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J.B. Rittgers, A. Revil, T. Planes, M.A. Mooney, A.R. Koelewijn, 4-D imaging of seepage in earthen embankments with time-lapse inversion of self-potential data constrained by acoustic emissions localization, Geophysical Journal International, Volume 200, Issue 2, February, 2015, Pages 758–772, https://doi.org/10.1093/gji/ggu432
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Abstract
New methods are required to combine the information contained in the passive electrical and seismic signals to detect, localize and monitor hydromechanical disturbances in porous media. We propose a field experiment showing how passive seismic and electrical data can be combined together to detect a preferential flow path associated with internal erosion in a Earth dam. Continuous passive seismic and electrical (self-potential) monitoring data were recorded during a 7-d full-scale levee (earthen embankment) failure test, conducted in Booneschans, Netherlands in 2012. Spatially coherent acoustic emissions events and the development of a self-potential anomaly, associated with induced concentrated seepage and internal erosion phenomena, were identified and imaged near the downstream toe of the embankment, in an area that subsequently developed a series of concentrated water flows and sand boils, and where liquefaction of the embankment toe eventually developed. We present a new 4-D grid-search algorithm for acoustic emissions localization in both time and space, and the application of the localization results to add spatially varying constraints to time-lapse 3-D modelling of self-potential data in the terms of source current localization. Seismic signal localization results are utilized to build a set of time-invariant yet spatially varying model weights used for the inversion of the self-potential data. Results from the combination of these two passive techniques show results that are more consistent in terms of focused ground water flow with respect to visual observation on the embankment. This approach to geophysical monitoring of earthen embankments provides an improved approach for early detection and imaging of the development of embankment defects associated with concentrated seepage and internal erosion phenomena. The same approach can be used to detect various types of hydromechanical disturbances at larger scales.
1 INTRODUCTION
Hydromechanical disturbances in water-saturated or partially saturated porous media generate both seismic and electrical disturbances that can be remotely detected and analysed to monitor remotely these processes (Moore & Glaser 2007; Revil 2007). These electrical disturbances are generated by the relative displacement of the pore water with respect to the skeleton of the porous material in presence of an electrical double layer coating the surface of the solid-water interface (e.g. Revil & Mahardika 2013). Haas et al. (2013) demonstrated recently that electrical disturbances associated with fracking events in a porous block can be inverted to localize spatially and in time the source of these events. Mahardika et al. (2012) developed a stochastic algorithm to jointly invert seismic and electrical signals associated with seismic source in a porous material characterized by a moment tensor. In this paper, we are interested to develop a new approach to jointly combined passive seismic and electrical signals to localize and image a spatially distributed source current field associated with slowly developing hydromechanical processes. We focus in this paper on an application associated with internal erosion in earthen levees and dams, but our approach is very general and can be used to detect and monitor various types of hydromechanical processes in the Earth's crust.
Earthen levees and dams constitute a major category of modern-day aging infrastructure that offer critical functionalities, including flood protection, fresh water transport and supply and energy production (Mooney et al.2014). In the Netherlands, which comprises about 42 000 km2 of landmass, approximately 25 per cent of this region is below mean sea level and 65 per cent of the country would be flooded or susceptible to regular flooding in the absence of current levels of protection from the sea and rivers (Wesselink et al.2007). Protection is provided by 3200 km of dykes, dams and levees along the main water bodies and 14 000 km of dykes and levees along smaller waters. For certain stretches of dykes, the inundation risk accepted under Dutch law may be as low as 1:100 000 yr–1. The high levels of economic and social risk associated with dam and levee failure creates a need for early and more precise remote detection, imaging and monitoring of poorly performing and elevated risk sections of earthen embankments. This motivates the work presented below, where we employ a combination of non-intrusive passive geophysical monitoring techniques to achieve this goal.
Considering the many challenges of active near-surface geophysical techniques, including the time of acquisition, cost, power consumption and temporal sparsity, passive data collection schemes are perhaps better suited for large-scale and long-term monitoring of embankments (e.g. Bolève et al.2009, 2012). In some cases, active source near-surface geophysical methods demand too much time for robust dataset collection, prohibiting their application to imaging of quickly dynamic processes. The current study focuses on combining the use of the passive seismic and self-potential techniques.
