Water Resources Research

Imaging rainfall drainage within the Miami oolitic limestone using high-resolution time-lapse ground-penetrating radar

Authors

  • Steven Truss,

    1. Division of Marine Geology and Geophysics, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA
    2. Now at School of Earth and Environment, University of Leeds, Leeds, U.K.
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  • Mark Grasmueck,

    1. Division of Marine Geology and Geophysics, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA
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  • Sandra Vega,

    1. Division of Marine Geology and Geophysics, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA
    2. Now at the Petroleum Institute, Abu Dhabi, United Arab Emirates.
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  • David A. Viggiano

    1. Division of Marine Geology and Geophysics, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA
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Abstract

[1] The vadose zone of the Miami limestone is capable of draining several centimeters of rainfall within a fraction of an hour. Once the water enters the ground, little is known about the flow paths in the oolitic rock. A new rotary laser-positioned ground-penetrating radar (GPR) system enables centimeter-precise and rapid acquisition of time-lapse surveys in the field. Two-dimensional (2-D) GPR time-lapse surveying at a 3-min interval before, during, and after rainfall shows how buried sand-filled dissolution sinks efficiently drain the bulk of the rainwater. Hourly repeated 3-D imaging of a dissolution sink in response to surface infiltration shows how the wetting front propagates at a rate of 0.6–1.2 m/h traversing the 5-m-thick vadose zone within hours. At the same time, some of the water migrates laterally into the host rock guided by stratigraphic unit boundaries. Average lateral propagation measured over a 28-hour period was of the order of 0.1 m/h. On a seasonal time frame, redistribution involves the entire rock volume. Comparing 3-D surveys acquired after wet summer and dry winter conditions shows good GPR event correspondence, but also time shifts up to 20 ns caused by the change of overall water content within the vadose zone. High-precision time-lapse GPR imaging can therefore be used to noninvasively characterize natural drainage inside the vadose zone ranging from transient loading to seasonal variation.

1. Introduction

[2] Subsurface fluid flow in carbonates is often controlled by a highly heterogeneous hydraulic conductivity field resulting from the interplay of small-scale sedimentary structure, diagenetic alteration, and fracturing [Duerrast and Siegesmund, 1999]. Rainfall/water table response times, well drawdown tests, slug tests, pump tests, and tracer experiments exhibit surprisingly high hydraulic conductivities, orders of magnitude higher than those derived from measurements on rock plugs taken from both outcrops and cores [Tidwell and Wilson, 1997]. Three-dimensional connectivity creates preferential flow paths allowing large volumes of water, nutrients, and contaminants to rapidly bypass the less permeable bulk rock volume. For example, in large parts of urban Miami the vadose zone is characterized by oolitic carbonates, where laterally varying small-scale stratigraphy and crosscutting dissolution features control transport pathways [Cunningham, 2004]. Water from heavy summer storms that ponds on the surface to depths of several centimeters disappears within a fraction of an hour. Subsequent to the rapid infiltration, little is known regarding the nature of water flow paths and rates in this complex environment. It is essentially impossible to characterize drainage using standard hydrogeological methods. Traditional investigations rely on interpolation between point measurements (rock samples and borehole tests), and/or low resolution two-dimensional (2-D) geophysical methods (e.g., surface or borehole resistivity and electromagnetic techniques). Even combined, these methods lack the resolution to describe how or where the water is moving on the centimeter to meter scales.

[3] This paper demonstrates how densely sampled and precisely repeated ground-penetrating radar (GPR) surveys can track fluid movement and characterize the subsurface flow regime at a field site in the Miami oolitic limestone. The objectives are twofold. The first is to test which of three end-member conceptual models describing water flow (plug flow, lateral flow, bypass flow) within the Miami oolite are effective in draining large amounts of rainwater into the subsurface. As bypass flow emerges to be the dominant flow regime, the second objective is to image how water enters the subsurface and spreads out in the limestone via infilled dissolution holes. This case study shows field-scale changes in densely sampled 2-D and 3-D GPR time-lapse data in response to water infiltration at decimeter resolution, sourced from both rainfall and artificial injection within a 5-m-thick natural vadose zone.

2. Time-Lapse GPR Method

2.1. Background

[4] Ground-penetrating radar (GPR) can noninvasively detect and image sedimentary structure to depths ranging from 0 m to over 30 m [e.g., Smith and Jol, 1992; Aspiron and Aigner, 1997, 1999; Beres et al., 1999; Corbeanu et al., 2001; Best et al., 2003; Grasmueck et al., 2004; Heinz and Aigner, 2004; Neal, 2004]. Depth range depends on the electrical conductivity of the subsurface material and GPR antenna frequency [Davis and Annan, 1989]. Clay-free matrix, air or fresh water in the pore space, and low signal frequency offer the best conditions for deep GPR imaging. The main cause for GPR reflections are boundaries following changes in water content [Van Dam and Schlager, 2000]. GPR has been successfully used to detect subsurface moisture [Greaves et al., 1996; Van Overmeeren et al., 1997; Gloaguen et al., 2001; Hubbard et al., 2002; Grote et al., 2003; Lambot et al., 2006]. With the sensitivity to changes in water content, GPR has great potential to monitor dynamic changes in the near surface. If a GPR survey is repeated with identical geometry, variations between time series radar images must be due to water movement as the internal geometry of the soil and rock volume remains unchanged. Repeated GPR surveys have tracked fluid flow in laboratory tests and in the shallow subsurface [Brewster and Annan, 1994; Birken and Versteeg, 2000; Endres et al., 2000; Trinks et al., 2001; Tsoflias et al., 2001; Binley et al., 2001, 2002; Versteeg, 2002; Bevan et al., 2003]. These previous studies have the following limitations in defining and characterizing preferential flow in natural environments: (1) Coarse data acquisition: Wider than quarter wavelength profile spacing undersamples the electromagnetic wave field preventing the use of 3-D migration processing to remove out-of-plane reflections and focus diffractions [Grasmueck et al., 2005]. (2) Lab experiments struggle to represent field conditions: Sand box experiments only image a small volume of disturbed soil with interfering GPR reflections from the enclosure walls. (3) Limited access by boreholes: Borehole time-lapse GPR surveys image just the plane between boreholes, providing limited information on the 3-D nature of flow geometry. (4) Difficulty of repeating GPR surveys in the field: Surface time-lapse GPR surveys of field sites are challenged with precise repeatability of the recording locations and data acquisition speed, reducing the ability to detect changes in the subsurface.

