Isostasy

• Isostasy is the state of equilibrium between the Earth's lithosphere (rigid outer layer) and the underlying asthenosphere (soft ductal layer) it is maintained by the buoyancy of the lithosphere, which floats on the denser underlying asthenosphere.
• First discovered by George Everest, he observed that in Andes the plumb lines experience reduced deflection than the expected angle. This reduction is caused by mountain ranges having root zones that have lower density.
• Isostasy was coined by C. E. Dutton for the compensation of a topographic load by a less dense subsurface structure.
• Isostasy explains why mountains and other large landforms do not sink under their own weight.
• Isostatic rebound is the process by which the lithosphere floats back to its original position after being pushed down by mountains or other features.
• Compensation depth: it is the weight of the crust is balanced by the buoyancy of the mantle
• Root zone: is directly beneath the mountain, it is part of the crust that extends deep into the mantle and it is less dense than the rest of the crust so it does not sink.
• There are 3 models of isostasy; the Airy-Heiskanen Model, the Pratty-Hayford Model, and Vening Meinesz Elastic Plate Model.
• Airy-Heiskanen Model
• this model assumes that the crust of constant density floats on a denser mantle
• its elevation is proportional to the depth of the root
• higher elevation the deeper the root, since it varies on the depth of the root
• have constant density but varies on depth of the root
• Oceanic crust have anti-roots or have thickness that is less than the thickness of normal crust.
• 
• Pratty-Hayford Model
• This model assumes topography varies inversely to topography
• Higher elevation, lower density of rocks
• Compensation depth is the same across vertical columns
• have unconstant density but have the same depth
• 
• Vening Meinesz Elastic Plate Model
• isostasy is not entirely local but is achieved by regional isostatic compensation.
• crust behaves as an elastic material that bends downward due to the topographic load.
• Local Compensation
• the root-zone is directly beneath a mountain and hydrostatic equilibrium is achieved at the compensation depth.
• Airy-Heiskanen and Pratt-Hayford models assume that isostasy is achieved by local compensation
• Vertical Crustal Movement
• Overcompensation causes uplift; caused by lowering of elevation after erosion of mountain but deeper root-zone
• Undercompensation causes subsidence; there is an increase in elevation due to additional load but the root zone is shallower.
• Isostatic gravity anomaly is the difference between the Bouguer gravity anomaly and the computed anomaly of the root zone, or .
• complete compensation:
• Overcompensation: Negative isostatic anomaly, or
• Undercompensation: Positive isostatic anomaly, or 

Magnetic Declination or magnetic variation

• is the angle formed between the magnetic north of the compass and the true geographical north.
• value of the declination changes with location and time.
• Positive if the magnetic north is along the east side of the true north.
• Negative if the magnetic north is along the west side of the true north.
• Isogonic lines is a join points on the earth’s surface which have a common declination value that is also constant
• Argonic lines are lines along with the value of declination is zero

Magnetic Inclination or magnetic dip

•  is the angle formed between the earth’s surface and the planet’s magnetic lines,  can be observed when a magnet is trying to align itself with the earth’s magnetic lines.
• the degree of inclination varies with the location on the earth. 
• Positive if the inclination is downwards.
• Negative if the inclination is upwards.
• Aclinic line is the location with 0 dip, this is present at the equator.

Types of Magnetism

1. Diamagnetism (opposite of the magnetic field)

•  property of materials that are repelled by a magnetic field
• all electron spins are paired.
• Opposite magnetic moment
•  is reversible, weak, negative, and independent of temperature
• quartz and calcite
•  have susceptibilities around -10^-6 in SI units
• often masked by stronger paramagnetic or ferromagnetic properties.

1. Paramagnetism (parallel)

• some materials are weakly attracted by an externally applied magnetic field
•  due to the presence of unpaired electrons in the material
• reversible, small and positive
•  k varies inversely with temperature (Curie Law)
• Curie law states that magnetic susceptibility of a paramagnetic material is inversely proportional to absolute temperature.
• temperature above which a solid is paramagnetic is called the paramagnetic Curie temperature or Weiss constant
• lay minerals and other rock-forming minerals (e.g., chlorite, amphibole, pyroxene, olivine) are paramagnetic at room temperature, with susceptibilities commonly around 10-5 to 10-4 in SI units.

