Tie up Gravity methods & begin Magnetic methods

Tie up Gravity methods & begin Magnetic methods
Environmental and Exploration Geophysics II Tie up Gravity methods & begin Magnetic methods tom.h.wilson Department of Geology and Geography West Virginia University Morgantown, WV Tom Wilson, Department of Geology and Geography

Simple Geometrical Objects
We make simplifying assumptions about the geometry of complex objects such as dikes, sills, faulted layers, mine shafts, cavities, caves, culminations and anticline/syncline structures by approximating their shape using simple geometrical objects - such as horizontal and vertical cylinders, the infinite sheet, the sphere, etc. to estimate the scale of an anomaly we might be looking for or to estimate maximum depth, density contrast, fault offset, etc. without the aid of a computer. Burger gets into a lot of the details in Section 6.5 of the text Tom Wilson, Department of Geology and Geography

Review of earlier discussions
Recall our earlier discussions of the gravity anomaly produced by a roughly spherical or equidimensional distribution of density contrast - Go to 31 Tom Wilson, Department of Geology and Geography

Two term solution with one of the terms describing the shape of the anomaly
g directly over the center of the sphere is gmax z Tom Wilson, Department of Geology and Geography

Shape term and maximum g directly over the sphere
gmax Tom Wilson, Department of Geology and Geography

We recognize the shape term as this ratio
Divide through by gmax gmax contains information about volume, density and radius Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography
The shape of the curve gv/gmax is scale independent. It is not affected by the depth or size of the sphere. Tom Wilson, Department of Geology and Geography

Shape of the anomaly is independent of the size of the sphere that produced it. The shape, the variation as a function of x/z is the same for all spheres regardless of their depth or size. Tom Wilson, Department of Geology and Geography

At what point does the anomaly fall off to one-half of its maximum value? Tom Wilson, Department of Geology and Geography

Let the ratio g/gmax = ½ and solve for X/Z Tom Wilson, Department of Geology and Geography

X1/2 /Z = 0.766 implies that Z can be expressed in terms of X1/2
Tom Wilson, Department of Geology and Geography

Diagnostic position and depth index multiplier
In the above, the “diagnostic position” is X1/2, or the X location where the anomaly falls to 1/2 of its maximum value. The value 1.31 is referred to as the “depth index multiplier.” This is the value that you multiply the reference distance X1/2 by to obtain an estimate of the depth Z. Tom Wilson, Department of Geology and Geography

A table of diagnostic positions and depth index multipliers for the Sphere (see your handout). 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 – to Z. Note that these constants (e.g ) assume that depths and radii are in the specified units (feet or meters), and that density is always in gm/cm3. Tom Wilson, Department of Geology and Geography

An estimate of z opens the possibility of solving for other parameters in the relationship For the sphere Since we know Z we could solve for R assuming a ; or, having some information on the possible size of the object, we could solve for . Note that these constants (e.g ) assume that depths and radii are in the specified units (feet or meters), and that density is always in gm/cm3. Tom Wilson, Department of Geology and Geography

We can undertake similar development for the Horizontal Cylinder (see section in our text) and Tom Wilson, Department of Geology and Geography

Diagnostic positions and multipliers for the horizontal cylinder
Again, note that these constants (i.e ) assume that depths and radii are in the specified units (feet or meters), and that density is always in gm/cm3. Tom Wilson, Department of Geology and Geography

Return to problem 6.5 We worked through most of this the other day: some assuming a horizontal cylinder and some assuming the sphere. Pb. 6.5 What is the radius of the smallest equidimensional void (such as a chamber in a cave - think of it more simply as an isolated spherical void) that can be detected by a gravity survey for which the Bouguer gravity values have an accuracy of 0.05 mG? Assume the voids are in limestone and are air-filled (i.e. density contrast = 2.7gm/cm3) and that void centers are never closer to the surface than 100 meters. Tom Wilson, Department of Geology and Geography

Solve for R: sphere (left), cylinder (right)
We assumed that since the instrument reads with an accuracy of 0.05 mGals the gravity anomaly would have to be larger than 0.05 mGals; so we picked a gmax of 0.1mGals. Tom Wilson, Department of Geology and Geography

Solve for R: sphere (left), cylinder (right)
For the horizontal cylinder (a long cave passageway), R~ 9.4 meters (a very large passageway!) For the sphere (a large chamber within the cave system), R~ 23.7 meters Tom Wilson, Department of Geology and Geography

In a problem similar to problem 6.9 (Burger et al.) you’re given three anomalies. These anomalies are assumed to be associated with three buried spheres. Determine their depths using the half-maximum technique. Carefully consider where the anomaly drops to one-half of its maximum value. Assume a minimum value of 0. A. C. B. Tom Wilson, Department of Geology and Geography

