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Chapter2: Lithospheric Mechanics This presentation contains illustrations from Allen and Allen (2005 ) and Press et al. (2004) Physical State of the Lithosphere Key Concepts – Surface Forces – Local Isostasy – Flexural isostasy – Thermal conductivity – Thermal Expansion – Heat transfer: A special case – Rock Rheology (2.3) – Relevant mantle rheological behavior – Rheology of continental crust • Elastic-perfectly plastic • Strain hardening and strain softening Key Concepts •Lithostatic stress(G3), deviatoric stress(G3), •uniaxial stress (G2), plane stress (G1) •bulk modulus(G1),flexural rigidity(G4) •thermal conductivity(G5), geotherm(G6) •Geoid(G7), Bouguer anomalies(G8) •Local vs. Regional Isostasy(G9) •diffusion and dislocation creep(G10), Byerlee’s Law(G2) (e-mail me your definitions to the above concepts as a PowerPoint slide– one illustration and two sentences … worth 1 point toward final curved grade; due , September 16. Originality (40%) and clarity (40%) and citations(20%) ) Surface (not surficial!) forces in geology We measure these forces of gravity and reaction to gravity not in terms of Newtons but by using the concept of stress, in Newtons per meter square, or Pascals. (See structural geology notes). What is atmospheric pressure? What is the hydrostatic state of stress? Lithostatic stress 1 cu. meter of water weighs 1000 kg x 10m/s2 or 10000 Newtons (N) 1 cu meter creates 10000N/m2 (Pa) of pressure at its bas 10 meters of water depth produces 100000 Pa (1 atm) of 0.1 MPa, that is every 10 m you dive down, pressure increases by 1 atm. 1000 vertically stacked 1-m-cubes of water weigh 10 million Newtons 1000 m (1 km) of stacked 1-m-cubes of water create 10 million Pascals (Pa) or 10 MPa at its base Lithostatic stress • If the above is true, then under 1 km of mud (2200 kg/m3) there should be about 22 MPa of pressure then under 30 km of granite (2670 kg/m3) there should be 801 MPa, or .8 GPa The rule to convert density into MPa of pressure per km is to take the density of the material in g/cc, move the decimal point over one space and change the units to MPa Other useful conversions to know are: To get MPa from psi mutliply Pounds/sq in by 0.689 x 10 ^-2 To get psi from MPa multiply MPa by 145.05 To convert to MegaPascals.... Divide by 1000000 Pa per 1 MPa Lithostatic stress • If you think you understand the previous slide, then answer the following question: On Planet Zog the average density of the 10 km-thick crust is 2500 kg m^-3 . Acceleration due to gravity is 3.2 m s^-2 . What is the pressure at the base of the crust? A. 80 MegaPascals B. 80 Newtons C. 800 Newtons D. 3 GigaPascals E. 30 Gigapascals F. None of the above • Lithostatic stress is responsible for the increase of pressure with overall depth in the earth but it is the differential stress that creates the faults and folds. • What is the vertical lithostatic stress gradient in granitic crust? What is the vertical stress gradient in the first 2 km of the ocean? Faults can develop: min max (Side view) max min min min (Side View) min max max (Bird’s Eye max View) min Brittle faults can develop: min max (Side view) max min min min(Side View) min max max (Bird’s Eye max View) min Sea of Galilea Dead Sea What is the direction of directed pressure (maximum principal stress direction)? How many orientations of faults can be generated for the same directed pressure direction?? Physical State of the Lithosphere Key Concepts – Surface Forces – Local Isostasy – Flexural isostasy – Thermal conductivity – Thermal Expansion – Heat transfer: A special case – Rock Rheology – Relevant mantle rheological behavior – Rheology of continental crust • Elastic-perfectly plastic • Strain hardening and strain softening Surface Forces (Pressure)LOCAL ISOSTASY Depth of compensation Isostasy or Archimedes’ Principle… States that the crust, mantle can float above the underlying material If the crust and mantle float then there exists a depth for which pressure above and pressure below are equal. This surface is known as the compensation depth General recommendations for local isostatic calculations (1) Define a surface of