Exploration and Environmental Geophysics Free-Air Gravity Exercise Jeffrey A. Nunn Louisiana State University

Laboratory Exercises Gravity Acquisition Gravity/Magnetics Interpretation Ray Paths Refraction Acquisition Landmark/Refraction Interpretation Reflection Acquisition Reflection Processing Reflection Interpretation Resistivity Survey Resistivity Interpretation Well Logs (BakerHughes) GPR Acquisition GPR Interpretation

Context Audience: Prior Skills Graduate/Undergraduate; Some PE students 20 Students Weekly Laboratory Prior Skills Instrument Drift/Earth Tides Free-Air Correction

Instrument Drift and Earth Tides Data are from: Wolf, A. Tidal Force Observations, Geophysics, V, 317-320, 1940. Graph from galitzin.mines.edu/INTROGP

Free-Air Correction To correct for variations in elevation, the vertical gradient of gravity (0.3086 mGal·m-1) is multiplied by the elevation of the station and the result is added, producing the free-air anomaly. The free-air gravity anomaly is given by the formula: FA = go - gt + (δg/δz) h where: go = observed gravity (mGal) gt = theoretical gravity (mGal) δg/δz = vertical gradient of gravity (0.3086 mGal·m-1) h = elevation above mean sea level (m).

Goals Content/Concepts Estimate Height of a Platform in Howe-Russell Atrium using gravity measurements Instrument Drift/Earth Tides Corrections Free-Air Correction Noisy Data Precise Corrections to raw data

Instructions We will take a series of gravity measurements to estimate the height of the walkway near the top of the atrium in Howe-Russell. After taking a measurement at a base station, we will take turns taking measurements around the pendulum. At each station, we will record the time, location, temperature, and instrument reading. Periodically we will return to an earlier station to document any instrument drift and/or earth tide effect. We will then return to the base station in Howe-Russell to make a repeat measurement. The instrument readings must be corrected for instrument drift/Earth Tides and converted to mGals. We will not make a latitude correction. Station Location Time Temp. Dial Gravity Drift

LaCoste Romberg Gravimeter Appreciate the precision of a Gravimeter Learn about measurement error first hand Appreciate the effort involved in data acquisition Work in a group Things I learned the hard way – 20-30 minutes a measurement if they spin the dial.

Measurements Above: Base of Pendulum Opposite: Top of Attrium

Data Acquisition Measurement Location Time Temp., F Reading G1_1 Loading Dock 12:20 48.2 2926.405 G1_2 Base Pend 12:43 2926.53 G1_3 Top Pend 1:01 2922.32 G1_4 1:20 2926.503 G2_1 1:37 48.3 2926.715 G2_2 1:45 2926.565 G2_3 2:08 2922.187 G2_4 2:19 2926.685

Drift Correction (linear) Base Base Top Top

Conversion to mGals

Drift Correction Time Location Meter Corrected mGals 0.000 Loading Dock 2926.405 3010.641 23.000 Base Pend 2926.530 2926.492 3010.731 41.000 Top Pend 2922.320 2922.253 3006.367 60.000 2926.503 77.000 85.000 2926.565 2926.499 3010.738 108.000 2922.187 2922.213 3006.326 119.000 2926.335

Sensitivity of Gravity Interpretation (4 mGal) Base Base Top Top

Estimate of Height from Free-Air Correction Location mGals   Loading Dock 3010.641 Measured Height Base Pend 3010.731 del_g meters feet Top Pend 3006.367 4.364 14.141 46.384 3010.738 3006.326 4.412 14.297 46.894  Observed Meters 4.563 14.787 48.500

Laboratory Report Turn in a copy of data sheet plus an explanation of how you converted dial measurements to mgals plot of instrument drift/Earth tides correction estimate of elevation of the walkway using a Free-Air Correction a brief (paragraph or two) discussion of potential errors in the survey.