Geodesy and earthquakes

Differences with seismology Geodesy measures permanent (or at least, long-term) displacements (hours to years). Seismic instruments measure short term (seconds) (usually temporary) displacements with respect to time (e.g. velocity, acceleration).

moment Mo =  SA Mo = moment  = shear modulus (Pa = 1 N/m 2 = 10-5 bar) ratio of shear stress to shear strain V s = sqrt(  /  ) S = average slip A = fault area u ~ 3 GPa Earthquake Potency is simply (S)(A) Relationship to magnitude: Mw = (2/3)(log10(Mo – 9.1)) [Mo in N m] Mw = (2/3)log10(mo – 16.1) [Mo in dyne cm]

Slip and fault size Average displacement scales with fault length for earthquakes (e.g. Wells and Coppersmith, 1994)

Signals 1)Tectonic strain (mm to cm/year) 2)Earthquakes (m) 1)Pre-seismic???? 2)Co-seismic 3)Post-seismic 3)Creep (typically mm) 4)Earth tides (mm to cm) 5)Other: 1)Groundwater 2)Volcanic 3)Landslide

Measuring geodetic motion Ground surveys –Trilateration –Distance measurements –Arrays Deformation –Creepmeters –Tiltmeters (borehole, water-tube) –Strain meters Space-based –GPS –Radar Lidar

Measurements Ideally, displacement in x,y, and z In practice, usually relative displacement with respect to one or more components (e.g. tilt) Not always on all three components

Ground surveys Measure angles and/or distance between points (theodolite/EDM) Use trigonometry to calculate strain Used for volcanoes and tectonic strain Requires pre-existing measurements Accuracy mm to cm

Instruments Creepmeters Tiltmeters Strainmeters From Agnew and Wyatt (2003)

creepmeters Superstition Hills Parkfield

GPS Measure location with respect to satellites Absolute location (meters) Relative (with post-processing – mm) Horizontal resolution better than vertical Surveys in campaign mode or permanent “Real-time” relative GPS available

Murray et al

InSAR (Interferometric Synthetic Aperture Radar) Figures courtesy of G. Bawden, USGS Two images (A and B) at different time Similar satellite positions Phase differences between images Stereo effect due to topography Path change from deformation Atmospheric water vapor Satellite geometry Topography effect and orbital geometry effects can be corrected (with DEM & precise orbits) Remaining phase difference due to deformation, water vapor change, and errors.

Align & subtract two images (in complex domain) Yields the phase difference Remove phase due to elevation and orbit 3 Dec Jan 2005 Fringes show the deformation from 12/26/04 Bam earthquake – 2.7 cm/fringe - ~100 km Example – (1999 Bam earthquake, Iran) Decorrelation (no signal)

Fialko et al, 2003

difficulties Does not work everywhere (snow, water, vegetation, extreme terrain) Requires previous images Resolves only one component of deformation. Covers a time span of data (may include post-seismic slip)

results ( stack, 67 images) Stack of 67 images –Null bins with < 50 hits –Divide by total time –Yields average motion –Much noise cancels –Positive indicate subsidence or motion away –Standard deviation ~ 0.2 cm Several areas of deformation –Borrego Springs –Coyote Creek fault (1968 M6.5) –Superstition Hills fault (1987 M 6.6) –Vertical or horizontal motion –May retain orbital or layered atmospheric effects. I-8 50 mm (GPS) LOS range change (cm/yr)

Modeling - Okada model Analytic expression to calculate displacement from a rectangular fault in an elastic half space. Widely used and matches predicted displacement well. Useful for both forward and inverse models. Variety of codes available. Description of fault differs slightly from common seismological convention but equivalent to focal mechanism/moment tensor. Need 10 parameters –Fault length and width –Location (x,y,z) [lower corner] –Dip, slip, and rake –Shear modulus (usually set in code) Calculates displacement at any other point in half-space Use multiple patches to allow for more complicated geometries and slip distributions.

Example Finite faults in an elastic half-space Focal mechanism from 1987 earthquakes Slip from creepmeter; Slip depth of 3 km (depth of shallowest earthquakes) Observed signal matches first order model for both Elmore Ranch and Superstition Hills faults even with an extremely simple geometry. Observed signal consistent with aseismic slip Not consistent with groundwater alone (both up and down motion) Between Elmore Ranch and Allegretti farms unclear…..

Earthquake forecasting We know tectonic motion (from GPS) We know strain accumulation on fault Therefore we should be able to estimate seismic rate and average moment release on fault(s) Question: are geodetic rates the same as seismic geologic rates? Not certain, but probably pretty close.

Other signals Episodic tremor and slip Cascadia Observed on GPS; seismic Every 14 months Near subduction zone…. From Rogers and Dragert (2003)

Slip from multiple earthquakes in a region Kostrov (1974) Sum moments of earthquakes with the same source mechanism to find total strain