Seismo-acoustic monitoring has many applications, attempting to localize natural or anthropogenic sources of seismic energy such as hydraulic fracturing events, earthquakes, sustained and localized natural sources of low-frequency and narrow-band surface wave energy, and acoustic emission events associated with concentrated seepage phenomena (Koerner et al.1976; Talwani 1984, 1997; Buck & Watters 1986; Shapiro et al.2006; Bolève et al.2012; Rinehart et al.2012; Akbar et al.2013; Xia et al.2013). Similarly, the self-potential monitoring technique has many geophysical applications, where source current densities are generated by a variety of cross-coupled flow phenomena, as discussed in detail by Revil & Linde (2006), Sheffer (2007) and Revil & Jardani (2013). However, one limitation of the self-potential technique (and other potential field methods) involves the non-uniqueness of the inversion process, where the application of appropriate model constraints is of particular difficulty (Kim 2005). Recent efforts have been made to improve spatio-temporal model constraints, such as depth weighting, model compaction and by incorporating multiple geophysical datasets into static and time-lapse inversion schemes (Kim et al.2009; Karaoulis et al.2011, 2014; Doetsch et al.2012; Caterina et al.2014; Supper et al.2014; Zhou et al.2014).
In this study, we extend the use of passive seismic monitoring of embankments by introducing a new 4-D acoustic emissions source localization algorithm, in order to spatio-temporally image discrete acoustic emissions events, and to help constrain the self-potential inversion process. Assuming that both techniques are sensitive to the same dynamic phenomena of concern (e.g., concentrated seepage and internal erosion processes that precede levee failures), we remove the sensitivity of self-potential model constraints to correlated noise (and any interpretation bias therein) by utilizing the independent results of acoustic emissions localization to formulate model constraints. Similar to the work of Legaz et al. (2009) and Vandemeulebrouck et al. (2010), we use passive seismic and self-potential monitoring to detect and image a subsurface phenomenon that both passive techniques are sensitive to. However, we extend this approach by utilizing the acoustic emissions localization results to help constrain and improve resultant models of source current density obtained from the inversion of self-potential data. While we only take this approach to develop static spatial constraints in this study, the technique can easily be extended to guide the incorporation of active space-time constraints to the self-potential (or other data type) inversion process.
The combination of passive seismic and self-potential techniques in this study is motivated by observations of acoustic emissions that may precede and occur simultaneously with concentrated seepage and any associate self-potential signatures (see Rinehart et al.2012). In addition to the relatively high-frequency acoustic emissions identified by Koerner et al. (1976) to be associated with turbid flow within fully saturated porous media, several examples of concentrated seepage-related phenomena that can produce acoustic emissions events may exist. These include cracking and collapsing of materials immediately adjacent to piping features during arching and redistribution of overlying lithostatic or engineering-induced stresses, suffusion of sediments that leads to non-laminar flow within open piping features, turbulent flow and bubbling of water and sediments at the outflow of a piping feature or sand boil, surface scour processes within piping features, small-scale slope stability failures and slope-creep events resulting from increased saturation and pore fluid pressures, and Haines jumps as discussed by Morrow (1970) that may occur in the vadose zone directly adjacent to or above concentrated seepage pathways.
We apply this approach to passive seismic and self-potential monitoring data recorded during a 7-d full-scale levee embankment failure experiment referred to as the ‘IJkdijk’ test (pronounced ‘ike-dyke’ and Dutch for ‘calibration levee’). In order to demonstrate the added benefit of merging the two passive monitoring techniques, we compare three 4-D self-potential models obtained by incorporating the same prior information while imposing three different spatial constraint scenarios: (1) no added spatial constraints, (2) elevation-based depth weighting from additional prior information and (3) added spatial constraints from acoustic emissions localization histories. For the sake of concise demonstration of this approach to merging two passive geophysical techniques, we apply the process to three time steps of self-potential data. These three time steps were carefully selected in order to encompass the onset and development of a self-potential anomaly related to concentrated seepage that was visually observed to develop around 100 hr into the 7-d experiment near the downstream toe of the test levee. The results are then validated by comparison to independent visual observations made during the IJkdijk test.