[5] Changes in GPR signature due to water flow in the subsurface are visible as amplitude changes and time shifts. Amplitude variations are due to changes in dielectric contrast between layers which alter the reflection coefficient. Within the unsaturated zone, a water content increase often enhances reflectivity contrasts and causes the GPR amplitudes to increase [Nobes et al., 2004]. Time shifts occur because increasing water content results in an increase in bulk dielectric constant which lowers the velocity and hence increases travel time, causing the reflection to appear at later recording times. Even in laboratory experiments [Trinks et al., 2001; Versteeg, 2002] with perfect repeatability and high data density, subtraction of repeated GPR surveys produces strong, spurious amplitude differences in zones unaffected by fluid infiltration. The fluid anomalies cause cumulative time shifts in the data at later two-way travel times, preventing cancellation of difference amplitudes in static zones after the electromagnetic wave has passed a wetted zone. Such time shifts make difference analysis a highly unstable operation [Birken and Versteeg, 2000], requiring frequent survey repetition to minimize time shifts between surveys.

[6] Whereas time-lapse seismic monitoring of hydrocarbon production is becoming widespread and practical [Calvert, 2005], the potential of time-lapse GPR for near-surface applications has not yet been fully realized. Time-lapse GPR imaging of the vadose zone can be used to monitor groundwater infiltration, contaminant migration, leaking pipes, irrigation efficiency, plant root water uptake, and fertilizer distribution. For time-lapse imaging at field sites to become effective, we have developed a new GPR data acquisition system and field procedures addressing the requirements of rapid data collection and centimeter-precise antenna positioning.

2.2. Time-Lapse GPR Data Acquisition at Field Sites

[7] Novel rotary laser positioning system (RLPS) technology was integrated with GPR into a highly efficient and simple to use 3-D imaging system [Grasmueck and Viggiano, 2007]. The new system enables acquisition of centimeter-accurate x, y, and z coordinates from multiple small detectors attached to moving GPR antennae. Laser coordinates streaming with 20 updates per second from each detector are fused in real time with the GPR data. For all the surveys reported here we used a bistatic, shielded 250-MHz GPR antenna and the CU-II control unit (Malå Geosciences) modified for integration with the RLPS. Antenna offset between transmitter and receiver was 0.36 m, and we recorded 602 samples per trace, eight stacks, and a sampling interval of 0.325 ns resulting in a maximum two-way travel time of 196 ns.

[8] For imaging of changes in the near surface it is very important that all repeated surveys are conducted with exactly the same survey geometry. Field tests with 250-MHz GPR antennae by Grasmueck and Viggiano [2005] showed that reoccupation errors of survey positions should be in the range of 1–3 cm. With such precision, subtraction of two “identical” repeat 3-D GPR data sets acquired during static subsurface conditions yields a difference volume with a root-mean-square (RMS) amplitude level 5–10 times lower than the RMS amplitude level in the original surveys. This ensures low repeatability noise and high sensitivity to changes in subsurface water content. For centimeter-precise reproduction of antenna positions during our field surveys we precisely followed a movable string guideline tensioned between two parallel fiberglass measuring tapes anchored in the ground by plastic stakes. As it takes time to acquire each time-lapse data set, survey size and repetition rate are closely linked. In order to determine the GPR survey repetition rates and to obtain a first assessment on where and how fast fluids are flowing, initial surveys consisting of repeated 2-D profiles were conducted. The next stage of our survey strategy involved acquisition of 3-D GPR surveys consisting of densely spaced, parallel 2-D profiles in one direction over areas of suspected preferential flow paths. Full-resolution GPR imaging requires at least quarter wavelength grid spacing in all directions [Grasmueck et al., 2005]. For example, grid spacing for a spatially unaliased 250-MHz GPR survey has to be 10 cm or less assuming 0.1 m/ns electromagnetic wave velocity. By starting a new GPR survey at regular time intervals, and acquiring each survey in the same profile sequence at an average antenna speed of 0.5 m/s, all subsurface points are imaged at constant time intervals. However, there is a time difference between recording the first and the last trace of each GPR survey. As the water is continuously migrating through the subsurface, the wetting fronts imaged in the GPR are not instant snapshots, but are slightly skewed with a linear acquisition time delay.

