Environmental and Exploration Geophysics II Gravity Methods VII

Environmental and Exploration Geophysics II Gravity Methods (VII) more wrap up tom. h. wilson tom. wilson@mail. wvu. edu Department of Geology and Geography West Virginia University Morgantown, WV Tom Wilson, Department of Geology and Geography

X z r Sphere with radius R and density Tom Wilson, Department of Geology and Geography

X gvert z r Sphere with radius R and density Tom Wilson, Department of Geology and Geography

Diagnostic position X 1/2 x½ is referred to as the diagnostic position, 1/x 1/2 is referred to as the depth index multiplier Tom Wilson, Department of Geology and Geography We solve for x 1/2/z and find that x 1/2/z = 0. 766.

The values at several points along the X/Z axis can be calculated to define the shape of the anomaly 3/4 1/2 1/4 Tom Wilson, Department of Geology and Geography

The other day we developed these tables of diagnostic positions and depth index multipliers Note that regardless of which diagnostic position you use, you should get the same value of Z. Each depth index multiplier converts a specific reference X location distance to depth. Tom Wilson, Department of Geology and Geography

Check it out …. Depth index multiplier for X 1/2 is 1. 305 Depth index multiplier for X 3/4 is 2. 17 What depth do you get? X 1/2 X 3/4 m Wilson, Department of Geology and Geography

Once you figure out Z - Solve for R or These constants (i. e. 0. 02793 or 0. 00852) assume that depths and radii are in the specified units (feet or meters), and that density is always in gm/cm 3. Tom Wilson, Department of Geology and Geography

X z Cylinder with radius R and density R Tom Wilson, Department of Geology and Geography

X z r At surface distance x away from a point directly over the cylinder Tom Wilson, Department of Geology and Geography

Results for Horizontal Cylinder and Tom Wilson, Department of Geology and Geography

We can ask the same kinds of questions we asked regarding the sphere. For example, Where does This tells us that the anomaly falls to ½ its maximum value at a distance from the anomaly peak equal to the depth to the center of the horizontal cylinder Tom Wilson, Department of Geology and Geography

X 3/4 X 2/3 Locate the points along the X/Z Axis where the normalized curve falls to diagnostic values - 1/4, 1/2, etc. X 1/4 X 1/3 0. 58 0. 71 The depth index multiplier is just the reciprocal of the value at X/Z at the diagnostic position. X times the depth index multiplier yields Z 0. 58 0. 71 1. 0 1. 42 Tom Wilson, Department of Geology and Geography X 1/2 1. 74 Z=X 1/2

Simple relationships and formula for the horizontal cylinder With Z, you can then speculate on the density contrast or radius of the object in question. Again, note that these constants (i. e. 0. 02793) assume that depths and radii are in the specified units (feet or meters), and that density is always in gm/cm 3. Tom Wilson, Department of Geology and Geography

Horizontal Cylinder Just as was the case for the sphere, objects which have a cylindrical distribution of density contrast all produce variations in gravitational acceleration that are identical in shape and differ only in magnitude and spatial extent. When these curves are normalized and plotted as a function of X/Z they all have the same shape. It is that attribute of the cylinder and the sphere which allows us to determine their depth and speculate about the other parameters such as their density contrast and radius. Tom Wilson, Department of Geology and Geography

Assume the anomaly below is produced by long horizontal tunnel – What is the depth to the tunnel? What are the depth index multipliers? X 1/2 Tom Wilson, Department of Geology and Geography X 3/4

What is the approximate shape of the object producing the anomaly below? Which estimate of Z seems to be more reliable? Compute the range. You could also compare standard deviations. Which model - sphere or cylinder - yields the smaller range or standard deviation? Tom Wilson, Department of Geology and Geography

Estimating other properties of the buried object To determine the radius of this object, we can use the formulas we developed earlier. For example, if we found that the anomaly was best explained by a spherical distribution of density contrast, then we could use the following formulas which have been modified to yield answer’s in kilofeet, where Z is in kilofeet, and is in gm/cm 3. Tom Wilson, Department of Geology and Geography

For the remainder of the class consider the inclass activity Tom Wilson, Department of Geology and Geography sphere 10 cylinder 10

Vertical Cylinder Tom Wilson, Department of Geology and Geography

For a given anomaly certain simple geometries can be assumed and tested Horizontal cylinder or vertical dyke Sphere or vertical cylinder Tom Wilson, Department of Geology and Geography

How about the anomaly below? Half plate or faulted plate Tom Wilson, Department of Geology and Geography