1. Ferromagnetism (aligned parallel in magnetic domain)

• Material becomes magnetized and remains magnetized
• atomic magnetic moments are parallel to the external magnetic field and produce a spontaneous magnetization.
•  residual magnetization is called the remanence, or isothermal remanent magnetization (IRM)
• ferromagnetic material is heated, its spontaneous magnetization disappears at the ferromagnetic Curie temperature.

1. Antiferromagnetism (spins aligned anti-parallel in magnetic domains)

• Spins pointing in opposite directions
• may exist at sufficiently low temperatures, but vanishes at and above the Néel temperature
• Above the Néel temperature, the material is typically paramagnetic
• weak and positive, and remanent magnetization is not possible
• example mineral is ilmenite (FeTiO₃)

1. Parasitic Ferromagnetism (anti-parallel)

• When an antiferromagnetic crystal contains defects, vacancies or impurities, some of the antiparallel spins are unpaired
• mineral hematite (α-Fe₂O₃)

1. Ferrimagnetism (anti-parallel but not cancelled)

• unequal in magnitude so a spontaneous magnetization remains.
• Ferrimagnetic materials (called ferrites) exhibit magnetic hysteresis and retain a remanent magnetization when they are removed from a magnetizing field.
•  magnetite (Fe₃O₄), but maghemite, pyrrhotite and goethite are also significant contributors to the magnetic properties of rocks.

Review of the Basics of Magnetism

• The magnetic pole that is near the geographic North Pole is the south magnetic pole.
• Curie temperature: is the temperature at which a ferromagnetic material starts to lose its magnetization.
• Hans Christian Oersted: first discovered that electrical currents cause magnetic effects, and His experiment involved a compass needle being deflected by a current-carrying wire.
• The north and south of a magnet cannot be separated.
• Gauss:  unit of the magnetic field strength equivalent to 10^-4 T
• In Coulomb’s Law of Magnetism, force is directly proportional to the product of two poles strengths.
• When a bar magnet is cut into two equal halves perpendicular to its length, the pole strength of each piece remains the same.
• The presence of a magnetic field can be determined using a magnetic needle.
• A magnet is broken into two pieces. If these two pieces are brought closer to each other, they will repel or attract.
• In terms of magnetic properties, oxygen belongs to paramagnetic properties.
• Maximum magnetic force of a magnet is at both poles.
• Earth’s magnetism is due to dynamo effect.
• Magnetism at the center of bar magnet is zero.
• Michael Faraday found that a time-varying magnetic flux through a loop of wire induced a voltage.
• Diamagnetism is a type of magnetism appears in all materials
• William Gilbert, published a landmark treatise called De Magnete in which he summarized all that was known about magnetism in the 1600s.
• Electromagnet is a type of magnet in which magnetic field is produced by an electric current.
• formula of the Lorentz force. 
• Magnetic domains known as Weiss domains.
• Remanence is the magnetization left behind in a ferromagnetic material after an external magnetic field is removed.

