The purpose of this investigation is to develop a semi-analytical procedure for quantifying aquifer and aquitard properties from a single extensometer record in lieu of the time-consuming development of more complex numerical models to quantify and constrain these parameter values. Despite a limited 12-year record and the fact that water levels both decline and increase on an annual basis, estimates of both aquifer and aquitard parameters have been reasonably estimated at the Lorenzi extensometer site in Las Vegas Valley, Nevada when compared to the estimates developed numerically. The key factors that allow for accurate estimates of elastic and inelastic skeletal specific storage and hydraulic conductivity of the aquitards and elastic specific storage and hydraulic conductivity of the intervening aquifers is the presence of pumping cycles at multiple frequencies, and measured heads at all the aquifer units covered in the extensometer record and the inherent assumption that the aquitards have identical hydrologic characteristics and are homogeneous and isotropic. This latter assumption is also a usual limitation in numerical modelling of these settings because of the complex temporal head relationships occurring within the aquitards that are rarely, if ever, measured.

Extensometers have some distinct advantages over the satellite-based methods such as GPS and InSAR. Firstly, if designed properly, they can accurately measure compaction at the sub-millimetre or even to a few 10's of microns. Secondly, the data can be continuous so even if pumping occurs at diurnal frequencies, it is possible for the extensometer to record possible compaction from these high frequency pumping events. Thirdly, in many localities we have a much longer historical record with extensometers than we do with satellite data. Extensometer data have been available at some sites since the 1960s, when subsidence rates were much higher due to the fact that subsidence was not as yet well known as a consequence to excessive groundwater pumping. Fourthly, extensometers measure the compaction over the depth of the extensometer pipe, typically within the zone of active pumping (which is how they tend to be designed) so that tectonic and eustatic changes are not part of the deformation record. They are also not subject to topographic effects that often plague InSAR processing and can interfere with signal coherence. The two biggest disadvantages to the implementation of extensometers is the cost and the fact that they are point measurements. As such, it is uncommon for more than a few extensometers to exist within an entire aquifer system or basin.

Map of Las Vegas Valley showing the location of the Lorenzi extensometer site and estimated and measured land subsidence for the period 1963–1990 adapted from Bell et al. (2002).

Extensometer data, when coupled with continuous time-series water-level data in the aquifers through which the extensometer penetrates, can yield important aquifer system hydrologic properties (Epstein, 1987), particularly when cyclical pumping patterns occur at multiple frequencies. In this analysis, water-level data responding to multiple-frequency pumping patterns are used along with compaction data from a single extensometer record extending through a multiple aquifer/aquitard system at the Lorenzi site in Las Vegas, Nevada. The aim is to estimate important hydraulic parameters including the specific storage and hydraulic conductivity of the aquifers, and the elastic and inelastic specific storage and hydraulic conductivity of the aquitards.

Las Vegas Valley (Fig. 1) represents an extensional structural basin filled
with more than 1500 m of alluvial deposits that have produced a complex and
heterogeneous sequence of aquifers and aquitards of varying thickness and
compressibility. A near-surface aquifer overlies a more extensive principal
aquifer system from which domestic water originates in the valley. The
principal aquifer system contains various confining layers that contribute
to land subsidence. Pumping has occurred in the valley for approximately 100 years causing as much as 90 m of water-level decline (Burbey, 1995)
and nearly 2 m of compaction in the northwest subsidence bowl since
1963 (Bell et al., 2002). The principal aquifer system contains
three confining layers and three aquifers, referred to here as the shallow,
middle, and deep confining layers and aquifers, respectively. The aquifers
are composed largely of sands and gravels with minor thin layers of silts
and clays, while the aquitard units are composed almost entirely of clays
and silts. Drilling logs from the extensometer borehole (244 m total depth)
and geophysical surveys have defined the depths and thicknesses of the
aquifer and aquitard units within the larger principal aquifer system of the
basin (Pavelko, 2000). Hourly water-level data from each of the three
aquifers along with hourly compaction data were collected at the
extensometer site from November 1994 to December 2007. The Lorenzi
extensometer site is located within 3200 m of approximately 14 municipal
pumping wells that pump at different diurnal and seasonal rates. Figure 2
shows the entire available water level and compaction record of the Lorenzi
site. Fluctuations in diurnal water levels are not evident at the scale of
Fig. 2. These daytime to-night-time water-level fluctuations are attributed
to differences in daily pumping of 5400 m

Mean daily record of the compaction and water level records for the shallow, middle and deep aquifers at the Lorenzi extensometer site for the entire measured record, 1995–2007.

The methodology used here is a three-step process in which the first step involves the evaluation of aquifer elastic storage and horizontal hydraulic conductivity using the Theis equation by taking advantage of the diurnal pumping signals that reflect the aquifer conditions only. The second step involves the evaluation of aquitard elastic skeletal storage and vertical hydraulic conductivity of the aquitard units. The assumption here is that all the aquitard units have the same hydraulic properties. The long-term inelastic signal is removed from the record using a low-pass filter. Seasonal periodic pumping is used as this frequency of pumping elastically deforms a portion of aquitards on a yearly basis. The portion of aquitard thickness undergoing elastic deformation is determined in this process. The third step involves the evaluation of aquitard inelastic storage, which is based on the known pumping history and the nature of the inelastic deformation time-series. In this approach, a time constant for the aquitard is approximated based on aquitard thickness, the calculated hydraulic conductivity (from step 2) and the nature of the inelastic compression.