2.3. Data Processing

[9] All GPR data acquired during a time-lapse survey are processed in exactly the same way. We use a combination of processing modules we developed in LabView (National Instruments) and, where mentinoned, commercially available seismic processing software. The seismic industry standard (SEGY) data format facilitates data transfer between different software applications. The processing steps are as follows: (1) “Data fusion” assigns laser-derived x, y, and z coordinates to each radar trace acquired. As a result, the GPR tracklines can be plotted on a map. (2) “Detrending” compensates for zero time drift due to temperature changes affecting the GPR electronics by automatic picking of first breaks. The spatially smoothed differences between the first break picks and a reference first break time are applied as vertical time shifts to traces. The smothing is applied to reduce the effect of random first break jitter. This step also removes zero time shifts between individually recorded data sets aligning all first breaks to one comon level throughout a survey and also between repeat surveys. (3) The zero time is adjusted by delaying the first break by the time it takes the direct airwave to travel from transmitter to receiver. (4) The “dewow” [Annan, 2003] step removes very low frequency components of the data associated with either inductive phenomena or analog/digital conversion. (5) The same gain curve is applied to all data aquired within a time-lapse series. The gain curve is based on a smoothed Hilbert transform of a representative data volume. (6) Regularization populates an identical bin grid for all surveys with the nearest available trace. For 2-D time-lapse surveys the regularization creates a pseudo 3-D data volume, with one of the horizontal axes displaying the acquisition time of the first trace recorded for each 2-D line. For the 3-D time-lapse surveys a new 3-D GPR data volume is generated for each repeat. (7) Velocity estimates are based on diffraction hyperbola analysis with ReflexW (Sandmeier Scientific Software). For the experiments reported in this paper we analyzed diffractions in the “dry” surveys acquired before rain or infiltration. (8) Normal-moveout (NMO) stretching [Yilmaz, 2000] of the GPR signal traces compensates for the transmitter-receiver offset of 0.36 m. This and the following migration step both use the same constant velocity model. (9) Migration processing is applied to increase the resolution of 3-D GPR data. GPR antennae have a wide-open antenna radiation cone (as much as 60° radiation angle measured from the vertical) which simultanoeusly receives both vertical and side reflections. Migration focuses diffractions and repositions dipping reflections. We did not apply migration processing to 2-D GPR data for two reasons: to clearly show the presence of diffraction hyperbolae indicative of local heterogeneities, e.g., caused by finger flow, and because migration processing requires high-density 3-D GPR data acquired with at least a quarter-wavelength grid spacing in all directions [Grasmueck et al., 2005]. Applying migration to 2-D data produces spurious results. For the 3-D time-lapse data we used the Promax (Landmark Graphics Corporation) 3-D phase-shift migration with a constant velocity model. (10) For analysis of the changes between repeat surveys, corresponding data are either visually compared or subtracted to highlight the differences.

3. Miami Oolitic Limestone Vadose Zone Case Study

3.1. Geological Setting

[10] The oolitic facies of the Miami limestone (Miami Oolite) was deposited as a network of Pleistocene (125 ka) ooid shoals, tidal channels, and seaward barrier bars during an interglacial sea level high-stand, where sea levels were approximately 6–7 m higher than today [Halley et al., 1977; Halley and Evans, 1983]. Modern topography still outlines the paleogeography (Figures 1a and 1b) and consists of a 50-km-long and 10-km-wide elevated coastal ridge extending along Florida's east coast [Hoffmeister et al., 1967]. Our field sites are located along this ridge, in the Coral Gables and Coconut Grove area of Miami, where the topography is highest and therefore the vadose zone is thickest (4–7 m). The Ingraham Public Park offers a 5-m-high vertical outcrop (Figure 2) close to the location of all GPR surveys reported here. The waterway next to the site causes a brackish water table at 5-m depth, limiting GPR imaging to the vadose zone above. Because large excavations were not permitted in the public park, we investigated two ongoing excavations at nearby active construction sites on Galiano Street and Franklin Avenue for fresh exposures of the Miami Oolite and its related dissolution features.

Figure 1.

(a) Map of the Florida peninsula with (b) depiction of the Pleistocene (125 ka) Miami oolitic limestone forming an elevated coastal ridge (redrawn from Halley et al. [1977]). The shapes of the facies distribution are based on the present-day 3-m topographic contour. Study locations included Ingraham Park (IP) and two nearby construction sites on Galiano Street (GA) and Franklin Avenue (FR). (c) Montage of Ingraham Park aerial photographs with street map overlay and locations of outcrop, time-lapse 2-D GPR and 3-D GPR surveys. (d) Enlarged view of rectified aerial photograph taken from a helium balloon with superimposed track lines of the time-lapse 2-D and 3-D GPR surveys. Color coding reflects topography in meters above sea level as measured during the GPR surveys with rotary laser positioning system (RLPS). Track line spacing of the 3-D GPR survey is 0.1 m. Surface depressions related to dissolution sink features can be recognized as darker shades in the grass cover. (e) Line drawing of sink and survey locations with topographic contour lines inside the 3-D GPR survey area. Contour interval is 3.75 cm. Dotted lines indicate additional GPR profiles recorded at 3-min intervals during the 2-D time-lapse experiment to verify drainage through the other sinks in the area (results are not shown in this paper).

Figure 2.

Photograph of the outcrop at the southern end of Ingraham Park. The outcrop was created by the excavation of the (brackish) Coral Gables Waterway. The mottled facies is overlain by cross-bedded oolitic grainstone sets of varying thickness forming the host rock of the vadose zone. Some of the set boundaries consist of well-cemented horizons.

[11] Halley and Evans [1983] described three distinct facies in the Miami limestone: (1) the bedded (cross-bedded oolite), (2) mottled (heavily bioturbated), and (3) Bryozoan facies. Lateral variations within the facies typically occur at a scale of 10 m, and facies of type 1 and 2 are exposed in the outcrop at the southern end of the Ingraham test site (Figure 2). High-energy, prograding ooid shoals with a highly variable internal structure and varying degrees of cementation lie directly upon low-energy, bioturbated, mottled limestone. The ooid shoal deposits display abundant large-scale (up to 1 m between erosive surfaces) cross bedding, often grading down into ripple bedding (1–2 cm foresets in 5–20 cm packets). This highly variable rock structure results in a wide variety of pore sizes ranging from open, centimeter-sized burrows to rocks with no visible porosity when viewed using a hand lens. Rock plugs have shown porosities larger than 40% and an average hydraulic conductivity of 10 μm/s.

