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Earthquakes and Water

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Encyclopedia of Complexity and Systems Science

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Introduction

The subsurface is a complex and heterogeneous environment. It stores much of Earth’s fresh water and houses a large portion of the Earth’s biosphere and human wastes intended for long-term sequestration. The study of this important but complex system is the subject of a workshop sponsored by the US Department of Energy (2010).

The present paper focuses on a less explored complexity introduced by large earthquakes that change the subsurface properties that, in turn, change subsurface flow and transport.

Earthquakes signify sudden changes in the state of the subsurface. Alterations in subsurface flow and fluid properties are thus not surprising. What is surprising is the large amplitudes of some hydrological responses and the great distances over which these responses occur. Shortly after the 2004 M9.2 Sumatra earthquake, for example, groundwater erupted from a hydrological monitory well in southern China, 3,200 km away from the epicenter (Fig. 1), and the water fountain...

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Abbreviations

Alluvial fan:

A fan-shaped deposit built up by sediments deposited by a stream that exits from a mountain front onto a plain. Over time the stream and its deposits move across different parts of the fan surface

Aquifers confined and unconfined:

Aquifers are layers of sediments or rocks with relatively high permeability in which groundwater can move comparatively freely. A confined aquifer is an aquifer bound by impervious sediments or rocks both on its top and on its base. An unconfined aquifer, on the other hand, is one where the upper boundary is the groundwater table that may rise and fall with seasonal changes in precipitation and with the withdrawal of groundwater

Baseflow recession:

During dry seasons the discharge in a stream is derived from groundwater that flows to the streambed and is called baseflow. Over long dry periods, the baseflow decreases with time. The decrease of stream discharge over time is the baseflow recession

Capillary fringe:

A layer above the groundwater table where groundwater seeps upward by surface tension (capillary force) to fill pores

Darcy’s law:

The basic law for groundwater flow discovered by Henry Darcy in 1856 through experimentation, which may be expressed in one of the following forms:

\( Q=\frac{K\;A\;\left({h}_1-{h}_2\right)}{L} \)

\( q=-K\frac{d\;h}{d\;L} \)

where L is the sample length along which water flows h 1 and h 2 (with h 1 > h 2) are the hydraulic head at the two ends of the sample, A is the cross-sectional area of the sample, K the hydraulic conductivity, and Q the amount of water flowing from the higher end to the lower end of the sample, q is the amount of flow per unit area also known as the Darcy’s velocity. The dimension of Q is L3/t where t is time, those for q and K are both L/t same as velocity. The transmissivity T of an aquifer of thickness b is defined as T = bK. The hydraulic conductivity of most rocks is anisotropic and is more properly expressed as a second-rank tensor K. Thus, Darcy’s law is often written in the following form:

q = − K ·∇h

Darcy’s law applies only for laminar groundwater flows. Deviation from laminar flow occurs when the Reynold’s number ≥ 5. In most situations, however, groundwater flow is laminar and Darcy’s law is valid.

Dynamic stresses:

Stresses produced by the passage of seismic waves.

Effective stress:

Experiments show that the mechanical properties of porous solids such as friction and strength, depend on the pressure of pore fluid, and the dependence follows the “effective stress” principle (Terzaghi, 1925) defined as

σ eff ij = σ ij − αpδ ij

where σ eff ij is the effective stress, p is pore pressure, α an empirical constant (the Biot-Willis coefficient) determined by experiment, and δ ij the Kronecker delta. When the effective normal stress is reduced to zero, faults in rocks slip without friction and sediments lose mechanical strength, i.e., they liquefy.

Effective vertical permeability and effective horizontal permeability:

A common source of permeability anisotropy in sedimentary basins is layering of sediments or sedimentary rocks of different permeability. Thus parallel to the bedding of the layered rocks, the bulk permeability of the assemblage is given by the arithmetic mean:

\( {k}_H={\displaystyle \sum_i{k}_i}\left(\frac{b_i}{b_t}\right) \)

where b i and k i are respectively, the thickness and permeability of the ith layer and b t is the total thickness of the layered assemblage. Normal to the bedding, on the other hand, the bulk permeability is given by the harmonic mean:

\( {k}_V=\left(\frac{b_t}{{\displaystyle \sum_i{b}_i/{k}_i}}\right). \)

Thus the average permeability in the horizontal direction (k H ) is dominated by the most permeable layer, while that in the vertical direction (k V ) by the least permeable layer.