2 IJKDIJK EXPERIMENT
The IJkdijk testing program comprised a series of full-scale levee embankment failure experiments conducted from 2007 to 2012 on a special test site in the northeast of the Netherlands. This test site has been extensively described by van Beek et al. (2011), Zwanenburg et al. (2012) and Koelewijn et al. (2013). The testing program was designed and organized by Deltares, Netherlands, and funded by Dutch government entities and several international commercial and university participants. Goals of the IJkdijk testing program included: (1) the construction and testing of physical embankment models for various failure modes, in order to verify semi-empirical numerical models for slope stability and internal erosion phenomena of concern and (2) to provide a test facility for validation of various sensing technologies, including in-situ measurement systems, remote sensing and geophysical techniques. The geophysical data presented herein were collected during the final IJkdijk experiment at the site in Booneschans in 2012 September.
The IJkdijk structure consisted of an approximately 28-m-long (at the crest) and 3.6-m-tall high-plasticity clay embankment constructed in two compacted lifts over a 3-m-thick foundation of saturated sand, and was built across an impermeable geomembrane-lined basin, forming a hydraulically isolated upstream reservoir and a constant-head downstream reservoir with gauged outlet works (Koelewijn et al.2014). This physical configuration was chosen to induce concentrated underseepage and the formation of internal erosion and open seepage channels referred to as ‘pipes’ within the sand foundation near the clay/sand foundation contact. A permeable geotextile membrane product was installed vertically across the foundation contact and along the entire length of the levee near the downstream toe of the embankment in order to test the material's ability to arrest backward propagation of internal erosion (Fig. 1).
During the experiment, the upstream reservoir was filled with filtered water in stages, as to simulate realistic flood or storm-surge hydraulic loading events. This was carried out until a critical hydraulic gradient was established and concentrated seepage and internal erosion was achieved for an extended period of time (Fig. 2). Water elevations and pore water pressures were monitored during the experiment using an array of piezometers installed in situ during construction. At approximately 90 hr into the experiment, concentrated and sustained seepage near the centre of the downstream toe began to form, resulting in the development of a self-potential anomaly at approximately 99 hr, and liquefaction and slumping of the embankment materials in this area at approximately 110 hr (Fig. 3)
3 BASELINE DATA AND ANALYSIS
Fig. 1 depicts the approximate locations of baseline tomography data collected across the downstream half of the IJkdijk levee. Here, compressional-wave (P wave) seismic tomography and direct current (DC) electrical resistivity tomography (ERT) data were collected along three collinear transects positioned across the downstream half of the test levee. These active data were recorded only while access to the levee was permitted prior to hydraulic loading of the structure.
P-wave tomography data were collected across linear arrays of 24 vertical axis geophones exhibiting 40 Hz centre frequency, using a 0.25 ms sample interval, 24-bit digitization and zero gain. A combination of dipole–dipole and Wenner array ERT data were collected along each transect with an ABEM resistivity meter, using 32 stainless steel electrodes, a constant 200 mA transmitter current, 2.6 s transmission time, and a rms data quality threshold of 1 per cent. Arrival times of P-wave energy for each source–receiver pair were digitized and inverted using an L2-norm (smooth-model), Tikhonov regularization and the 2-D multistencil forward marching method of curved ray tracing for each tomogram (Tikhonov & Arsenin 1977; Hassouna & Farag 2007). The RES2DINV program was used to perform inversion of the ERT data, which employs a smoothness-constrained least-squares inversion approach (Sasaki 1992).
The resultant models of P-wave velocity and electrical resistivity were then interpolated onto regular 3-D grids bounded by the spatial extent of the test levee for use in performing acoustic emissions localization and modelling of streaming source current densities. Fig. 4 shows example P-wave velocity (a) and electrical resistivity (b) tomograms obtained for baseline data collected along the crest of the test levee. While there is some difference seen between the estimated construction boundaries and the recovered baseline models shown in Fig. 4, the two models share similar structure and spatial gradients in their independently recovered model parameters. While the baseline data were only inverted in 2-D, no apparent 3-D effects were observed in the results. This is likely due to the overall homogeneous distributions of resistivity and velocity within the clay embankment, and the perpendicular orientation of the survey lines relative to the dipping abutment interfaces.