[12] Diagenetic processes have increased the degree of heterogeneity. Selective cementation, which often preserves and enhances small-scale sedimentary features, is common [Halley and Evans, 1983]. Large-scale karstic dissolution holes tens of meters across are relatively uncommon, but smaller-scale infilled dissolution holes 1–4 m in diameter and 1–4 m deep are abundant. Several holes that intersect the water table have been observed both at the Franklin and the Galiano construction sites, leading to the concept of “sinks,” which are preferential pathways with the potential to transfer fluids rapidly through the rock mass (Figure 3). Typically the sinks are infilled with a thin layer of dark sandy top soil, with light brown fine quartz sand probably of aeolian origin forming the core. The transition from light brown sand fill into white oolite host rock is via dark brown sand with oolite clasts and a 10–50 cm thick layer of orange/brown-stained altered oolite. The dissolution process generally leaves a large, irregularly shaped contact surface between the sink fill and the surrounding rock, assisting fluid transfer across the interface.

Figure 3.

Sink anatomy exposed on a vertical face at the Galiano construction site. The sink is filled with highly permeable well-sorted fine quartz sand.

3.2. Conceptual Models for Rainfall Drainage

[13] The degree of rock heterogeneity strongly influences the nature of rainwater infiltration, affecting poststorm drainage, groundwater recharge, and pollutant transport in a subtropical climate characterized by short-duration high-intensity rainfalls. Following heavy rainfall, several centimeters of standing water drain completely into the rock mass within 15–30 min at the undisturbed Ingraham site, whereas some newly excavated rock surfaces at the nearby Franklin Avenue construction site retain standing water for several days. Hence the undisturbed Miami oolitic limestone appears to be efficient at draining water from the frequent tropical summer storms, even if some of the individual rock layers are resistant to vertical water movement.

[14] To help explain this dichotomy, three end-member conceptual models describing water flow within the Miami Oolite are illustrated in Figure 4. The three models are (1) plug flow, (2) lateral flow, and (3) bypass flow.

Figure 4.

End-member conceptual models for drainage in the Miami Oolite vadose zone: (a) plug flow, (b) lateral flow, and (c) bypass flow.

[15] 1. In the plug flow model the rainfall enters the ground and travels vertically toward the water table, in a manner independent of stratigraphy. This model assumes that the lateral hydraulic gradient is always small compared with the vertical hydraulic gradient, so that all flow is directly downward. Hence the flow rate within the rock matrix will be a function of the pore size distribution and the hydraulic gradient. This is the model most used in flow simulations, and while it normally suffices on a whole-aquifer scale, it has limitations when applied at field-site scale by not accounting for geological heterogeneity.

[16] 2. In the lateral flow model the rainfall travels along stratigraphic pathways that follow sedimentary structure. This model is dependent on hydraulic conductivity variations, which are controlled by lithology, biological action, and diagenesis. In this case, relatively impermeable zones retard water movement, causing localized pressure head conditions. These provide a hydraulic force which can be sufficient to drive the water in a nonvertical manner, following more permeable horizons situated directly above less permeable ones [Truss, 2004]. Under normal rainfall conditions the water flow obeys Darcy's law, but it is possible that at extremely high loadings sufficient hydrostatic pressure may be available to force water out of the rock matrix and into the centimeter-sized karstic macropores and allow free draining to occur.

[17] 3. In the bypass flow model, storm rainfall flows laterally along the ground surface and fills slight surface depressions above sand-filled dissolution sinks (Figure 3) which provide a rapid pathway to the deeper subsurface. “Flooding” of the sink allows the initiation of large pressure heads which are able to overcome matric pressure and “force” fluids into the surrounding rock. Under these conditions fluids flow at a much greater rate than in the cases of plug flow or lateral flow, possibly initiating non-Darcyan flow under significantly lower rainfall loadings. Once expelled from the sink and into the rock mass, the water flows as per plug or lateral flow.

[18] The true nature of water infiltration is likely to be a continuum between these three end- members, which may vary as rainfall loading and initial saturation values change seasonally. Using repeated 2-D and 3-D GPR surveys we tested the validity of these three models for rainfall and artificial infiltration.

3.3. Rapid 2-D Time-Lapse GPR Monitoring of Rainfall Infiltration

[19] The purpose of this time-lapse 2-D GPR surveying before, during, and after rainfall was to determine which of the three conceptual flow models was the prevalent draining mechanism: whether the water was evenly soaking into the ground, moving along permeable stratigraphic layers, or passing through infilled vertical sinks. In order to capture rapid drainage patterns we acquired a series of repeat radar profiles at 3-min intervals. Initial tests using an odometer wheel to position the GPR measurements along a fixed profile proved to be too inaccurate for data differencing to highlight the changes caused by water infiltration. Repeatability noise due to positioning errors was prevalent. In a second series of experiments we used the new laser-positioned GPR system [Grasmueck and Viggiano, 2007]. For the best repeatability of the GPR profiles we chose straight lines (instead of a curved path) directly crossing over surface depressions to determine if they were active sinks. From the air (Figures 1d and 1e) such depressions can be recognized by their darker shade of green when compared with the surrounding grass. During rainfall, the depressions develop into shallow puddles. We continuously recorded a loop of three profiles, starting a new loop every 3 min, as it took 1 min to record each profile. Results from all three profiles were similar so we selected only the 24-m-long profile 1 crossing depressions S1 and S3 for display in Figures 5, 6, and 7. The first set of repeat GPR lines was recorded on 10 March 2006 in dry conditions, 14 days after the last 37 mm of rain and a total of 117 mm of rain over the last 3 months. The start and end points were permanently marked with survey nails for precise relocation during later surveys. We waited for the first rainfall, which occurred on 23 March 2006 in two showers. The first shower started at 1420 LT, yielding 22.5 mm of rain in 50 min. Another 12 mm of rain followed in a second shower between 1650 and 1710 LT. The continuous recording of GPR profiles started at 1500 LT in 3-min intervals until 2140 LT. Figure 5 shows the same GPR profile recorded before, during, and after the rain. Data processing included all steps described in section 2.3 except the migration step.

