How does time series data of land deformation help in quantifying storage properties ?

Important advances include

1) Identifying structural or lithostratigraphic boundaries (e.g. faults or transitional facies) of groundwater flow and deformation.

2) defining the material and hydraulic heterogeneity of aquifer-systems (e.g. antelope valley)

3) estimating system properties(storage co-efficients and hydraulic conductivities)

4) constraining numerical models of groundwater flow, aquifer-system compaction, and land subsidence."

"Estimates of inelastic and elastic storage co-efficients that govern the vertical deformation of the aquifer system were constrained by previous estimates based on the compaction history of other alluvial aquifer systems in california (Helm, 1978)."

"The boundaries of groundwater basins and subbasins frequently are defined on the basis of faults. Faults impeding flow may juxtapose hydrogeologic units of contrasting horizontal hydraulic conductivity, contain low-permeability fault gouge, and(or) drag, smear, and compress interbedded aquitards into steeply dipping barriers to flow, resulting in elevated heads (water levels) upgradient from the fault and very steep hydraulic gradients through the fault zone."

The reason for the faults in coachella valley to act as a barrier is not exactly known!

'Where sufficient water-level information is available, large hydraulic gradients generally identified from regional potentiometric surface map are used to infer the presence of buried faults or substantiate the effect of mapped faults on groundwater flow.'

"Estimates of the aquifer-system elastic skeletal storage coefficient (S*) were computed at six locations from the measured displacements and concurrent water level changes in nearby wells (Hoffman et. al., 2001)"

'The linear shape of the displacement surface across the Silver creek faults suggest that, 1) the fault zone juxtaposes sedimentary sections of contrasting time-consolidation characteristics and/or 2) lateral groundwater flow across the fault is impeded (Galloway et. al, 2000a).

'The Coachella Valley is a 100-km (65 mi) long, northwest-trending valley in southeastern California. The valley covers about 1,000 km^2 (400 mi^2) (California Department of Water Resources, 1964).'

What is the approximate dimensions of the area I am modeling ?

'InSAR can detect relative changes in vertical position as small as 5 mm (0.02 ft) (Hoffmann and others, 2001)'

'Its important to know where the wells are screened. The water level changes along with the land-subsidence information derived from a monitoring site(s) would be useful in estimating aquifer-system hydraulic parameters that govern ground-water flow and land subsidence. This information could be used to construct a numerical model of ground-water flow and aquifer-system compaction to refine estimates of governing parameters and to predict potential aquifer-system compaction which could be used by CVWD to manage water resources while considering land subsidence.'

The degree to which a particular fault impedes groundwater flow depends on the materials found in the fault zone, the type and distribution of adjacent aquifer materials, and the occurance of diagenesis in the fault zone, as well as the externally imposed flow regime. (Heynekamp et. al., 1999).

why do faults act as impermeable zones ? 1. cataclasis, or grain-size reduction 2. offsetting of permeable beds by impermeable beds 3. rotation of elongated and flat clasts parallel with the fault surface, reducing the hydraulic conductivity perpendicular to the fault. 4. tectonic mixing or smearing of beds of low hydraulic conductivity sediments(i.e, clays) in the fault zone 5. deposition of minerals in the fault zone reducing the pore-space and ,hence, the hydraulic conductivity

Recharge from local precipitation is very small (less than 13 cm anually on the valley floor), the amount of water contributed across the fault could form a significant portion of the overall recharge to the aquifer in the local subbasin.

The hydraulic properties of the fault zone are estimated by inverse modeling,

• regional-scale groundwater-flow model is calibrated with groundwater elevations collected from over 40 locations over six decades. m
• ultiple hydrogeologic parameters are estimated by minimizing a weighted least-square objective function that accounts for measurement error.
• The quality of the parameters estimated is assessed by determining the confidence intervals and testing for covariance between parameters (how does this work ?).

key assumptions: outflow rates remain constant over the study period

Study Area: Mission Creek subbasin+Desert hot springs subbasin

The upper coachella valley is filled with alluvium, with estimates of depths to underlying bedrock of more than 1 km (extreme case may be ?).(Proctor, 1968) Proctor(1968) suggests typical sediment thicknesses in the upper coachella valley are greater than 400 m.

