Geology 5660/6660Applied Geophysics

11 Apr 2014

© A.R. Lowry 2014For Mon 14 Apr: Burger 302-340 (§5.5-5.11)

Last Time: DC Electrical Resistivity Modeling• One-Dimensional Sounding: Layer-over-halfspace: Wenner app ~ for a/z small;

~ 2 for a/z large

Two layers over halfspace: May or may not pick up sandwiched layer depending on thickness, contrast Resist does multiple layers, 1D, log a-spacing steps• Profiling: Simple variations (e.g. vertical contact) have complicated profiles that depend on where resistivity contrasts occur relative to electrodes• Sensitivity kernels indicate positive resistivity anomalies increase app in most regions but decrease app if between a current and voltage electrode!

€

app = ρ1 1+ 4 k n 1+2nz

a

⎛

⎝ ⎜

⎞

⎠ ⎟2

n=1

∞

∑ −2k n

1+ nz a( )2

n=1

∞

∑ ⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

-4.5

-3.5

-2.5

-1.5

-0.5

0 20 40 60 80

~Profile Distance (m)

Observed Gravity (mGal)

(This is probably an erroneous measurement…)

Saturday’s measurements of gravity on the West Cache fault:

“Sensitivity kernels”for apparent resistivity (assumes a homogeneous Earth model). This isa measure of how much a perturbationof resistivity at a givenpoint in the Earth canbe expected to changethe measurement ofapparent resistivity ofthe array (reds positive,blue-greens negative,yellow = zero).

Resistivity “Pseudosection”:• Measurements are a combination of profiling (different x) & sounding (different a-spacings)• Plot / contour app versus distance x and a-spacing increment n, where n = a/a0 and a0 is smallest a-spacing

(The image I showed on Wednesday is an example of an apparent resistivity pseudo-section):

Clear from the earlier modelingof Wenner apparent resistivityacross a verticalcontact that thisapproach will give a VERY approximate imagewith potential fora lot of “false”anomalies…

True inversion of the data will yield a much more reliableimage (for much the same reasons that depth migrationdoes in the seismic case!)

Resistivity pseudosection from the western trench location for the East Cache Valley fault zone near Paradise…

Resistivity pseudosection from the western trench location for the East Cache Valley fault zone near Paradise…

Used resistivity sounding & two layer model:

Vertical sounding at 25.7 m. Maroon line is measured; blue linemodeled using Excel spreadsheet based on Burger’s Table 5-4. Modeling with Resist (with interpolated a-spacing) differs inresulting estimates of thickness, but the differences are small.

10.000

20.000

30.000

40.000

50.000

60.000

70.000

80.000

90.000

3.000 6.000 9.000 12.000 15.000

Array Spacing a (m)

Apparent Resistivity (Ohm m)

1 = 101 m, h = 3.22 m

2 = 16.7 m

RMS Misfit 1.897 m

Can model equally well by using constant thickness and varying the resistivities, or using constant resistivities & varying the thickness…

Because these data did not go to a small enough a-spacing to nail down in the upper layer.

10

20

30

40

50

60

70

80

90

3 6 9 12 15 18 21 24 27

Array a Spacing (m)

Apparent Resistivity (Ohm m)

1 = 101 m, h = 1.72 m

2 = 16.7 m

RMS Misfit 0.847 m

1 = 100

2 = 17

Layer-over-halfspace modeling suggested a variable-thickness upper layer with ~ 100 m (Bonneville deposits)over = 17 (Great Salt Lake fm). The data imply the trenchedgeomorphology represents a beach burm deposit.

Little Mountain DC Resistivity Profile…

The inverted model of resistivity structure…

Unsmoothed (top) and smoothed(bottom) inversion images areshown left. The differences indata misfit are relativelysmall despite the differencesin resulting resistivity structure,so these are about equallyreasonable. The near-surface,small-scale variations in the first model are likely morerealistic than the smoothed 2nd

image, but either is possibleat depth… Which tells us thatthe deep resistivity structure ispoorly determined by our data.

Grey line approximates a 15-m contour used to define apolygon for gravity modelingin GravMag.

The best-fit gravity modelcorresponding to the polygonfrom the first (more variable)resistivity model is promising: Itreduces the RMS gravityresidual from 0.4855 (no model)to 0.4188 mGal and hints at anexplanation for the hillside gravityvariations that were not matchedby earlier modeling of end-member polygons. However thepolygon has an unlikely high = 1600 kg/m3, and thecenter-of-mass of the polygonis offset to the east of thecenter-of-mass implied by thegravity anomaly.

RMS = 0.4188 mGal

= 1600 kg m-3

The best-fit gravity model for thepolygon from the second(smoother) resistivity model hasslightly lower RMS gravityresidual (0.4046 mGal) and amore believable = 900 kg/m3

(near the range that might beseen, e.g., for a sulfide-rich orebody in high-porosity limestone).But center-of-mass of thepolygon remains offset to theeast of the center-of-massimplied by the gravity anomaly.

RMS = 0.4046 mGal

= 900 kg m-3

Just for fun, here’s a gravitymodel assuming just such asteeply west-dipping polygonalbody, with surface contactcorresponding to the low-resistivity body from our DCresistivity data inversion.

RMS = 0.2053 mGal

= 760 kg m-3

East Cachefault in GreenCanyon

Pseudosection and inversion can be very similar though…

Lithology application: Sand/clay in a study of agricultural groundwater contaminant plumes.

Mapping an intrusive dike feature…

Mapping cave locations in karst terrain.