Figure 5.

Selection of time-lapse 2-D GPR data (profile 1 in Figure 1e) recorded on 10 and 23 March 2006 in 3-min intervals before, during, and after rainfall. The repeated profile crosses surface depressions S1 and S3. Processing for all profiles is identical with the same gain curve applied and no migration. The velocity used for depth estimates is 0.075 m/ns. The GPR profiles shown were acquired in (a) dry conditions 14 days after the last rain and 13 days before the next rain, (b) toward the end of the first rain shower on 23 March, (c) 12 min after the first rain shower stopped, and (d) 79 min after the end of the second rain shower. This sequence of profiles shows how the GPR signatures change within minutes during and just after the rainfall. The sections just below S1 and S3 show the most pronounced and sustained response. Small white triangles at the surface of GPR profile (Figure 5b) mark the location of small trench excavations used to ground truth the origin of shallow diffractions. Numbers in millimeters are cumulative rainfall amounts measured in two rain gauges deployed on the site during the experiments. The readings from both gauges were in better than 0.5-mm agreement.

Figure 6.

Difference sections corresponding to Figure 5 highlight the changes occurring at the different stages of the 2-D GPR rainfall time-lapse experiment. The sections were computed by subtraction of GPR profiles acquired with a 3-min time gap for Figures 6a–6c and a 95-min time gap for Figure 6d. The strongest difference amplitudes occur below surface depressions S1 and S3, corroborating the hypothesis that rainfall drainage predominantly flows through sinks related to surface depressions.

Figure 7.

GPR time shifts based on picking corresponding reflections on the dry (Figure 5a) and postrainfall (Figure 5d) GPR profiles. (a) Two-way time picks for reflector elements which are part of a continuous unit boundary visible across both profiles. (b) Time shifts computed by subtracting “wet” minus “dry” picks. Positive values indicate delay in reflector two-way time caused by an increase in water content within the material above the reflector. Gaps in the curve represent zones where there were no clear picks on either or both profiles.

[20] The GPR profile recorded before the rain (Figure 5a) shows the subhorizontal layering of the Miami Oolites to depths of 5 m. At the position of the two surface depressions S1 and S3 the shallow (<30 ns) reflection amplitudes are slightly increased, probably due to the higher soil moisture content indicated by the greener grass growing in the depressions. The amplitudes below 30 ns are weakest below the depressions compared with the rest of the profile. As the data are not migrated, the exact boundary of the potential sinks can not be resolved. Figure 6a depicts the corresponding difference section generated by subtracting two profiles repeated within 3 min. The gray scale used for plotting the data is identical for both Figures 5 and 6. As expected for the prerain case, the difference between repeat profiles is small. The difference RMS amplitude level computed over a window of 20–100 ns in Figure 6a is only 9.7% of the original profile RMS level of Figure 5a, which shows the excellent repeatability of the measurements. The weak horizontal bands at the top of the profile are due to clipping of the first arrival amplitudes. As the repeat profiles were recorded in dry conditions, there should theoretically be no change in the GPR signals of geological origin. Therefore the faint difference amplitude patterns of Figure 6a which are related to geological reflectors provide a useful visual measure to help distinguish changes caused by water flow from GPR survey repeatability noise in Figures 6b–6d.

[21] The GPR profile collected in pouring rain (Figure 5b) shows enhanced amplitudes throughout. A similar effect has been observed by Nobes et al. [2004]. The thin superficial fully saturated layer increases antenna coupling. The sinks display the most amplitude enhancement. At the same time, numerous crisscross patterns caused by diffractions develop. The apices of the diffractions are either near the surface or inside the sinks. The cause of these diffractions is likely to be the wetting front with a strong reflection coefficient at the transition from wet to dry material. The diffractions indicate the wetting front to have subwavelength-scale irregularities such as finger flow causing the numerous point scatterers. To determine the cause of the diffractions originating near the surface, we excavated four small trenches (30 cm × 30 cm) through the soil layer until reaching the oolite rock surface. The two trenches at profile positions 7.55 m and 16.75 m with no diffraction patterns revealed a flat, contiguous rock surface with 19–24 cm of sandy soil cover. The other two trenches at profile positions 6.00 and 16.10 m featured 26–33 cm of sandy soil, oolite rubble, tree roots, and an irregular rock surface with finger-sized sand-filled dissolution features. The diffractions invisible in dry conditions and appearing during rainfall are therefore an indication of small-scale preferential flow paths besides the larger-scale sinks. The difference section computed between two profiles repeated within 3 min during rain (Figure 6b) further highlights the diffraction patterns and shows strong amplitudes everywhere caused by omnipresent time shifts. The superficial drenching with water also causes time shifts on deeper geological reflections unaffected by any water flow.