The average annual precipitation is from 76-102 cm in the mountains and less than 13 cm in the valley (Harding Lawson Associates 1985)

Banning Fault and Mission Creek Fault - Both, right-lateral reverse, dipping 80-90 deg to the northeast (Proctor, 1968)

Proctor(1968) first suggested that the presence of phreatophytic vegetation(plants that extract water from water tables via their root system) was an indication of high water tables (northen side of the mission creek fault trace).

In general, there is a distinct contrast between the chemistry and temperature of the groundwater in the two subbasins. (Geotechnical consultants, 1979, 1992) The groundwater in the Desert Hot Springs subbasin has a geothermal character, with total dissolved solids concentrations of over 1000 mg/L and temperatures exceeding 50 C.

Conceptual Model: The groundwater system is treated as a single layer aquifer under unconfined conditions.

No laterally continuous units can be indentified from lithologic logs from well-installation records, which are separated on the order of hundreds of meters to kilometers.

The water recharging the aquifer originates as precipitation in the mountains forming the northern and wstern boundaries and enters the study area almost exclusively as subsurface inflow via the major canyons.

Net annual pumpage for the Desert hot springs and mission creek subbasins: approx 20% of the pumped groundwater is transported out of the study area. The remainder of the pumped water is used in the study area and is either returned to the subsurface through irrigation and sweage-effluent return or is lost to evapotranspiration or other sinks. It is assumed that on an average 35% of the pumped groundwater is returned to the subsurface (Tyley 1971).

K for aquifers (mission creek -desert hot springs) is in the order of 10^-4 to 10^-6 m/s. K for mission creek fault is in the order of 10^-8 to 10^-9 m/s. (mayer et. al., 2007)

Numerical model: maximum density difference of less than 1 % is associated with the extremes in temperature( 30- 55 C) and dissolved solids concentrationzs (100 - 1,500 mg/L). This density difference is not considered to appreciably effect the processes considered in the study.

numerical model used: MODFLOW HFB (horizontal flow barrier) package was utilized here to simulate the effect of mission creek fault on gw flow. assumptions: fault is vertical and flow is horizontal.

Inflows are simulated as constant-flux terms at the relevant grid cells, as are the outflows along the banning fault and the eastern flux boundary. All other grid cells along the boundary are no-flow.

Data: 40 observation wells head data over a 60 period interval (from historical records)

Calibration: phase 1: A steady-state calibration based on observations collected in a year (1936), where little of no pumping occured, and a transient calibration based on observations from 1937 through 1998. Inflow and outflow rates, transmissivities, storativity and fault conductances were estimated via model calibration. It is assumed that the 'observed' groundwater elevations are equivalent to the vertically averaged hydraulic heads predicted by the model at the corresponding nodal location.

Best parameter estimates were found using the PEST package for nonlinear parameter estimation (Doherty 1994). The objective of the parameter estimation is to find the minimum global sum of the squares of the residuals (SSR) between the observations and the model predictions, as in SSR = sum(1,N)[h_i_model-h_i_obs]^2 where N is the number of observations and h_model and h_obs are the groundwater elevations obtained from model simulations and from observations, respectively.

variances were assigned to all observations (of different types - e.g. maps of gw elevations, historical records of gw elevations from public water supply wells, direct measurements of gw elevations in observations wells, groundwater elevations interpreted from electrical resistivity surveys). The individual SSRs are weighted by the inverse of the variance giving observations less prone to error more importance in determining parameter values).

Results and Discussion: CI(Confidence Interval ) The estimated values of the parameters in the transmissivity equations indicate that, for both subbasins, the transmissivities decrease to the southeast, or in the direction away from the mountains. The higher values of transmissivity for the Desert Hot Springs subbasin are likely due to the proximity of the subbasin to the mountains, indicating that the aquifer materials, on average,have higher grain sizes, and thus, higher hydraulic conductivities. Storativity - 0.12 , reasonable for an aquifer under unconfined conditions consisiting of unconsolidated alluvium. spatially distributed values of the storage coeffiecient could not be justified, because the groundwater elevations are relatively insensitive to the storage coefficient.