4 MONITORING DATA AND ANALYSIS
4.1 Passive seismic monitoring
Fig. 1 depicts the locations of geophones installed on the levee for monitoring purposes, where each sensor was buried approximately 0.25–0.75 m below the embankment surface to maximize coupling and sensitivity to signals of interest while minimizing the negative impacts of random and high-energy vibrations from wind and rain. The same seismic equipment utilized for P-wave tomography was used for the purpose of passive seismic monitoring data acquisition. Here, the seismic system recorded nearly continuously during the 7-d test, utilizing 16 s record lengths with approximately 4 s downtime between records. A sampling interval of 0.25 ms was used for days 1–4 of the test, and 1.0 ms sampling interval was used for the last 3 d of testing due to software issues. In this fashion, the majority of seismic energy propagating across and within the IJkdijk levee was recorded within the frequency band of approximately 10–250 Hz. The data were subsequently filtered by applying a 150 Hz low-pass filter and a series of notch filters designed to remove persistent electrical noise and associated harmonics.
4.2 Acoustic emissions localization
In addition to anthropogenic seismic events external to the embankment, spatially variable and temporally intermittent-to-persistent acoustic emissions events occurring within the levee were identified in the passive seismic data, similar to those identified by Rinehart et al. (2012), which were not accounted for by coincident human activities or weather-related phenomena. In this study, localization of these acoustic emission event sources was achieved via a new modified grid-search algorithm, similar to those employed by Xia et al. (2013) and Shapiro et al. (2006). Here, a staggered horizontal grid of 88 possible acoustic emission source locations was populated across the clay–sand interface directly below the passive seismic array. The 88 candidate source locations were evenly populated across this staggered grid using a 1.5 m in-line spacing and a 0.75 m cross-line spacing, resulting in an approximate 1 m spacing between nearest-neighbour source points. The choice of source point spacing is somewhat arbitrary, but comes with a trade-off between computational cost and resolution of the localization results. The source spacing could be further refined if desired in subsequent analysis based on initial results. Using these coordinates, along with known coordinates of the monitoring geophones and the interpolated velocity field obtained from baseline tomography surveys, curved-ray tracing was performed for each source–receiver pair. The calculated arrival times of P-wave energy at each geophone for each source location were then time-shifted as to zero the earliest arrival time for each source candidate location. While the assumption that most acoustic emission sources would be located along the clay–sand interface is made, and only a horizontal 2-D grid across this plane was used for this study, the technique can be extended to incorporate a 3-D distribution of candidate locations.
In eq. (1), windowed data containing some seismic event will exhibit a large maximum amplitude relative to background noise levels. Additionally, the application of time-shifts |${\boldsymbol \tau }_{(i,n)}$| for a good candidate acoustic emission source location will flatten a given seismic event, resulting in a relatively small sum of the residual cross-correlation lag-times Tmax . The output of this algorithm, having SI units of (V S−1), is conceptually similar to the energy values output by the brute-force methods applied by Xia et al. (2013), and Shapiro et al. (2006), where high values of Es(i, t) correspond to a high likelihood of a localized seismic event occurrence at a given time and candidate source location. For each 1 s time step, Es(i, t) reveals the locations of any seismic energy originating within the grid as a focused anomaly, and shows a more broad projection of Es(i, t) values in the vicinity or direction of sources located outside search grid. The focusing of Es(i, t) anomalies for acoustic emission sources within the grid depends on the accuracy of the velocity model and ray tracing approach used for calculating |${\boldsymbol \tau }_{(i,n)}$|. A general outline of how this algorithm can be applied to embankment monitoring is presented in the flowchart on Fig. 5.
