1. Geology 5660/6660 Applied Geophysics 23 Mar 2016 © A.R. Lowry 2016 For Fri 25 Mar: Burger 378-419 (§6.5-6.8) Last Time: Density; Gravity Anomalies & Modeling Model structures as having anomalous mass density   lithology, porosity, temperature (lowest for soils/seds, higher for lithified sed rocks, highest for crystalline rocks) Gravity anomaly due to a sphere: (represents only the vertical component of the total vector anomaly!) Discussed nonuniqueness :  Different density (but same mass, same center of mass) can yield an identical gravity anomaly!  Different shape at a shallower depth can yield the exact same gravity anomaly! (But all geophysics is nonunique… Provides info others can’t!)

2. Last Time (Cont’d): Gravity Modeling Anomalies for: horizontal cylinder: vertical cylinder: fault-bounded basin : Geology 5660/6660 Applied Geophysics 23 Mar 2016 © A.R. Lowry 2016

3. t = 3 km;  = 500 kg/m 3 t = 1.5 km;  = 1000 kg/m 3 Note asymptotes depend on t  !

4. Example: Green Canyon A low-resistivity anomaly consistent with Paleozoic bedrock suggested the mapped trace of the ECF is ~30 m east of the true fault location, near the dotted line.

5. Example: Green Canyon The drift correction is highly correlative with the measurements, which is a bit worrying… But it is such a small fraction of the observations that we needn’t worry too much about it. Tide-Corrected Gravity Drift Correction Model Drift-Corrected Gravity

6. The free air correction is actually larger than the raw obs (as is generally true in high-relief areas). The gravity base site appears as a worrisome outlier in both the correction & anomaly though. Inspection reveals a ~1.6m height error in week-one (non-RTK) GPS measurement of the elevation. Latitude-Corrected Gravity Free Air Correction Free Air Anomaly

7. The error was corrected by interpolating the heights at the nearest geophones (which were about the same elevation) to the x -position of the gravity base. The free air correction and anomaly with elev corrected at the gravity base are cleaner, but the western-most site may have a similar height error. Latitude-Corrected Gravity Free Air Correction Free Air Anomaly

8. The complete Bouguer anomaly looks reasonable, and similar to what we might expect at a normal fault, save for a few outlier points (e.g., Grav 6 at x = 34.4 m). However we have no valid reason to throw these out at this stage. Free Air Anomaly Bouguer Slab Correction Complete Bouguer Anomaly Terrain Correction

9. RMS Misfit: 0.1046 mGal Fault Model Used:  = –196 kg/m 3 x 0 = 75 m  = 49.8° h = 1.06 km The density contrast between basin sediments and Paleozoic bedrock clearly dominate the measured gravity. Misfit (largely in the footwall) may partly reflect fault damage- zone effects, but probably mostly out-of-plane effects &/or measurement errors.

10. The x 0 = 75 m model prediction for the projection of the East Cache Fault to the surface at Green Canyon reinforces the possibility that fault trace is a few tens of m further west than previously mapped, and thus that the low resistivity, high chargeability anomaly found on the eastern side of the resistivity/IP profile is Paleozoic bedrock in the footwall of the fault. The model is very sensitive to choice of x 0 : Putting the fault trace at ~10 m where it is mapped (& keeping other parameters the same) yields an RMS misfit of 0.1443 mGal; in my experience, a model with (19 – 4 =) 15 degrees of freedom that yields a 38% larger misfit than the minimum error solution can be ruled out at very high confidence. However given the scale of mass averaging and likely near- surface complexities & geometrical effects associated with fault rupture, the most we can really say with confidence is that a fault trace somewhere west of the mapped trace is favored by the data.

11. Magnetics: Like gravity, a potential field method governed by Laplace’s equation:  2 u = f (sources) Unlike gravity, source term is a vector rather than a scalar Gravity : Monopole source  field is always directed radially toward a “sink” location Magnetics : Dipole source  field direction & strength depend on one “source”, one “sink” S N

12. Coulomb’s Law describes the force of attraction exerted between two magnetic poles: where is the distance & direction between two poles p 1 & p 2 are pole strengths  is magnetic permeability, a property of the medium (usually ~1) p1p1 p2p2 Magnetic Field Strength is the force that would be exerted on a hypothetical “unit monopole” p 2 due to p 1 : (MKS units of Tesla; magnetic anomalies usually given in nT or  s)

13. Definitions: Magnetic Dipole Moment : Two poles +p and –p separated by a distance l have moment Intensity of Magnetization : (where V is volume) is a material property of the magnetic source. *** If a material that can produce a magnetic field (  > 1 ) is placed within an external magnetic field, then intensity of the induced magnetization is where k =  – 1 is magnetic susceptibility of the material. (e.g., magnetite-rich body)