Geodesy & Crustal Deformation Geology 6690/7690 Geodesy & Crustal Deformation 29 Sep 2017 GPS Reference Frames • GPS Reference Frame relates Earth-fixed to satellite motion; reference frame effects are part of position error • Glacial isostatic adjustment (GIA) is a transient effect that is ~secular on decadal timescales; has vertical, horizontal (including plate-like!) expression • Early GPS reference frames were updated annually; now ~2x per decade… Still find small adjustments to plate motion rates • Geological evidence also exists for changes in plate motion (perturbations of Australian hotspot paths during Ontong-Java Plateau collision; decreasing Nubia-South America rates) Read for Fri 29 Sep: Wahr §3.1-3.2 (67-75) © A.R. Lowry 2017

Read for Monday, Oct 2: Herring et al. (2016) Plate Boundary Observatory and related networks: GPS data analysis methods and geodetic products, Reviews of Geophysics, 54(4), 759-808

Introduction to Gravity Gravity, Magnetic, & DC Electrical methods are all examples of the Laplace equation of the form:  2u = f (sources), Where u is a potential, is the gradient operator Notation: Here, the arrow denotes a vector quantity; the carat denotes a unit direction vector. Hence, the gradient operator is just a vector form of slope… Because Laplace’s eqn always incorporates a potential u, we call these “Potential Field Methods”. → ^

Gravity We define the gravitational field as And by Laplace’s equation, (1) given a single body of total mass M; here G is universal gravitational constant = 6.672x10-11 Integrating equation (1), we have (2) Nm2 kg2

IF the body with mass M is spherical with constant (or radially symmetric) density, equation (2) has a solution given by: Here r is distance from the center of mass (CoM); is the direction vector pointing toward the CoM Newton’s Law of gravitation: So expresses the acceleration of m due to M! has units of acceleration  Gal in cgs (= 0.01 m/s2) On the Earth’s surface, m/s2

HOWEVER, r is not radially symmetric in the Earth… so is not constant! Gravity methods look for anomalies, or perturbations, from a reference value of at the Earth’s surface: gobs gref r1 r0

Example: Global Free-Air Gravity Field from GRACE + GOCE + surface measurements… WGM2012 model from Bureau Gravimetríque International

Gravity Measurements: I. Absolute Gravity: Measure the total field  time of a falling body prism vacuum laser ~2m Must measure time to ~10-11 s; distance to ~10-9 m for 1 mgal accuracy! Nevertheless this is the most accurate ground-based technique Disadvantages: unwieldy; requires a long occupation time to measure

Gravity Measurements: II. Relative Gravity: Measure difference in at two locations Pendulum: difference in period Errors in timing of period T  ~0.1 mgal Mass on a spring: MDg = kDl or Dg = kDl/M Worden and Lacoste-Romberg are of this type (“zero-length” spring of L-R yields errors around 6 mgal) l mass M length l spring constant k

Gravity Measurements: III. Satellite Gravity: Measure (from space) the height of an equipotential surface (called the geoid, N) relative to a reference ellipsoid

Gravity Measurements: III. Satellite Gravity: Measure (from space) the height of an equipotential surface (called the geoid, N) relative to a reference ellipsoid Ocean Altimetry: Measure the height of the ocean surface using radar or laser (e.g., JASON) Satellite Ranging: Satellite orbits follow the geoid Measure orbits by ranging from the ground to the satellite or ranging between two satellites (e.g., GRACE) N

Global Free-Air Gravity Field from GRACE Example: Global Free-Air Gravity Field from GRACE Image from UT-CSR/NASA

GRACE and the modern static (i.e., time-invariate) geoid… Note that the free air gravity anomaly field can be calculated directly from the geoid.