compensation (2) Define a reference column of crust and mantle (3) Compare the weight of the reference column with the unknown (4) Simplify algebra in terms of two unknowns (4) Keep physical units the same See syllabus (Tuesday, 23 September) for elaborated examples Isostasy homework due Thursday, 25 2008 • Derive the relation between ocean-floor depth and Moho depth for continental crustal settings. • Assuming that under the North Sea the continental crust and mantle is homogeneous, calculate the expected thickness of continental crust. • Do the same for the continental crust under the Grand Banks of Newfoundland • Show all your work–type it up and e-mail it to me Physical State of the Lithosphere Key Concepts – Surface Forces – Local Isostasy – Flexural isostasy – Thermal conductivity – Thermal Expansion – Heat transfer: A special case – Rock Rheology – Relevant mantle rheological behavior – Rheology of continental crust • Elastic-perfectly plastic • Strain hardening and strain softening Local/Regional Isostasy • • • • Picture from answers.com Local Isostasy - Different topographic heights are accommodated by changed in crustal thickness and rock density. Illus. a, b show the region surrounding the load will be horizontal, unaffected by the load. Regional Isostasy – The crust acts as an elastic plate and its inherent rigidity spreads topographic loads over a broader region. Illus. c shows the surrounding regions being deflected down toward the load. Flexure of the lithosphere • The outer skin of the earth down to depths where the temperature is cool enough and rock properties permit the earth can be visualized to be effectively elastic (e.g., rubber ball) over long periods of time, i.e., hundreds of millions of years. • A conclusion is that mountain belts will not sag over time but will maintain their mechanical strength indefinitely for practical purposes. A measure of the strength of the crust is how much it bends to a given load. This value is known as the flexural rigidity (D – units 23 of Nm) 10 Nm is equivalent to about 34 km of elastic thickness (Te) or moderately strong elastic lithosphere (TB 2006) Definition taken from: http://en.wikipedia.org/wiki/Flexural_rigidity • Flexural rigidity is defined as the force couple required to bend a rigid structure to a unit curvature. • The thin lithosphere plates which cover the surface of the Earth are subject to flexure, when a load or force is applied to them. On a geological timescale, the lithosphere behaves elastically and can therefore bend under loading by mountain chains, volcanoes and so on. • The flexure of the plate depends on: • The plate thickness • The elastic properties of the plate • The applied load or force One view on flexure in basins • Use local isostasy as a reference • Assume stationary conditions • Deviation from this reference is a measure of internal strength balanced against an applied load Measure of elasticity If the load is exceptionally narrow and small then the lithosphere will appear (infinitely) very strong because it does not give way at all to the load! But, if we use the other extreme case …. the case of a weight that is very wide… (i.e. > 1000 km)…..????? When it is very wide the condition reaches that of local isostasy and all the weight pushing down is balanced by the reaction of the mantle pushing up. Uniaxial Stress • When only one principal stress is acting on a body within the earth’s crust. • Example: – s1 ≠ 0, s2 = s3 = 0 • This is a rare occurrence. LITHOSTATIC AND DEVIATORIC STRESS •Lithostatic Stress= Equal pressure from all directions •Deviatoric Stress= Stresslithostatic •Affects textures and structures Tension• Deviatoric Stress http://myweb.cwpost.liu. edu/vdivener/notes/stre ss-strain.htm Boudinage Compr ession Shear • • Fold Fractures = + = + = + = + + + + + + + = + + + + + + + + + + Finite (reasonable and not extreme) geological load versus infinite (very wide) load Maximum depth of subsidence of the base of the crust in the case that the load is very wide and that hydrostatic compensation is local… i.e. some the elastic lithosphere has no internal strength. Now compare the case where the load is relatively narrow…. Our