Groundwater flow equation:

A continuum approach is adopted in deriving the differential equation for groundwater flow where a representative elemental volume is defined that is very much greater than the sizes of the individual pores in rocks and sediments but is very much smaller than the domain of study. Together with Darcy’s law and the continuity equation, this approach allows the derivation of the differential equation for groundwater flow:

\( {s}_s\frac{\partial h}{\partial t}=\nabla \cdotp \left(\boldsymbol{K}\cdotp \nabla h\right). \)

where K is the conductivity tensor and S s the specific storage defined as

\( {s}_s\equiv \frac{1}{\rho_f}\frac{\partial \left(n\;{\rho}_f\right)}{\partial h} \)

with a unit of m−1. In deep sedimentary basins the effect of temperature on the properties of pore fluid may be significant, while the effect of pressure is relatively small and can be neglected.

If permeability is isotropic and the effect of temperature is negligible the flow equation reduces to a linear diffusion equation

\( {s}_s\frac{\partial h}{\partial t}=K{\nabla}^2h. \)

sometimes expressed as

\( \frac{\partial h}{\partial t}=\kappa {\nabla}^2h. \)

where κ is the hydraulic diffusivity defined by

κ ≡ K/s s .

Groundwater level saturated and unsaturated zone:

Going down from the Earth’s surface, a depth is reached below where the sediments or rocks are saturated with groundwater. This is the local groundwater level (or water table). Above the water table is the unsaturated zone (or the “vadose zone”) in which pore water is held in place by adhesion and capillary tension.

Hydraulic head:

The hydraulic head h is defined as the sum of the gravitational potential energy related to elevation z and pore pressure P and can be expressed as

\( h=\frac{P}{\rho_fg}+z. \)

The hydraulic head in a confined aquifer is measured by the water level in a well that is opened only to this aquifer. In modern monitoring wells the hydraulic head of aquifers is measured using pressure gauges.

Peak ground acceleration and peak ground velocity:

The maximum acceleration and velocity of the ground respectively, during an earthquake as recorded by strong motion seismographs, often used to characterize the intensity of shaking at a given location

Permeability:

The hydraulic conductivity K is a composite of the properties of the transmitting fluid and the porous solid:

\( K=\frac{\rho_fg\;k}{\mu } \)

where ρ f and μ are respectively, the density and viscosity of the fluid k is the permeability of the porous solid with dimension m2 and g is the gravitational acceleration.

Pore pressure:

Pressure in the fluids in the pores of sediments and rocks. Elevated pore pressure (above 1 atm) can only occur in saturated rocks and sediments

Poroelasticity:

A description of the coupled processes of deformation and pore fluid diffusion in saturated porous elastic solids

Rayleigh waves and Love waves:

Two types of waves that travel along the surface of solids. Rayleigh waves include both longitudinal and transverse motions with respect to the direction of wave propagation while Love wave include only transverse motions. Both types of waves are produced by earthquakes and travel along the Earth’s surface

Seismic energy density:

The total kinetic energy per unit volume in a seismic wave train as recorded by a seismograph at a given location. It is the maximum seismic energy available to do work in a unit volume

Soils:

A term commonly used in earthquake engineering in referring to unconsolidated sediments

Static stresses:

Stresses produced by the permanent displacement of the crustal blocks across the fault that ruptured during an earthquake

Unconsolidated sediments:

Loose sediments that have not been cemented or substantially compacted

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Acknowledgements

We thank Steve Ingebritsen and Barbara Bekins for their excellent reviews that significantly helped us in improving the paper. This work is partially supported by NSF grant EAR-1344424 and EAR-1345125.

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  1. Department of Earth and Planetary Science, University of California, 307 McCone Hall, Berkeley, CA, 94720, USA

    Chi-yuen Wang & Michael Manga

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  1. Chi-yuen Wang
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Correspondence to Chi-yuen Wang .

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  1. Ramtech Ltd., Larkspur, California, USA

    Robert A. Meyers

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Wang, Cy., Manga, M. (2014). Earthquakes and Water. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-3-642-27737-5_606-1

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  • DOI: https://doi.org/10.1007/978-3-642-27737-5_606-1

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