Fig. 6 presents two example results of the localization algorithm applied to 16 s passive seismic data files that contain both anthropogenic events and enigmatic acoustic emissions events. Here, Fig. 6(a) shows a spectrogram for seismic files recorded 70.16–70.72 hr after the start of the experiment, that is characterized by a long period of quite background noise followed by a period of large amplitude anthropogenic noise from activity on the left abutment of the levee. Two selected seismic files are indicated on the spectrogram, where Figs 6(b) and (c) show detailed views of selected seismic events propagating across the monitoring array at times T1 and T2, respectively. Here, approximate arrival times are indicated with red lines. Finally Fig. 6(d) shows two 2-D colour contour plots of the 88 Es(i, t) values averaged and normalized for each extracted 16 s data file, where the approximate source location is indicated with a red star in both cases. As we see here, the new proposed algorithm successfully targets the source locations in each case.
Once Es(i, t) was calculated for the duration of the experiment, a median absolute deviation (MAD) weighted average of these values was calculated for each search gridpoint for all times preceding the development of the self-potential anomaly. By averaging values of Es(i, t) in this way, we create a static spatial map of sustained and spatially coherent acoustic emission source localizations preceding the self-potential anomaly and visual development of concentrated under-seepage and internal erosion phenomena, while suppressing more spurious sources such as wind and rain or anthropogenic vibrations. We refer this averaged set of values as Es(i) (Fig. 7).
In this experiment, AE events associated with the concentrated seepage near the downstream toe are seen to develop in a spatially and temporally coherent manner, where AE events are seen to increase in frequency throughout the experiment within the general vicinity of developing seepage and prior to tow liquefaction. The observed spatial coherency of Es(i, t) was conducive to the use of the MAD weighted averaging, helping to reduce the more spurious/random anthropogenic sources when calculating Es(i) and the final SP model parametrization penalties discussed below. For other applications exhibiting less spatio-temporally coherent AE event distributions, a more complex approach to isolating non-anthropogenic events of interest, such as multidimensional clustering, may be justified or required.
4.3 Self-potential monitoring
Seepage through or beneath an earthen embankment (in cases of charge at the surface of the minerals is negative) will typically create a dipolar or bipolar self-potential signature with a positive pole on the downstream side and a corresponding negative pole on the upstream side. The negative charge on the mineral surface is usually expected for clay-minerals from potentiometric titrations and electrical double layer theory. In order to image subtle fluctuations in the electrical field resulting from fluid flow through and below the IJkdijk structure, a multiplexed self-potential system was implemented. This system consisted of a laptop computer connected via Ethernet to a Keithley 2701 digital multimeter (DMM) with multiplexed cards, supporting a total of 80 analogue sensor input channels (see Jardani et al.2009 for a field application of this equipment to the self-potential monitoring of pumping tests). The DMM was connected to 74 Pb-PbCl non-polarizable electrodes, with 17 electrodes installed across the upstream face and 57 electrodes installed across the downstream face of the levee. A reference electrode was installed within the left abutment of the test facility. Due to equipment issues, only the downstream electrodes were used for the duration of the experiment, and utilized for analysis and modelling presented herein (Fig. 1). This array was designed to capture any voltage fluctuations associated with streaming current, in order to invert these fluctuations for source current distributions related to the formation of preferential fluid flow pathways.
The self-potential electrodes were installed approximately 0.75 m below ground surface to minimize diurnal temperature fluctuations and associated drifts of the electrodes, and to improve the proximity of the electrode array to any possible seepage pathway locations. During steady-state conditions prior to the experiment, 24 hr of baseline self-potential data were recorded to characterize electrode drifts for the purpose of removing this drift from the monitoring data. During the experiment, the near-surface thermal gradient was monitored for a 24 hr period, and temperature fluctuations at the nominal electrode depth were negligible. Data acquisition parameters were configured to sequentially cycle through each electrode and record a self-potential measurement each 0.5 s, enabling the voltage distribution across the levee to be imaged approximately every 30 s throughout the 6-d test. These data were then linearly interpolated to common time intervals for processing and modelling.
