms that undergo strong qualitative changes over time. In this monitoring case, where we are only concerned with a targeted volume, it would be inappropriate to use more sensitive measurement techniques (e.g., MWCS Brenguier et al., 2008; Poupinet et al., 1984) which measure changes in bulk properties by exploiting the multiply scattered coda. In addition, we do not require subsample precision since the travel time changes caused by cave growth should be on the order of several percent. Nevertheless, there is still valuable information on cave growth contained in the coda although it is more difficult to extract and interpret. For example, qualitative changes (e.g., breaks or new branches) in the coda would indicate that the cave has interfered with a certain multiply scattered path. With enough of these measurements it should be possible to more precisely locate where changes have occurred in the rock mass (see Larose et al., 2015).

3 Results and Discussion

As expected we see no significant changes in the waveform of the reference pair (Figure 3, left) as the direct crusher-sensor raypath should not be affected due to its distance from the cave. In comparison, the CCF for the sensor pair S1-S5 undergoes significant qualitative and quantitative changes over time (Figure 3, right). Zooming in on the S × S portion of the waveform for this sensor pair (Figure 4) reveals a clear moveout of the signal which we interpret as the additional travel time incurred by the direct S wave having to now partially circumvent the cave. This additional travel time is equivalent to ∼40 m of additional propagation distance at a velocity of 3,200 m/s, consistent with the estimated changes in cave geometry with respect to this raypath.

Figure 3

Comparing CCFs for two sensor pairs (S1-S2 and S1-S5) over 40 days. For both pairs the CCFs have been selectively stacked to isolate periods where the blue crusher is active. Dashed lines indicate where we expect to see the P and S arrivals assuming straight raypaths and homogeneous velocities of 3,200 and 5,600 m/s, respectively. Note that only positive lag times are shown here as we do no expect any arrivals at negative lag times given these source-sensor geometries. Pink box shows lag time window where we make measurements in Figure 4.

Figure 4

(left) Cross correlations for the S1-S5 sensor pair over 40 days zoomed in on the main wave packet outlined in Figure 3). We follow a minimum in the CCF using a simple marching method (dashed line) to obtain the travel time change. (right) Cartoon example comparing estimated original raypath (solid line) with new raypath (dashed line) assuming additional travel time is due to path length increase.

The same measurements for all crusher-sensor raypaths over the 40 day period are shown in Figure 5. The interpretation of these changes is intuitive when looking at the raypaths with respect to the cave geometry. Since the purple raypath already intersects the cave on day 0, it exhibits travel time changes throughout the whole 40 day period. Comparing this with the blue raypath, significant travel time increases only start to be seen around day 20, the time at which the cave has grown high enough to begin affecting the ray. Finally, the small steady increase in the orange and green path lengths is most likely caused by lateral cave growth. Although we interpret the travel time increase as purely path length increases, it could also be partly due to a decrease in the bulk velocity of the rock (due to fracturing or a decrease in stress as shown in Olivier & Brenguier, 2016; Olivier, Brenguier, Campillo, Roux, et al., 2015).

Figure 5

(top) Geometry of the crusher-sensor raypaths with respect to the cave. (bottom) Travel time changes measured along each respective path. Secondary y axis shows path length change assuming additional travel time is purely due to path length increase.

In addition to the quantitative changes, the cross-correlated waveforms also exhibit interesting qualitative changes. One example is a splitting (or branching) effect of a peak in the CCF as the cave grows directly through the associated crusher-sensor raypath (Figure 6 near day 27). We believe that this effect is due to the waves, which previously traveled directly between crusher and sensor, now propagating around both sides of the cave with slightly different travel times. In general, these qualitative changes prove difficult to interpret and will require a detailed comparison with synthetics. Once we can confidently interpret our measurements the next step will be to estimate the cave shape in near real time.

Figure 6

CCFs for sensor pair S1-S6 showing interesting branching behavior as cave grows through the blue raypath. This effect could be due to the waves now propagating around both sides of the cave with slightly different travel times.

Although we have demonstrated this technique in an industrial environment, it should extend to any environment where persistent sources exist. For example, perhaps volcanic tremor (Ballmer et al., 2013; Droznin et al., 2015) could be used to detect expansion of the volcanic edifice, an eruption precursor. Other potential natural seismic sources include bubble cavitation in hydrothermal systems (Vandemeulebrouck et al., 2013) as well as microseisms and storms (Gerstoft et al., 2008; Shapiro et al., 2006; Zhang et al., 2010).

This technique is best suited for sources with either fixed locations (e.g., crushers) or stable time-averaged locations (e.g., hydrothermal bubble cavitation will occur randomly but within a fixed volume) but could also be extended to nonstationary sources (e.g., migrating storms) as long as they can be well localized at each time step. For example, any changes in travel time difference which deviate from theoretical changes (calculated from the change in source position) would indicate a changing medium. The cross-correlation window length in this case becomes very important and will depend on the source velocity. Care must also be taken in interpreting measurements as the source-sensor raypaths would be continually sampling different medium. In summary, for a moving source there will be many trade-offs and optimal processing will depend on the specific case (e.g., source-sensor geometries, source velocity, source strength, and desired measurement sensitivity).

4 Conclusion

We have shown the potential of using cross correlations of time periods where multiple persistent sources (ore crushers) are active to monitor temporal changes in the rock mass (tracking a propagating block cave). To isolate the contribution from a single crusher (and facilitate interpretation), a template matching approach was used to selectively stack CCFs based on relative crusher activity. From the resulting CCFs, a simple marching method was used to measure travel time changes in these waveforms over the 40 day period. We attribute these travel time changes to the additional path length incurred by the crusher-sensor raypaths having to circumvent the growing cave. Although we have shown an example from an industrial environment, this technique should extend equally well to persistent natural sources such as volcanic tremor, hydrothermal bubble cavitation, and microseisms.

Acknowledgments

Thanks to IMS research patrons (A-CFT) for supporting this research. This work was funded by Natural Science and Engineering Research Council of Canada through Discovery grant 418288-2012 and Engage grant EGP 469949-14 to P. A. The cross-correlation functions used to produce the results in this paper can be found as Data Set S2 in the supporting information.