[22] Only 12 min after the first rain shower stopped and most of the superficial water had run off, Figures 5c and 6c show more stable conditions with a decrease in amplitudes and diffraction patterns. The 3-min difference amplitudes of the surface reflections above sink S3 are back near the repeatability noise amplitude gray level of Figure 5a. Field logs indicate the standing water at the surface of this sink had completely drained by the time this line was recorded. The difference amplitudes suggest drainage processes in sink S3 were now active below 20 ns or about 0.75 m depth. In contrast, sink S1 was still flooded. Increased surface amplitude difference zones at profile locations 1.8–5.1 m, 5.8–7.3 m, and 13.7–16.4 m indicate the zones identified by shallow diffractions had not completely drained yet.

[23] The profile of Figure 5d acquired 79 min after the second rain shower shows a further decrease in amplitudes and diffractions. Compared with Figure 5a the most significant changes are associated with the sinks. Below sink S3, amplitudes have increased over the entire depth range, while in sink S1 amplitude changes are confined to the top 100 ns. It appears that sink S3 with a smaller diameter had been flooded to the groundwater level at 5 m depth, bypassing the entire vadose zone. For sink S1, water-related changes stop above the groundwater level. Difference plots over 3-min intervals do not show any significant changes at this stage of infiltration, clear evidence for a slowdown of the operative flow processes. Increasing the time interval between the subtracted profiles to 95 min (Figure 6d) shows the strongest difference amplitudes below the surface depressions.

[24] Similar GPR responses during and after rain confirm all surface depressions shown in Figure 1e as active sinks. Interestingly, the spacing of sink depressions appears to be related to the size of surface depression and underlying sink. Assuming the midpoints between sinks are watershed boundaries, circular watershed area estimates range from 6 to 64 m2. As shown in the controlled infiltration experiment described in the next section, sink S1 is capable of draining 1100 L/h. On the basis of a 64-m2 watershed this sink could accommodate 17 mm/h rainfall as pure overland flow. As the sink depressions fill with 5–10 cm of standing water within minutes during rain showers, overland flow must be very efficient in delivering large volumes of water to the sinks.

[25] GPR time shift analysis further elucidates the relative importance of sink drainage versus drainage through the surrounding soil and rock volume. In Figure 7 corresponding reflections of the same event were picked on the dry (Figure 5a) and well-drained (Figure 5d) GPR profiles. By the time this last profile was recorded, the grass and superficial soil had dried off, providing similar surface antenna coupling conditions to the dry case, thus allowing accurate time comparisons of the deeper GPR events. The sinks display pronounced time shifts up to +5 ns due to wetting, while outside the sinks the time shifts range from −1 to +1.5 ns. For comparison, the 34.5 mm of rain evenly soaking into the ground would only create a +2 ns shift at the same depth according to the Topp equation for mineral soils [Topp et al., 1980; Huisman et al., 2003]. Therefore the +5 ns shift within the sinks is clear evidence for rainwater preferentially draining through the sinks. If 100% of the 34.5 mm of rain falling in the estimated 64-m2 watershed of sink S1 would be present in a vertical cylinder with a cross section of 6 m2 the time shift would be +24 ns. Several factors may explain the reduction to the observed +5 ns: (1) The dry GPR profile was recorded 12 days prior to the rain. The ground dried out during this time as evidenced by the −1 ns shift observed outside the sinks. (2) Some water is retained in the soil, especially in the zones with increased soil thickness and disturbed rock surface characterized by the shallow diffractions during the rain. These are the zones in Figure 7 with up to +1.5 ns time shifts outside the sinks. (3) The 34.5 mm of rain fell in two showers separated by 100 min. Some of the water from the first 22.5 mm rain shower probably already had flowed to deeper levels below the picked event at 65 ns. (4) The two GPR profiles only give a bulk estimate of changes in water content. A 3-D time-lapse survey would better resolve the location of the flow and related changes.

[26] In summary, the precisely positioned 2-D time-lapse experiment recorded with a 3-min repeat rate established the importance of sink drainage during and after rainfall. Overland flow fills the surface depressions with water and the sinks rapidly drain the water. An augering test revealed well-sorted fine-grained sand as fill material very similar to the fill material excavated from the sink in Figure 3. The GPR data show the superficial saturation and infiltration to happen within minutes during and shortly after the rainfall. Once the water enters the sinks, GPR survey repetition rates of over 1 hour appear to be sufficient to capture the changes taking place in the subsurface. This opens the opportunity to acquire full-resolution 3-D surveys and apply 3-D migration processing to better image the sinks and associated flow processes.

3.4. Full-Resolution 3-D Time-Lapse GPR Imaging of Flow Through a Dissolution Sink

[27] We selected sink S1 from the previous experiment as an example to image geometry and wetting front migration. For this experiment, the open end of a water hose was attached to the ground with plastic pegs at the center of the surface depression shown in Figure 1d. The sink was not augered in order not to disturb the natural flow paths. The water was freely flowing out of the hose at a rate of approximately 1100 L/h over 4 hours. The total volume of 4400 L is at least double the water infiltrated during the rainfall experiment discussed in the previous section. Assuming 100% overland flow and no soil retention, 34.5 mm of rain falling in a watershed of 64 m2 would yield only 2208 L.