4.4 Nature of the self-potential signals
Here, the right-hand side of eq. (5) represents the self-potential source-term (e.g. streaming current), and the left-hand side represents the self-potential response in the presence of electrical conductivity distribution σ. In this study, σ is obtained by 3-D interpolation of the baseline 2-D ERT modelling results discussed in Section 3 above. For the relatively short duration of this particular experiment, the saturation front within the (low permeability clay) embankment is not expected to have changed significantly. Similarly, the changes in porosity within the underlying sand layer are not expected to have had a significant influence on electrical conductivity distributions, to the point of adversely affecting self-potential models. However, these factors may be an issue for longer-term monitoring efforts, and may warrant the collection of several baseline resistivity datasets during different stages of hydraulic loading. This approach would allow for the incorporation of time-varying conductivity in the forward modelling of self-potential data, where an appropriate conductivity distribution can be selected for a given state of hydraulic loading prior to modelling of a specific time step of self-potential data.
4.5 4-D Self-potential modelling
Our goal is to apply a dipole based inversion algorithm in an effort to recover the 3-D vector distribution of source current JS throughout the downstream-half of the levee and foundation sand, in order to image the major causative regions of electrical disturbances observed in the self-potential data. In other words, we look for to invert directly for source current density JS responsible for the observed self-potential disturbances (see Jardani et al.2008), and at various time steps as discussed by Kim et al. (2009) and Karaoulis et al. (2014) for the electrical resistivity problem. The determination of the source current density distribution in space and time should allow to image the focusing of the flow in the dam over time.
In eq. (8), Wm is a 3M × 3M matrix operator that acts to regularize model mt, and is designed with two parts: (1) a diagonal matrix that enforces model smallness or flatness and (2) second-order derivative (Laplacian operator) that enforces model smoothness. Additionally, there is a third term in ϕ(mt) composed of a first-order derivative (gradient operator) that imposes temporal smoothness in recovered model parameters for adjacent time steps. This term is weighted by a second Tikhonov regularization factor αt = β/5, which is a pre-determined ratio as discussed by Kim et al. (2009).
4.6 Self-potential model constraint using acoustic emissions
Vector components . | Smallness . | Spatial smoothness . | Temporal smoothness . |
---|---|---|---|
Jx | ax = 10, Ps(m) = f(x, y, z) | ax = 1, axx = 1 | αt = β/5 |
Jy | ay = 1, Ps(m) = f(x, y, z) | ay = 10, ayy = 2 | αt = β/5 |
Jz | az = 5, Ps(m) = f(x, y, z) | az = 5, azz = 1 | αt = β/5 |
Vector components . | Smallness . | Spatial smoothness . | Temporal smoothness . |
---|---|---|---|
Jx | ax = 10, Ps(m) = f(x, y, z) | ax = 1, axx = 1 | αt = β/5 |
Jy | ay = 1, Ps(m) = f(x, y, z) | ay = 10, ayy = 2 | αt = β/5 |
Jz | az = 5, Ps(m) = f(x, y, z) | az = 5, azz = 1 | αt = β/5 |
Vector components . | Smallness . | Spatial smoothness . | Temporal smoothness . |
---|---|---|---|
Jx | ax = 10, Ps(m) = f(x, y, z) | ax = 1, axx = 1 | αt = β/5 |
Jy | ay = 1, Ps(m) = f(x, y, z) | ay = 10, ayy = 2 | αt = β/5 |
Jz | az = 5, Ps(m) = f(x, y, z) | az = 5, azz = 1 | αt = β/5 |
Vector components . | Smallness . | Spatial smoothness . | Temporal smoothness . |
---|---|---|---|
Jx | ax = 10, Ps(m) = f(x, y, z) | ax = 1, axx = 1 | αt = β/5 |
Jy | ay = 1, Ps(m) = f(x, y, z) | ay = 10, ayy = 2 | αt = β/5 |
Jz | az = 5, Ps(m) = f(x, y, z) | az = 5, azz = 1 | αt = β/5 |
5 RESULTS
Three independent inversion approaches were taken to recover the 4-D distribution of streaming source current densities (Js). In all three cases, the same smoothness constraints were employed based on prior information about the experiment. However, we compare models recovered using (1) no additional spatial constraints (Ps(m) = I in eq. 10), (2) incorporation of additional prior knowledge with depth-weighting (smallness) based on vertical distances of model parameters from Z = 0 m (clay–sand interface) and (3) spatial constraints (smallness) applied to model parameters with Ps(m) penalties as discussed above. In the second approach, the vertical distances of model parameters from Z = 0 were normalized between 1 and 2 to apply less penalty to parameters close to Z = 0, and more penalty to parameters far from this interface. These elevation-based penalties serve to replace Ps(m) in eq. (10). The same approach to distance-based depth weighting was used to extrapolate Ps(m) values from the Z = 0 plane, taking the assumption that most fluid flow will occur near or at this interface (Fig. 8).