Calibrated hydraulic conductivity and storage parameters for the shallow, middle and deep aquifers using the Theis equation (Eq. 1) for cyclical daily pumping.

The first step in analysing the aquifer system of the Lorenzi extensometer
site is to attempt to quantify the aquifer properties by using daily
periodic water levels attributed to diurnal fluctuations caused by daily
pumping cycles, which isolates the aquifer response and is too quick to
induce leakage and subsequently compaction of the intervening confining
units. For this analysis a 5-day period in June 1998 is chosen where pumping
and recovery periods are known as well as the pumping rates (Pavelko, 2000).
Under diurnal pumping cycles the aquifers behave as confined units, which
can be readily analysed using the Jacob formulation of the Theis equation
and implementing periodicity (Eq. 1):

The second step is to evaluate the elastic aquitard parameters from the seasonal periodic pumping patterns associated with high summer pumping demand and winter recovery, which is enhanced with a known quantity of artificial recharge (injection). Because no water-level data are available from within any of the aquitards and because only one composite compaction record is available, it must be assumed that each of the three aquitards (thicknesses are 78, 34 and 32 m, respectively) exhibit the same behavior and thus have the same parameter values of vertical hydraulic conductivity and elastic storage. Furthermore, it is hypothesized that the seasonal elastic response of the total compaction is attributed largely to the confining units and is associated with the seasonal head changes in the aquifers. From the seasonal pumping cycle, a cross-spectral analysis over the 12-year record showed that no significant lag exists between what is deemed as the elastic aquitard response and the seasonal water-level record.

To isolate the seasonal elastic response of the system, a low-pass filter is
used to remove the long-term decadal trend (inelastic component) of system
compaction (Fig. 3) and then to fit a periodic sine function to the seasonal
elastic response. The mean seasonal elastic recovery can then be readily
calculated from the mean fitted periodic curve and is 2.7 mm. Next, we can
identify the seasonal compaction contribution of each aquifer from the total
seasonal compaction record through the following equation:

For a singly draining unit (aquifer head decline causes an elastic response
to one side of the aquitard) the time constant is defined as:

Plot of aquitard thicknesses responsible for contributing to elastic compaction associated with seasonal head changes for a range of elastic skeletal specific storage values and hydraulic conductivity values of the confining units. The orange box represents the range of parameter values found in the literature for extensometer sites in the United States. The red circle represents the optimal values from the numerical analysis of Pavelko (2004).

Since we have assumed homogeneous conditions for the aquitards we can
realistically only use a mean value for the skeletal specific storage.
Furthermore, since we calculated the thickness of the compacting confining
unit to be 8, 8, and 4 m, respectively surrounding the upper, middle and
deep aquifers, the elastic skeletal specific storage can also be readily
calculated. The mean optimal skeletal storage and skeletal specific storage
values are calculated to be

Step three in the parameter estimation process involves estimation of the inelastic skeletal specific storage of the confining units. The difficulty in this estimation lies in the fact that the heads in the confining layers are not in equilibrium with the measured heads in the aquifers due to the slow release of water from these units, creating a hydrodynamic lag between the heads in the aquifer and the observed compaction. Because the heads in the first few years of the data set (Fig. 2) are decreasing and the heads in later years are recovering, the resulting heads in the confining units show a continual decline at their centers (expulsion of water), but show both declining and increasing heads in the portions of the aquitards nearest the aquifers (the elastic aquitard response).

The long-term trend (annual to decadal compaction) in compaction (Fig. 3) shows a significant change in slope that is associated with the slowing of drainage from the aquitards as the heads in the aquifers begin to recover. A linear annual trend can be found when plotting heads against compaction data with a high degree of correlation. However, the slope associated with such a trend does not reflect the inelastic specific storage of the confining units.

In this analysis, a semi-analytical approach is used to estimate

The goal of this investigation is to determine if a simplistic semi-analytical approach could be used to reasonably quantify the aquifer and aquitard parameters at a point site (extensometer) in lieu of having to build a more complex and time-consuming numerical model to estimate parameter values. With careful examination, extensometer data can provide more than just a continuous record of the total compaction history associated with the lowering of hydraulic heads within the measured zone of the extensometer pipe. This investigation reveals that important parameter values of the aquifer and aquitards including the hydraulic conductivities and elastic and inelastic specific storage can be reasonably quantified under the following conditions: (1) all hydrostratigraphic units important to the overall compaction record have been identified and their thicknesses established, (2) all the intervening aquifer hydraulic heads are measured over the length of the extensometer pipe, (3) cyclical pumping patterns are available for the length of the record and preferably at multiple temporal frequencies, and (4) a reasonable historic understanding of the length of the pumping history affecting the measured record.

The time series data used in this investigation will be available on the CUAHSI HydroShare web site and is available upon request to the author in the meantime.

The author declares that there is no conflict of interest.

This article is part of the special issue “TISOLS: the Tenth International Symposium On Land Subsidence – living with subsidence”. It is a result of the Tenth International Symposium on Land Subsidence, Delft, the Netherlands, 17–21 May 2021.