Problem 6. 5 What is the radius of the smallest equidimensional void (e. g. chamber in a cave) that can be detected by a gravity survey for which the Bouguer gravity values have an accuracy of 0. 05 m. Gals? Assume the voids are formed in limestone (density 2. 7 gm/cm 3) and that void centers are never closer to the surface than 100 m. Take a few minutes to work through this one. Tom Wilson, Department of Geology and Geography

Consider another in-class problem 12 sectors with Ri=1100 and Ro=2200 Ring The butte fits into one sector Tom Wilson, Department of Geology and Geography Butte

Graphical separation of residual Examine the map at right. Note the regional and residual (or local) variations in the gravity field through the area. The graphical separation method involves drawing lines through the data that follow the regional trend. The green lines at right extend through the residual feature and reveal what would be the gradual drop in the anomaly across the area if the local feature were not present.

Mark off anomaly intersections with an interpolated regional field The residual anomaly is identified by marking the intersections of the extended regional field with the actual anomaly and labeling them with the value of the actual anomaly relative to the extended regional field. After labeling all intersections with the relative (or residual ) values, you can contour these values to obtain a map of the residual feature. 0 -1 -0. 5

Circular in shape … What is the depth?

Just for general discussion > (see 6. 8, Burger et al. ): The curve in the following diagram represents a traverse across the center of a roughly equidimensional ore body. The anomaly due to the ore body is obscured by a strong regional anomaly. Remove the regional anomaly and then evaluate the anomaly due to the ore body (i. e. estimate it’s deptj and approximate radius) given that the object has a relative density contrast of 0. 75 g/cm 3 Tom Wilson, Department of Geology and Geography

You could plot the data on a sheet of graph paper. Draw a line through the end points (regional trend) and measure the difference between the actual observation and the regional (the residual). You could use EXCEL or PSIPlot to fit a line to the two end points and compute the difference between the fitted line (regional) and the observations. residual g Re Tom Wilson, Department of Geology and Geography l a ion

Just as with the graphical approach, the idea is to remove the regional so you can investigate the residual. Tom Wilson, Department of Geology and Geography

Are alternative acceptable solutions possible? Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography

The large scale geometry of these density contrasts does not vary significantly with the introduction of additional faults Tom Wilson, Department of Geology and Geography

The differences in calculated gravity are too small to distinguish between these two models Tom Wilson, Department of Geology and Geography

Gravity applications span a variety of scales Shallow environmental applications Roberts, 1990 Tom Wilson, Department of Geology and Geography

http: //pubs. usgs. gov/imap/i-2364 -h/right. pdf Tom Wilson, Department of Geology and Geography

The influence of near surface (upper 4 miles) does not explain the variations in gravitational field observed across WV c c’ The paleozoic sedimentary cover Morgan 1996 Tom Wilson, Department of Geology and Geography

The sedimentary cover plus variations in crustal thickness explain the major features we see in the terrain corrected Bouguer anomaly across WV Morgan 1996 Tom Wilson, Department of Geology and Geography

In this model we incorporate a crust consisting of two layers: a largely granitic upper crust and a heavier more basaltic crust overlying the mantle Morgan 1996 Tom Wilson, Department of Geology and Geography

Gravity model studies help us estimate the possible configuration of the continental crust across the region Derived from Gravity Model Studies Tom Wilson, Department of Geology and Geography

Locate your swimming pool … Ghatge, 1993 Tom Wilson, Department of Geology and Geography

Items on the list …. • Gravity paper summary(s) (both sections) due this Thursday, Nov. 14 th • Gravity lab will be due on Thursday November 21 st (writing section submission is self-reviewed showing track changes). • • Keep working up the gravity lab • There will be a short magnetics lab component. The lab report will be less extensive than prior reports. • We will have two final exam review sessions: December 5 th and December 10 th. We’ll be getting into magnetics this Thursday so start reading chapter 7. Tom Wilson, Department of Geology and Geography

Regular section submissions All those in the regular section submit paper copies of your paper summaries and lab reports. Tom Wilson, Department of Geology and Geography

Writing Section reminders (electronic submissions only) • Revised paper summary 1 and self-reviewed paper summary 2 are to be turned in this Thursday. • The gravity lab is self reviewed and is due on Thursday, November 21 st. All those in the writing section submit their papers and lab electronically. Don’t forget to turn on track changes while doing your selfreview. Only submit the self-reviewed file. Tom Wilson, Department of Geology and Geography

What’s coming up? Some due date reminders Tom Wilson, Department of Geology and Geography