Magnetic Methods Tom Wilson, Department of Geology and Geography

Magnetic polarity reversals on the sea floor provide Tom Wilson, Department of Geology and Geography

Charged particles from the sun stream into the earth’s magnetic field and crash into the gasses of the atmosphere Tom Wilson, Department of Geology and Geography

Protons and electrons in the solar wind crash into earth’s magnetosphere. Tom Wilson, Department of Geology and Geography

We are also interested in local induced magnetic fields Gochioco and Ruev, 2006 Tom Wilson, Department of Geology and Geography

Data Acquisition Tom Wilson, Department of Geology and Geography

water kerosene & alcohol
Measuring the Earth’s magnetic field Proton Precession Magnetometers water kerosene & alcohol Steve Sheriff’s Environmental Geophysics Course Tom Boyd’s Introduction to Geophysical Exploration Course Tom Wilson, Department of Geology and Geography

Magnetic Fields – Basic Relationships
Source of Protons and DC current source Proton precession generates an alternating current in the surrounding coil Tom Wilson, Department of Geology and Geography

Proton precession frequency (f) is directly proportional to the main magnetic field intensity F and magnetic dipole moment of the proton (M). L is the angular momentum of the proton and G is the gyromagnetic ratio which is a constant for all protons (G = M/L = /  sec). Hence - Tom Wilson, Department of Geology and Geography

Magnetic Fields Locating Trench Boundaries Theoretical model
Examination of trench for internal magnetic anomalies. actual field data Tom Wilson, Department of Geology and Geography Gilkeson et al., 1986

Trench boundaries - field data Trench Boundaries - model data Tom Wilson, Department of Geology and Geography Gilkeson et al., 1986

Abandoned Wells From Martinek Tom Wilson, Department of Geology and Geography

Locating abandoned wells Tom Wilson, Department of Geology and Geography

Abandoned Well - raised relief plot of measured magnetic field intensities From Martinek Tom Wilson, Department of Geology and Geography

Magnetic Fields – Basic Relationships Magnetic monopoles p1 r12 Fm12 Magnetic Force  Magnetic Permeability p1 and p2 pole strengths Coulomb’s Law p2 Tom Wilson, Department of Geology and Geography

Magnetic Fields – Basic Relationships
Force Magnetic Field Intensity often written as H pt is an isolated test pole The text uses F instead of H to represent magnetic field intensity, especially when referring to that of the Earth (FE). Tom Wilson, Department of Geology and Geography

Magnetic Fields – Basic Relationships The fundamental magnetic element is a dipole or combination of one positive and one negative magnetic monopole. The characteristics of the magnetic field are derived from the combined effects of non-existent monopoles. Dipole Field Tom Wilson, Department of Geology and Geography

Magnetic Fields – Basic Relationships Toxic Waste monopole vs. dipole Tom Wilson, Department of Geology and Geography

The earth’s main magnetic field Tom Wilson, Department of Geology and Geography

Magnetic Elements Tom Wilson, Department of Geology and Geography

Location of north magnetic pole

Magnetic Elements Tom Wilson, Department of Geology and Geography

The compass needle points to the magnetic north pole.
Magnetic north pole: point where field lines point vertically downward Geomagnetic north pole: pole associated with the dipole approximation of the earth’s magnetic field. The compass needle points to the magnetic north pole. Tom Wilson, Department of Geology and Geography

Main field intensity Magnetic Intensity in Morgantown Tom Wilson, Department of Geology and Geography

Magnetic Inclination Tom Wilson, Department of Geology and Geography

Variations of inclination through time
Magnetic Inclination Variations of inclination through time Tom Wilson, Department of Geology and Geography

Magnetic Declination Tom Wilson, Department of Geology and Geography

Variations of declination through time
Magnetic Declination through time W Turn north about 10 degrees clockwise Tom Wilson, Department of Geology and Geography

Magnetic Elements for your location

Magnetic Elements Today’s Space Weather Tom Wilson, Department of Geology and Geography

Introduction to the magnetics computer lab Anomaly associated with buried metallic materials Bedrock configuration determined from gravity survey Results obtained from inverse modeling Computed magnetic field produced by bedrock Tom Wilson, Department of Geology and Geography

Where are the drums and how many are there? Tom Wilson, Department of Geology and Geography

Enjoy the Break! Hand in the gravity lab today hand in the in-class problems for credit. Magnetic papers are in the mail room. Magnetic paper summaries will be due Tuesday, December 6th. Continue reading Chapter 7 – Look over the magnetics lab. We’ll launch into this effort on Tuesday, Novemner 29th. Tom Wilson, Department of Geology and Geography

Tie up Gravity methods & begin Magnetic methods

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