aim, now, is to understand the following: Downward directed invisible load creates space that fills with water and adds more vertical load Use reference at infinity (very far away) and pressure at level of compensation. At level of compensation pressures are in equilibrium. Level of compensation g(h.rhom + hw. rhow + w .rhom) Point load versus infinite (very wide) load Compare the case where the load is relatively narrow and the strength of the lithosphere becomes apparent…. Point load versus infinite (very wide) load (At infinity) g(h.rhom + hw. rhow + w .rhom) = (Under load) qa (Point load) + g(w.rhow + hw.rhow + h.rhom)-internal resistance to bending g(h.rhom + hw. rhow + w .rhom) = qa (Point load) + g(w+hw) rhow + h.rhom) – internal resistance to bending If there is internal strength in the lithosphere, then hw will not be as deep as it should be because the oceanic lithosphere resists! (Under load) (At infinity) g(h.rhom + hw. rhow + w .rhom) = internal resistance to bending + = qa (Point load) + g( (w+hw).rhow + h.rhom) – internal resistance to bending qa (Point load) g (rhom-rhow) w d 4w d 2w D 4 P 2 gw qa ( x ) dx dx “Equation 2.28” Equation 2.28 Physical State of the Lithosphere Key Concepts – Surface Forces – Local Isostasy – Flexural isostasy – Thermal conductivity – Thermal Expansion – Heat transfer: A special case – Rock Rheology – Relevant mantle rheological behavior - Rheology of continental crust • Elastic-perfectly plastic • Strain hardening and strain softening • Thermal Conductivity References Byerlee’s Law The thermal conductivity of a material describes • Defines criteria the effect of kinetic energy passing failure through a substance by intramolecular collisions. Its value for movement along a depends on several factors such asplane. composition, fault The NGS Geoid Page. (2008, April 22). Retrieved chemical structure, temperature, and pressure of September 15, 2008, Web site: • Movement depends rocks. It is represented by k and measured in: on http://www.ngs.noaa.gov/GEOID/ Wm-1°C-1. overcoming frictional resistance. Allen, P. and Allen, J. (2006). Basin analysis: • σ < 200 MPa Principles and applications. Malden, MA: Blackwell. σ = 0.85σ • 200 MPa<σ <2000MPa • σ = 50 MPa + 0.6σ From Earth Structure n s n n s n (2004) Allen, Philip A., and John R. Allen. Basin Analysis: Principles and Applications. 2nd ed. Malden, MA: Blackwell, G5 2005. 20-60. Equation Source: http://en.wikipedia.org/wiki/Thermal_conductivity Image Source: http://www.defluteglass.co.nz/images/studio_blowin Geotherm (G6) A curve that represents the increase of temperature with depth. • Because the crust is granitic, it contains radioactive elements that per capita produce a higher heat flow than the mantle. • References: Basin Analysis Principles and Applications, www.earthsci.org Thermal conductivity measures how well… for a given temperature gradient, conductive heat transfers/ moves through rock. Heat moves from higher temperature to areas of lower temperature. Halite: 7 kW/m/ºK Shale: 3 kW /m/ºK Thermal conductivity • The efficiency of that transfer is the thermal conductivity. So, for a given temperature gradient – dT/dz (continental or oceanic geotherms) the amount of heat being passed across any given portion of the earth’s surface (heat flux-Q) per unit time will depend on the coefficient of thermal conductivity (K). Fourier’s Law: dT Q K dz Q for continents is ~ 60 mW/m^2 or 60W/1000 m^2 Q for continents is ~ 80 mW/m^2 Geotherm Temperature variation with depth in solid crust indicates how much heat is flows from the mantle, and how much heat is generated within the crust. Q0 A 2 T T0 z z K 2K Q- heat flow (negative is upward) K- thermal conductivity A- internal heat generation Z -depth Geotherm Temperature oceanic z continent Heat Production versus depth Heat production at surface (Hs )is maximum H eat production = Hs exp (-z/ar) Heat production Z Depth (km) K 3W / m / C Q0 70mW / m3 A0 2.5 10-6Wm3 ar 10km Geotherms Surface heat flow (Q0) observations indicate that heat flow increases linearly with the heat production of surface rocks. This is mathematically best accomplished by assuming that heat production