Fig. 9 presents the real and recovered self-potential data plotted for the three selected time steps (99.6, 100.4 and 101.1 hr after the start of the experiment). For each time step, each of the three inversion constraint approaches recovers the self-potential data equally well. For each inversion, an optimal value for β was determined via the L-curve approach to Tikhonov regularization (see Jardani et al.2008 for an application of the L-curve to the self-potential problem), in order to minimize eqs (6) and (10) without over or underfitting the data.
For the sake of having a meaningful comparison between the three independent sets of recovered models, a similar data misfit should be obtained for each model at a given time step. Here, the mean squared error (data misfit) changes for each time step, due to the corresponding changes in observed data magnitudes. While the L-curve approach was used to guide the final inversions in this study, the target data misfits for each time step (T1, T2 and T3) were approximately 0.2, 1.0 and 2.0 mV, respectively.
While we see a good fit to the observed data in each case, Fig. 10 indicates significant differences in recovered models using the various spatial constraints. Here, the model recovered using acoustic emissions localization constraints is deemed superior, where the recovered streaming source current density vector field follows a more realistic pattern of fluid flow, concentrating and emanating upwards at the location of visually identified concentrated seepage and toe liquefaction. While the other two models recover the self-potential data equally well, they are characterized by extensive distributions of dipoles that support the recovered data, but do not follow reasonable flow paths (e.g. perpendicular to the hydraulic gradient, along model domain edges and within the low-permeability clay material). Fig. 11 presents the same plots of the recovered models for only T3, expanded for better comparison. In Figs 9 and 10, the magnitude of the source current dipoles is normalized for each recovered model, in order to emphasize the spatial distribution of dipoles recovered using each approach to model constraint.
In order to better compare the recovered models for each time step (T1–T3), the magnitudes of recovered dipole were calculated and plotted in Fig. 12. In each case, we see an increase in modelled source current density for each time step, however, the spatial distributions of source current density varies between the two methods. Here, the first two approaches are seen to parametrize the model space in a more diffuse fashion (Fig. 12a), and with spurious distributions of source current densities that do not corroborate visual indicators of seepage (Fig. 12b), while the 4-D model recovered by utilizing the acoustic emissions localization constraints is seen to parametrize the model space predominantly in the vicinity (and immediately upstream) of the concentrated seepage area near the toe (Fig. 12c).
6 DISCUSSION
Certain ambiguities and limitations of the technique can arise, such as the assumption that acoustic emissions will coincidently occur prior to or simultaneously with concentrated seepage, which may not always be the case. For example, using the spatial constraints posed by the localization results, the first time step model reveals similar parametrization gradients (yet vanishingly small amplitudes) in comparison to later time step models. This is likely the result of the constant spatial constraints, as well as the imposed smoothness in time (temporal constraints) relative to adjacent time steps. One approach for minimizing this effect is utilizing shorter time-windows for averaging localization results prior to a given time step of the inversion process, allowing for independent sets of spatial constraints at each time step by varying parameter c in eq. (9) for different time steps. This later point is of particular importance, as the parameter c used in calculating Ps(m) in eq. (9) dictates the extent to which source current parametrization is constrained to acoustic emission localizations. For example, there is no added constraint from localization results if c = 0. Alternatively, virtually all source current parametrizations will be influenced by localization results if c ≫ 1 and the Tikhonov regularization parameter is not varied accordingly (data misfit is allowed to increase). Here, c could be assigned a dynamic value related to the maximum amplitude of the windowed data, for example.
Additionally, localization results from the method presented herein could be utilized to develop active time-constraints independent of changes seen in preliminary self-potential models recovered statically for each time step, as proposed by the ATC approach in Karaoulis et al. (2011). Furthermore, calculated ratios of spatial correlation scale-lengths for recovered distributions of Es(i, t) could be used to automatically provide scalar values presented in Table 1. Here, spatial patterns in localization results could be exploited to enforce more or less smoothness in a given direction of the model space.