[28] Hourly repeated 3-D GPR surveys, covering an area of 10 m × 10 m with parallel E-W oriented profiles spaced by 0.1 m (the track lines are visible in Figure 1d) were collected with RLPS and a 250-MHz antenna. At an antenna speed of 0.5 m/s, a GPR trace was acquired approximately every 0.025 m for assignment into a 0.05 m × 0.10 m regularized data grid. It took 50 min to record each 3-D survey. Each survey started in the SW corner of the survey area. Immediately before turning on the water, one “dry” 3-D data set was acquired. Three GPR surveys were acquired while the water was running. The fifth data set was acquired 28 hours after the infiltration had started (24 hours after the water shutoff) to see how the infiltrated water would drain and redistribute over a longer time frame. The data recorded during the infiltration with standing water on the surface were dominated by diffraction patterns similar to those in Figure 5b. All data sets were processed in exactly the same way, including a Promax 3-D phase-shift migration utilizing a constant velocity of 0.075 m/ns. This velocity was determined by analysis of diffraction hyperbolae in the dry 3-D survey acquired before infiltration. The migration focused the diffractions and improved imaging of the sink and wetting fronts. The satisfactory focusing also at the later stages of the infiltration experiment indicates the 3-D migration to be relatively robust against the localized velocity changes caused by the infiltration of water. Because of time shifts caused by the increase in water content, depth conversion becomes less accurate. Topographic corrections based on the z coordinates acquired together with the GPR data were applied as time shifts to the migrated data volumes assuming a velocity of 0.075 m/ns.

[29] Figure 8 shows different views of the migrated data at five consecutive time instances of the infiltration experiment. The top row displays a vertical cross section taken from the center of the sink. The middle row consists of a horizontal slice extracted from the 3-D data volume at a two-way travel time of 63 ns (approximately 2.4 m depth). The lower row are 3-D views of interpreted sink boundary (yellow), wetting fronts (blue), and extent of surface water puddles (red).

Figure 8.

Full-resolution 3-D GPR time-lapse imaging of a surface infiltration experiment at sink S1. During 4 hours, 1100 L/h of tap water flowed freely out of a garden hose at the center of the sink S1 depression. The infiltration was monitored by repeated 3-D GPR surveys covering an area of 10 m × 10 m with parallel GPR profiles spaced by 0.1 m utilizing a 250-MHz antenna. The figure shows different views of the migrated data at five consecutive time instances of the infiltration experiment. The top row displays a vertical cross section taken from the center of the sink. The middle row consists of a horizontal slice extracted from the 3-D data volume at a two-way time of 63 ns (approximately 2.4 m depth). The bottom row shows 3-D views of interpreted sink boundary (yellow), wetting fronts (blue), and extent of surface water puddles (red). Topographic contours plotted on the top surface show how the surface depression and underlying sink are centered relative to each other.

[30] At dry condition the sink boundary can be interpreted to follow a series of stratigraphic terminations. The interpretation was made in three dimensions by rapidly animating vertical and horizontal slices with Geoprobe (Landmark Graphics Corporation). As sinks are filled with sandy soil and fine-grained sand, their internal structure is less stratified and more transparent in the dry GPR records when compared with the surrounding oolitic rock. The GPR events gradually change across the sink boundary in the transition from unaltered oolite to sand (Figure 3). The slope of the conic sink boundary dips with an angle of 60°, reaching a maximum depth of 3.75 m. The surface depression and underlying sink are centered relative to each other.

[31] After 1 hour of running water (1100 L), a spherical wetting front with a radius of 1.2 m has developed inside the sink. The interpretation of the full-saturation wetting front follows a chain of focused diffractions at the border of a zone with increased amplitudes. The 1-hour horizontal slice shows only little changes as the wetting front had not yet reached this depth level. Imprint of surface water ponding is minimal at the horizontal slice depth of 2.4 m.

[32] After 2 hours (2200 L) the wetting front has laterally progressed beyond the upper part of the sink boundary and entered the oolite. The vertical section and horizontal slice show time shifts and amplitude changes also outside the interpreted full-saturation wetting front. This is probably a combined effect of gradual wetting ahead of full saturation and delay of the electromagnetic waves partially passing through wet material.

[33] After 3 hours (3300 L) the wetting front has almost reached the bottom of the sink. The asymmetric shape of the wetting front indicates preferential flow on the SE side of the sink. In reality this asymmetry may be slightly more pronounced as 3-D data acquisition started on the south side and ended 50 min later on the north side of the sink. This linearly skews the GPR image of the wetting front as the northern part had more time to propagate.

[34] The GPR data recorded on the next day show how GPR reflectivity of the upper 60 ns has almost returned to the dry state observed before the infiltration had started. The horizontal slice just below 60 ns shows a progression of the strong amplitudes outward from the sink. The lobes of strong amplitudes at 2.4-m depth, which had already been initiated during the infiltration, have further developed, indicating lateral flow along a stratigraphic boundary. In cores drilled within 30 m of the survey site such stratigraphic boundaries consist of 2–3 cm thick very coarse grained and well-cemented beds which can be effective flow barriers if laterally extensive. Below this horizon of amplitude brightening the amplitudes are again similar or weaker when compared with initial conditions. We can interpret this loss of contrast as the effect of a more even distribution of retained moisture levels when compared with initial conditions. As the wetting front had almost reached the bottom of the sink after 3 hours, the infiltration water pulse must have reached the groundwater level well before the 28-hour survey was recorded. This last survey therefore shows the effects of redistribution and retention by gravity and capillary forces with the 60 ns flow barrier holding up water and causing locally enhanced GPR reflectivity. Two-way travel times of corresponding “dry” and “28-hour” events are delayed for the majority of the later data set caused by an overall increase of water retained in the vadose zone.

[35] In summary, this experiment clearly shows how the three conceptual flow models asserted at the beginning of this paper operate at different timescales. Bypass flow rapidly transports the vast majority of the water within hours at a propagation rate of 0.6–1.2 m/h toward the water table. Redistribution of the remaining water then follows both the lateral and the plug flow models. Redistribution rates measured after the infiltration event are of the order of 0.1 m/h and can be observed with GPR surveys repeated at daily intervals. The next experiment involves seasonal monitoring as plug flow also takes place at an even slower pace.