decreases with depth in an exponential manner. Q0 A0 ar2 a T T0 z 1 e r K K y ar is the depth at which heat production is ~halved A0 is the surface heat production Global heat production • Continental surface heat flow comes about 50% from the mantle (U,K,Th) and about 50% from radioactive sources. • Heat flow was x2 what it is now, about 3 billion years ago • Oceanic heat flow largely depends on thermal age of the lithosphere and not on the radioactivity Sampling thermal conductivity On board R/V Joides Resolution, Leg 150 New Jersey Margin, US Atlantic Coast, B. Hoppie (right) (MNSU, Mankato), C. Fulthorpe(left) (UT Austin) Thermal conductivity • We can measure thermal conductivity with respect to standards as you can see in this overhead of a thermal conductivity measurements on board Leg ODP 150 New Jersey Margin in the summer of 1993. People are (L toR) Bryce Hoppie and Craig Fulthorpe. These needles contain heaters and temperature sensors. These needles measure the speed at which the temperature changes over time to calculate the conductivity of the material into which they are inserted. Physical State of the Lithosphere Key Concepts – Surface Forces – Local Isostasy – Flexural isostasy – Thermal conductivity – Thermal Expansion – Heat transfer: A special case – Rock Rheology (2.3) – Relevant mantle rheological behavior – Rheology of continental crust • Elastic-perfectly plastic • Strain hardening and strain softening Thermal Expansion • At a constant pressure, the average silicate rock will expand 1/100,000 th of its entire length for every degree that it goes up in temperature. This of course affects the density of the rock. • The amount that the rock contracts or expands, at an assumed constant pressure, for a given temperature change is known as the thermal expansion coefficient, or the volumetric coefficient of thermal expansion, written as v Thermal expansion • 100,000 m * 10^-5 * 1ºK = 1m/ºK Thermal contraction • The converse is true as well…. for every degree that temperature drops, the lithosphere will contract 1/100,000 th of its entire length Thermal contraction O km 125 km Start (at time=0) 1300º After 200 my 1300º Thermal contraction • So, a 125-km piece of mantle that is initially at, say 1300ºK, and which then cools by an average of about 650ºK will shrink by how much …..? Choose an answer • (a) 2km • (b) 4 km • (c) 10 km • (d) 20 km • (e) none of the above Answer • 125,000 m * 650ºC * 10^-5 = 812 m Isostatic consequences of cooling mantle • If the mantle contracts as it cools it also becomes denser for doing so…. • Final density = original density * thermal expansion coefficient (temperature drop) final start (1 T ) v Physical State of the Lithosphere Key Concepts – Surface Forces – Local Isostasy – Flexural isostasy – Thermal conductivity – Thermal Expansion – Heat transfer: A special case – Rock Rheology – Relevant mantle rheological behavior – Rheology of continental crust • Elastic-perfectly plastic Time-dependent heat conduction We observe that (1) heat flow decreases away from the mid-ocean ridges as a function of age and (2) water depth increases as a function of age Heat flow versus age Plate Model for Sea-floor spreading • Parsons and Sclater (1977) Temperature (from model) and thickness versus age Leeds et al. (1974) Physical State of the Lithosphere Key Concepts – Surface Forces – Local Isostasy – Flexural isostasy – Thermal conductivity – Thermal Expansion – Heat transfer: A special case – Rock Rheology – Relevant mantle rheological behavior - Rheology of continental crust • Elastic-perfectly plastic Bulk Modulus (K) (G-1) www.ux1.eiu.edu/.../10FldRst/Images/bulk.gif -measures a substance's resistance to uniform compression -defined as the pressure increase needed to effect a given relative decrease in volume - is the reciprocal of a substances compressibility(β) which is the measure of the relative volume change of a fluid or solid as a response to a pressure (or mean K=1/β stress) change Plane Stress (G1) σ3 σ2 σ 1 http://maps.unomaha.edu/Maher/GEOL3300/week4/ellipse.j peg -a state of plane stress exists when one of the three principal stresses is zero σ1≥σ2>0 σ3=0 -the other two stresses