Magnetic Surveying

• Magnetic anomaly is the difference between the measured magnetic field of the earth and that which would be expected from the International Geomagnetic Reference Field (IGRF).
• The difference between the observed or measured magnetic field and expected values is a magnetic anomaly.
• The expected value of the field at any place is taken to be that of the International Geomagnetic Reference Field (IGRF)
• It can be measured by magnetometer.
• Induced magnetization is the alignment of minerals in the current magnetic field.
• When the rock is in a magnetic field, the alignment of magnetic moments by the field produces an induced magnetization proportional to the field, the proportionality constant being the magnetic susceptibility.
• The direction of the induced magnetization is parallel to the earth’s magnetic field in the rock.
• The remanent magnetization of the rock is not related to the present-day geomagnetic field, but is related to the Earth’s magnetic field in the geological past.
• The total magnetization of a rock is the sum of the remanent and induced magnetizations.
• Königsberger ratio (Q_n) is defined as the ratio of the intensity of the induced magnetization to that of the remanent magnetization.
• Qn>1 – remanent is prevalent.
• Qn<1 – induced is prevalent.
• 3 types of magnetometer : Flux-gate magnetometer, Proton-precession magnetometer, and Absorption-cell magnetometer.
• Flux-gate magnetometer
• Composed of nickel-iron alloys (high magnetic susceptibility and low remnant magnetization).
• Examples are permalloy (78.5% Ni, 21.5% Fe) and nonmental (77% Ni, 16% Fe, 5% Cu, 2% Cr)
• The sensor of a flux-gate magnetometer consists of 2 parallel strips.
• Primary coil generates magnetic field
• Secondary coil detects changes in magnetic field (detects changes in the coil in terms of voltage).
• When a current flows in the primary coils, the parallel strips become magnetized in opposite directions. A secondary coil wound about the primary pair detects the change in magnetic flux in the cores. An output voltage is produced in the secondary coil that is proportional to the strength of the component of the Earth’s magnetic field along the axis of the sensor.
• The flux-gate magnetometer is a vector because it measures the strength of the magnetic field along the axis of the sensor.
• The flux-gate magnetometer does not yield absolute field values.
• Voltage is proportional to strength of magnetic field, and it is the output of magnetometer.
• It is robust and adaptable to being mounted in an airplane or towed behind it.

Proton-precession magnetometer (PPM)

Are capable of detecting tiny changes in magnetic flux density as small as 0.1nT.

Precession is the frequency that depends on the mass and rotation speed and the gravitational field strength.

Larmar precession measures the frequency of the precession of

Sensor is cylindrical container the is filled with proton-rich like water.

• The proton-precession magnetometer depends on the fact that the nucleus of the hydrogen atom, a proton, has a magnetic moment proportional to the angular momentum of its spin.
• The sensor of the instrument consists of a flask containing a proton-rich liquid, such as water.
• When the current in the magnetizing solenoid is switched on, the magnetizing field aligns the magnetic moments of the protons along the axis of the solenoid, which is oriented approximately east-west at right angles to the Earth’s field. 
• After the magnetizing field is interrupted, the proton magnetic moments precess about the direction of the ambient magnetic field.
• The frequency of the precession (the larmar frequency) can be measured and is proportional to the Earth’s magnetic field, as the spin and charge of the proton are constants.
• In contrast to the flux-gate instrument, which measures the component of the field along its axis, the proton-precession magnetometer cannot measure field components; it is a total field magnetometer.

Video: https://www.youtube.com/watch?v=VUYyHNzQ2AM

• Absorption cell magnetometer
• The absorption-cell magnetometer is also referred to as the optically pumped magnet or alkali-vapor magnetometer. Since it uses alkali metal in gaseous form.
• Ground state is the lowest/ no magnetic field.
• The magnetic moment associated with the spin of an electron can be either parallel or anti-parallel to an external magnetic field. This results in the ground state splitting into two sublevels with slightly different energies. The splitting of energy levels in the presence of a magnetic field is called the Zeeman effect
• Intensity of light is used to measure the strength of the magnetic field.
• Absorption-cell magnetometers utilize the Zeeman effect in vapors of alkali elements such as rubidium or cesium, which have only a single valence electron in the outermost energy shell.
• Polarized light which aligns by the alkali metals is passed through an absorption cell containing rubidium or cesium vapor and falls on a photoelectric cell, which measures the intensity of the light-beam.
• Optical pumping is the mechanism where irradiating the cell will empty sublevel G1 and fill level G2.
• In the rubidium-vapor and cesium-vapor magnetometers a polarized light-beam is shone at approximately 45 degrees to the magnetic field direction.

Video: https://www.nist.gov/video/measuring-field-strength-optically-pumped-magnetometer