3.5. Impact of Seasonal Moisture Content Variation on 3-D GPR Data

[36] To investigate the hydrologic conditions in the Miami Oolite over a seasonal time frame, the last time-lapse experiment reported here involves a time interval of almost 8 months, comparing two 3-D GPR surveys recorded after a rainy summer and a dry winter. Climate in Miami is subtropical. Winters are relatively dry and summers are wet with almost daily thunderstorms and occasional hurricanes accompanied by strong rainbands. The rainy season starts in June. The first survey was acquired on 3 October 2004 with a total rainfall of 778 mm over the last 3 months. The second survey was acquired on 24 May 2005 with 269 mm of rain in the preceding 3 months. Grass and tree leaves were brown at the time of this survey. The survey area was located on the wide open grass area of Ingraham Park adjacent to the 2-D and 3-D GPR time-lapse experiment sites shown earlier. Four permanent survey nails inserted at the corners of the survey area enabled precise relocation of the repeat survey. Figure 1c indicates the location of the profile chosen for display in Figure 9. Processing for both surveys was identical except for the velocity used for NMO compensation and 3-D migration. Velocity analysis using diffractions in the 3-D common-offset data indicated an average velocity of 0.075 m/ns for the October and 0.085 m/ns for the May survey. Figure 9 shows time shifts of 6–20 ns between corresponding reflections. Time shifts are fairly constant along the profile but increase with depth as the radar waves travel longer distances causing a cumulative time stretch of the recorded GPR waveforms. Overall geometry and configuration of reflection events remains the same between seasons indicating an even distribution of water content change throughout the entire oolite rock volume. This is in contrast to the localized and short-term changes related to sinks shown earlier. It appears the vadose zone is taking up and losing significant amounts of water on a seasonal cycle like a sponge. As both bypass flow and lateral flow only affect part of the rock volume, the plug flow conceptual model driven by gravimetric and capillary forces is most representative for the seasonal hydrologic variation.

Figure 9.

Seasonal 3-D GPR time-lapse experiment. (a) Vertical cross section from the center of a 3-D GPR survey acquired after the rainy summer season. (b) Same cross section after the dry winter season extracted from the repeated 3-D GPR survey. (c) Two-way time shifts of 6–20 ns between corresponding reflectors show how the oolite host rock takes up and loses significant amounts of water over a seasonal cycle.

4. Conclusions

[37] The results show that a realistic vadose zone hydrologic model of the field site in the Miami oolitic carbonates should incorporate all three initially proposed end-member models. Such a model including plug flow, lateral flow, and bypass flow can be used to characterize hydrologic conditions ranging from transient storm water drainage to seasonal water budget. Such wide temporal variability of flow models is likely to occur in other geohydrologic settings where macropore and highly unstable flows occur. The time-lapse GPR method and survey strategy for the field example shown in this paper is applicable to sites dominated by karstic drainage and should be tested for other sites with suspected preferential flow paths. Rapid 2-D time-lapse GPR surveying before, during, and after rainfall provides an initial assessment of the importance and location of preferential flow zones and an estimate of required survey repeat rates to adequately image the changes occurring in the subsurface related to flow. Full-resolution 3-D time-lapse imaging including 3-D migration to focus the diffractions then provides the geometry of preferential flow paths and wetting fronts. Propagation rates can be estimated by comparing different stages of the infiltration. By inserting permanent survey markers in the ground, identical surveys can be acquired at field sites for long-term monitoring of annual and decadal changes of the vadose zone without disturbance of the natural flow paths. The key requirement for successful time-lapse imaging is centimeter-precise positioning and reoccupation of GPR measurement locations. For field sites such precise and rapid imaging has become possible for the first time with the recent development of a rotary laser-positioned GPR system.

[38] After gaining this new qualitative insight into the different drainage mechanisms operating in vadose zones, the next logical step is toward noninvasive quantification of hydrological parameters by extraction of the GPR time shifts caused by the changes of water content. Promising approaches in matching and warping of disparate 3-D data volumes have already been developed in seismic [Rickett and Lumley, 2001] and medical imaging. Warp processing cross correlates corresponding GPR traces over a user-selectable sliding time window and extracts the local time shifts between reflection events from two repeat surveys. This last step will be essential to improve the resolution of amplitude difference volumes resolving the flow paths where water content changes take place. In addition, the 3-D time shift volume is directly related to time differences caused by changes in water content. The time difference volume can be inverted to water content changes using petrophysical relationships. The time-lapse GPR derived preferential flow path geometry and quantification of changes in water content inside the undisturbed vadose zone can then be used to develop and constrain the next generation of numerical unsaturated flow models. Such models will incorporate the realistic space-time variability crucial for prediction of the hydrologic behavior of the vadose zone.

Acknowledgments

[39] This research was supported by the University of Miami Innovative Teaching and Technology Initiative, the Comparative Sedimentology Laboratory, the donors of the American Chemical Society Petroleum Research Fund, and the National Science Foundation (grants 0323213 and 0440322). The University of Miami acknowledges the support of this research by Landmark Graphics Corporation via the Landmark University Software Grant Program. We thank Donald McNeill and Robert Ginsburg for sharing their expertise on the Miami limestone and facilitating access to sites. Guillaume Koerner, Frank Despinois, and Adrian Neal helped with field work and figures. We gratefully acknowledge David Brown, city manager of Coral Gables, for granting permission to conduct this research in a city park. The paper was greatly improved with the excellent ideas and the constructive suggestions from three anonymous reviewers, Associate Editor James R. Hunt, and Editor Scott W. Tyler.

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