are nonzero and act on the same plane creating plane stress At least 6 factors control how rock deforms e.g. at shallow depth a rock may fracture whereas at depth it may flow. Factors are: (1) rock type (2) Confining and directed pressure (3) temperature (4) Fluids (5) Time (6) Rate of deformation Physical State of the Lithosphere Key Concepts – Surface Forces – Local Isostasy – Flexural isostasy – Thermal conductivity – Thermal Expansion – Heat transfer: A special case – Rock Rheology – Relevant mantle rheological behavior – Rheology of continental crust • Elastic-perfectly plastic • Strain hardening and strain softening Diffusion and Dislocation Creep Andrew Sampson David Smolkin Creep is defined as deformation that results from long periods of stress. It is time-dependent with respect to stress. Creep becomes exaggerated with greater thermal activity and is the result of mantle convection. Diffusion Creep Diffusion Creep occurs as vacancies, or point defects, in the material move in the direction of maximum stress due to high temperatures (near the melting point). Diffusion creep occurs at low stress and results in crystals behaving as a Newtonian fluid (similar to water). Its viscosity depends exponentially on pressure and inverse absolute temperature. Dislocation Creep Dislocation Creep occurs as high stress levels moves dislocations, or linear/planar defects, and behaves as a non Newtonian fluid. Like diffusion creep, its viscosity depends exponentially on pressure and inverse absolute temperature. Occurs primarily in mantle and can occur in lower lithosphere and is the dominant form creep in the mantle. Mantle viscosity Models • Diffusion creep – Very Low stress – Newtonian fluid, linear behavior – Atoms diffuse e v V ( fluid ) Mantle viscosity • High stress creep • Dislocation creep • Model for mantle plasticity is non-linear Qc RT Power Law Creep e Ae n Q is activation energy A is a creep-mechanism parameter Viscosity depends on stress and temperature 1 f V e stress T (º K ) Dislocation Creep • Temperature-activated creep – Movement of mantle by microfractures at the subcrystal scale and synchronous healing of these imperfections Physical State of the Lithosphere Key Concepts – Surface Forces – Local Isostasy – Flexural isostasy – Thermal conductivity – Thermal Expansion – Heat transfer: A special case – Rock Rheology – Relevant mantle rheological behavior – Rheology of continental crust • Elastic-perfectly plastic • Strain hardening and strain softening Rheology of continental crust Byerlee’s Law • Linear relation between shear stress and normal stress for rock strength Shear stress Normal stress Byerlee’s Law (G2) • Defines failure criteria for movement along a fault plane. • Movement depends on overcoming frictional resistance. • σ < 200 MPa σ = 0.85σ • 200 MPa<σ <2000MPa σ = 50 MPa + 0.6σ n s n n From Earth Structure (2004) s n Physical State of the Lithosphere Key Concepts – Surface Forces – Local Isostasy – Flexural isostasy – Thermal conductivity – Thermal Expansion – Heat transfer: A special case – Rock Rheology – Relevant mantle rheological behavior – Rheology of continental crust • Elastic-perfectly plastic • Strain hardening and strain softening Elastic-Plastic model for breaking rock strain stress strain Elastic-Plastic model for breaking rock strain stress strain Strain hardening strain stress strain Strain softening strain stress strain Elastic-plastic stress strain Dislocation Creep (AL)• Thermally activated deformation that occurs at relatively higher shear stress than diffusion creep. Diffusion creep happens at very small scales (atomic and molecular), and the crystalline solid flows as a Newtonian fluid. Dislocation creep happens at larger scales and causes the solid to exhibit non-Newtonian behavior because of the higher shear stress. Elastic-plastic stress strain Elastic-plastic stress strain Elastic-plastic stress strain Diffusion Creep (RR) • Diffusion is the propagation of cracks in a crystal structure in response to stress where the parting goes from an area of high stress to low stress. Diffusion Creep is the movement of atoms along partings from areas of high stress to low stress