Verification: A separate data set collected in the vicinity of the fault zone, not used during any phases of calibration, was used to verify the model.

Sensitivity analysis: Sensitivity to basic assumptions in the conceptual model are assessed.

1. Non-linear model: the model properties depend on the variables for which you solve (the dependent variables)

2. Specifying discontinuos functions - If a co-efficient or a material property contains a step function or some other discontinuity, convergence problems can arise. For time-dependent problems, the time-stepping algorithm can run into problems. For stationary problems, mesh-resoltuion issues can arise such as overshooting and undershooting of the solution due to infinite flux problems.

To avoid problems with a discontinutiy, try replacing it with a smoothed switch function that emulates steps. Doing so serves two purposes:

a) Numerical reliability and convergence are improved.

b) What you think of a step function is, in reality, a smoothed continuous function because of inertia.

The following smoothed functions are available in comsol:

• flsmhs, a smoothed Heaviside function with a continuous first derivative and overshoot on both sides of the step. The overshoot ensures that the integral from 0 to infinity is correct. y=flsmhs(x,scale) approximates the logical expression y = (x>0) by smoothing the transition within the interval −scale < x < scale. fldsmhs is the derivative of the smoothed Heaviside function.

• flsmsign, a smoothed sign function with a continuous first derivative. y = flsmsign(x,scale) approximates the function y = sign(x) by smoothing the transition within the interval −scale <fldsmsign is the derivative of the smoothed sign function.

• flc1hs, a smoothed Heaviside function with a continuous first derivative without overshoot. Its syntax is similar to the functions just described.

• flc2hs, a smoothed Heaviside function with a continuous second derivative without overshoot. Its syntax is similar to the functions just described.

In the interval -scale<x<scale, the functions flsmhs and flsmsign are defined by a 7th-degree polynomial chosen so that the 2nd derivative is continuous. Moreover, the moments of order 0, 1, and 2 agree with those for the Heaviside function and the sign function, respectively. This implies that the functions have small overshoots.

3. Dependent variable: The variables which the application mode solvs for.

4. The generalized Neumann condition is also called a mixed boundary condition or a Robin boundary condition.

In finite element terminology, Neumann boundary conditions are called natural boundary conditions because they do not occur explicitly in the weak form of the PDE problem. Dirichlet conditions are called essential boundary conditions because they restrict the trial space. Dirichlet boundary conditions often represent constraints.

5. The Poroelasticity analysis predicts a similar vertical compaction and also predicts the horizontal displacements that compensate for the change in vertical thickness. The results from poroelastic analyses such as these ones naturally fold into criteria that predict fissuring and compaction at the soil surface as well as failure of wells, pipes, and other infrastructure elements.

6. Comsol flow and deformation model example: Because the aquifer is at equilibrium prior to pumping, you set up this model to predict the change in hydraulic head rather than the hydraulic head values themselves. The main advantage to this approach lies in establishing initial and boundary conditions. Here you specify that the hydraulic head decreases linearly by 60 m over ten years, then simply state that hydraulic head H0 is zero and remains so where heads do not change in time.

1. South Branch San Andreas Fault (Banning Strand)

Also called South Branch San Andreas Fault - Dibblee (1967, 1981) and Jennings (1994); Coachella valley segment, Banning fault - Matti and others (1992)

2. North Branch San Andreas Fault (Coachella Strand)

Also called North Branch San Andreas Fault - Dibblee (1971, 1981) and Jennings (1994); Mission Creek Fault - Allen (1957); Coachella valley segment, San Andreas Fault - Matti and others (1992)

Reference style - U.S. Geological Survey and California Geological Survey, 2009, Quaternary fault and fold database for the United States, accessed Mar 17, 2009, from USGS web site: http//earthquake.usgs.gov/regional/qfaults/.