Despite the presence of wet areas seen mid-slope in the photo of Fig. 3, there is likely negligible seismicity and source current density generation associated with this through-seepage, because it is related to very slow crack-flow associated with a ‘lift-line’ created during construction and placement of the clay embankment material. It is apparent that inclusion of acoustic emissions localization results in the spatial constraints applied to the self-potential inversion process helps to confine and guide the modelled Js vector parametrization in the vicinity of the observed concentrated seepage, and to provide a better image of fluid flow beneath the levee.
The approach developed in this study for merging passive seismic and self-potential monitoring data could be useful in other applications, including more generalized infrastructure monitoring efforts or for monitoring fluid injections such as during hydraulic fracturing and proppant injection in oil and gas reservoirs and in geothermal fields. Additionally, the techniques employed here for spatially (and temporally) constraining the self-potential inversion process could be carried out using results from other passive seismic monitoring analyses, such as relative surface wave velocity changes or modelled 2-D/3-D shear wave velocity changes obtained from seismic interferometery and Rayleigh wave dispersion analysis. Finally, results from active monitoring techniques, such as seismic tomography or DC resistivity tomography, could be used in a similar fashion, where changes observed in resulting models could be used to help spatiotemporally constrain the inversion process of self-potential data.
Finally, we want to discuss if this approach or a similar approach could be used for real time monitoring in field conditions. The localization of the acoustic data can be performed in nearly real time using, for instance, cross-correlation techniques that are highly parallelizable. These techniques can be used with an installed sensor network or even a mobile robot to localize in a complex environment the source of any acoustic disturbance with several ‘ears’. The localization algorithm, including prior signal processing such as trace normalization and frequency filters, cross-correlation operations and memory allocation/retrieval for sequentially (1 s) windowed data during a give file scan can be run in equal or less time relative to the seismic record length. This means that the algorithm can be applied to the most recent seismic file recorded to disc while simultaneously collecting the next record. This approach would allow for fast computation and updating of the output penalty matrix with any number of desired characteristics or statistical weights being applied for updating spatio-temporal constraints for self-potential signal inversion. In the self-potential inversion process, the construction of an appropriate kernel matrix is the most computationally expensive step (due to forward models that need to be calculated) but this step can be done prior to the monitoring effort, Consequently, we strongly believe that our approach, with some specific adaptations to speed up the computation time, could be used as a realistic monitoring technique.
7 CONCLUSIONS
Controlled full-scale embankment failure experiments, such as IJkdijk, provided valuable opportunities for validation of various geophysical monitoring techniques and approaches to modelling. In this study, we have shown the effectiveness of passive geophysical monitoring techniques in identifying and imaging hydromechanical disturbances associated with concentrated embankment seepage and internal erosion phenomena. By developing a new modified 4-D grid-search algorithm for localizing seismic sources (applying this algorithm in 2-D + time here), and combining the averaged localization results with the self-potential data inversion process, we have shown that the resulting models of source current density can be better spatially constrained in comparison to the use of only basic prior information. This approach was successful at focusing self-potential model parametrization in the immediate vicinity of observed seepage and the eventual compromise of embankment stability near the down-stream toe of the IJkdijk facility.
Help with organization and logistics, geophysical experimental design and baseline and monitoring geophysical data acquisition was provided by Minal Parekh, Benjamin Lowry and Jacob Grasmick. LIDAR imagery was provided by Benjamin Lowry for comparison with geophysical data. Funding for this study was provided by the National Science Foundation under the SmartGeo Program (Project IGERT: Intelligent Geosystems; DGE-0801692) and the Partnerships for International Research and Education (PIRE) Program (PIRE: Advancing Earth Dam and Levee Sustainability through Monitoring Science and Condition Assessment; OISE-1243539). We thank Deltares and the IJkdijk Foundation for allowing Colorado School of Mines to participate in the 2012 IJkdijk experiment. Finally, we would like to thank the Editor and two anonymous referees for their constructive comments.