Introduction to the use of gravity measurements in Ge111A Background & basic intuition Data reduction Use of the instrument See Reynolds for detailed quantitative discussion
What and Why Gravity measures the distribution of mass Variations in density Variations in interface locations Very non-unique => use in conjunction with other constraints (geologic, seismic, ) Targets include: Topographic compensation - the crustal root (long λ) Fault structures/offsets (best for dip-slip faults or large offset strike-slip) Aquifers Tunnels Buried objects (tunnels, ore deposits, ) Basin sediment fill depth (together with magnetic field variations)
Data Availability Regional: Carry the gravimeter around Land, boat, plane Arbitrary resolution Global: Satellite tracking/altimetry (over water)/other ~2 km resolution over oceans ~100 km resolution from harmonic models None of these useful for our purposes
Basic intuition Everything we need can be worked out from basic potential field theory (see Reynolds or Turcotte & Schubert): 2 A = where A is the gravitational potential 0 g z A = z where g z is the vertical component of the gravity field Units: 1 mgal = 10-5 m/s 2 1 Gal = 1 cm/s 2 (named after Galileo) 1 g.u. = 0.1 mgal = 10-6 m/s 2
Attraction from harmonic distribution of mass I Z ρh k cos( kx)= σ k cos( kx) Why? Intuition Decompose any mass distribution into individual harmonic (Fourier) contributions and sum linearly Example: Topography, density variations on a 2D or 3D grid X
Attraction from harmonic distribution of mass II We won t derive solutions today, but you can imagine integrating over our given harmonic mass distribution. The vertical component is: where k = 2π/λ, h<<λ δg = Gδm ˆ r r 2 g z = 2πG ρh k cos( kx)e kz = 2πG σ k cos( kx)e kz The e -kz term corresponds to the 1/r 2 decay with distance (the peaks and troughs tend to cancel when viewed from increasingly large distances) Z ρh k cos( kx)= σ k cos( kx) X
Attraction from harmonic distribution of mass III At long λ, k 0 g z = 2πG ρh = 2πG σ No z-dependence Attraction from an infinite sheet of mass Will be used in making the Bouguer correction For z 0 If z increases (or k increases λ decreases): e -kz 0 Upward continuation: e.g., Z=λ, e -2π =0.002 (faint signals) Downward continuation: e.g., Z=-λ, e 2π =500 (amplification of short λ noise)
Standard gravity corrections earth tide correction, which corrects for tidal effects of moon & sun instrument drift correction to compensate for drift in the instrument's spring; the latitude correction, which incorporates the variation of the Earth's gravity with latitude; the free-air correction, which accounts for the variation in gravity due to elevation relative to sea level; the Bouguer correction, which corrects for the attraction of material between the station and sea level; the curvature correction, which corrects the Bouguer correction for the effect of the Earth's curvature; the terrain correction, which removes the effect of topography to a radial distance of 166.7 km; the isostatic correction, which removes long-wavelength variations in the gravity field inversely related to topography. The Eötvös correction for a moving platform
Free Air Correction Bring all observations to a common horizontal reference surface (E.g., a datum or geoid) Effect of distance not mass Results in Free Air Gravity Commonly used for airborne and marine data g 0 = Gm R 2 ; g h = Gm (R+ h) 2 δg FA h = g h g 0 h 2g 0 = 0.3086 mgals/m R The L&R gravimeter has a sensitivity of ~3µGal h = δg FAR 1cm 2g 0 Careful with surveying (know your target)
Bouguer Correction Effect of mass (not distance) - Assume λ>>h, ignores dh/dx + g B = 2πG ρh ρ h h x What density to use? Standard is 2670 kg/m 3 You can also use this to estimate density Nettleton s Approach - assume all variations are due to topography Clever differencing of gravity profiles is sometimes useful More sophisticated approaches Terrain corrections (graphical) Talwani (2D and 2.5D prisms - Matlab) Parker s Method (finite amplitude harmonic summation) Common Shapes (see textbook)
The LaCoste & Romberg Model G Gravimeter Read Reynolds p. 50-51 for how this works. Needs power to keep isothermal - keep plugged in somewhere Highly sensitive spring and mass system (read Reynolds) - Do not move it without clamping the mass Getting data Level gravimeter (you want all of g z ) Unclamp Get a reading by adjusting the spring s.t. mass is in the right place - can be tedious if you have changed location a lot A manual raw data point is also derived by reading off the counts and converting to mgals using a calibrated table (or Matlab) Typically, take a manual reading at a base station, then lock the beam and use the feedback system to record values relative to the base station reading Reclamp Return to base station every hour for tide/drift correction.
The next 3 figures relate to the problem of a terrain correction. The circular chart (hammer chart) is used to assess the effect of mass at different distances from the measurement point. See Reynolds p. 61-65 for more details.
Isostatic residual gravity map (Langenheim & Jachens, 2002, BSSA v. 92(4) p. 1606-1620).
Magnetic anomaly map (Langenheim & Jachens 2002)
Remember from last week: magnetic anomaly strength goes as 1/r 3 ; gravity anomaly goes as 1/r 2. Magnetic potential goes as 1/r 2 ; gravitational potential goes as 1/r. Therefore the magnetic potential and the gravity anomaly have similar form (if they arise from an object of uniform density & magnetization). See figure to the left showing that the magnetic anomaly looks like the derivative of the gravity anomaly. If you integrate the magnetic anomaly you can make a pseudogravity anomaly which can help with your 3-E structural interpretation. Read about this and see Fig. 6 in the Langenheim & Jachens paper. Figures at left from Langenheim & Jachens 2002
Homework 1. The measurements listed at right were made sequentially in the Caltech library building during the course of one hour. Base is outside the door at ground level. What is distance between each floor? How high is the library? Show your work. Explain what assumptions you are making. Millikan library, Caltech Floor Gravity (mgal) Base 0.990 Third -1.891 Sixth -5.817 Ninth -9.700 Roof -11.263 Base 0.970 2. Look up the coordinates (lat-long-elevation) of Caltech and Bombay Beach, on the E side of the Salton Sea. How will the gravity change between Caltech and our field area? Again, show your work.