creating foliations. Lithostatic Stress – C.A. The stress applied to a rock in equal directions due to the weight of an overlying rock column. At the surface of the earth the lithostatic stress would be zero, but as you move further below the earth's surface the weight of the overlying rock causes an increase in stress. Source: http://myweb.cwpost.liu.edu/vdivener/notes/stress-st Bouguer Anomalies (TJH) • The difference between measurements of gravity based on the value used by a theoretical model of what it should be at that latitudinal position, and a different value that compensate for latitude, elevation, free-air corrections, and *Bouguer correction. • *Developed be Pierre Bouguer proved that gravity differs with elevation Bulk Modulus (K) (MB) The ratio of pressure change (P) to volume change (V) K = P/ V This describes a materials ability to resist changes in volume Deviatoric Stress (TA) • • A condition in which the stress components operating at a point in a body are not the same in every direction. Is the difference between the mean stress (Sum of stress in three directions divided by 3) and total stress Geotherm (SE): The variation of temperature with depth. • Major Influences – Thermal Conductivity – Concentration of Radiogenic Elements – Temperature at Surface – Proximity to Magma or other Heat Sources Eugene Island Field Gulf of Mexico Thermal Conductivity (AD) Heat transfer is achieved by processes of: 1) Conduction- a diffusive process in which kinetic energy is transferred by intermolecular collisions. Conduction is the primary thermal process in the lithosphere. 2) Convection- requires motion of the medium to transmit heat. Convection of heat from the core is the principal thermal process of the mantle. 3) Electromagnetic radiation- only important in determining surface heat budget, not the internal heat budget Fourier’s Law • Fourier’s Law is the central relation for conductive heat transport • It states that the heat flux Q is directly proportional to the temperature gradient • Q = -K (dT / dy) K = coefficient of thermal conductivity T = temperature at a given point in the medium y = coordinate in the direction of the temperature variation Continental Crust • • Generally, regions of high heat flow correspond to active volcanic zones or regions of extensional tectonics. Areas of continental collision are related to low or normal surface heat flows. Oceanic Crust • • • The surface heat flow of the oceans is related to the age of the seafloor rather than the concentration of radioisotopes. Newly created oceanic crust cools by conduction as it travels away from the mid-ocean ridge. About 60% of the Earth’s heat loss takes place through the ocean floor. One-Dimensional Heat Conduction • • Temperature change of a piece of lithosphere has 3 components: These components are a basal heat flow term, an internal heat generation term, and an advective term Advective Heat Flow • Advective heat flow can be one of two things. • It can be movement towards the surface associated with downcutting action of erosion, or the velocity of deposition. Uniaxial stress(MS) • Uniaxial stress is stress in only one direction and zero stress in the perpendicular direction. This XYZ graph shows that there is only stress in the Y direction, both X and Z directions show a stress of Zero. North pole is up & black line runs through Greenwich Geoid (HF) GEOID – a surface on which the earth’s gravitational forces are equal everywhere and coincides with mean sea-level. Based on these concepts: - sea covered the earth - no disturbing forces like winds, tides, ocean currents, ect. - the force of gravity is perpendicular to the geoid everywhere. - Ellipsoid represents the bulk shape of the earth. -Geoid departs above or below the ellipsoid resulting in a smoother representation of the earth’s actual surface. For more info: http://www.answers.com/topic/geoid, http://solid_earth.ou.edu/notes/geoid/earths_geoid.htm H. FOLEY Geoid- equipotential reference surface of Earth based on gravity anomalies; best fits mean sea level. • Vertical datum of the Earth • Where we see high topography, we do not necessarily see a high variation in geoid due to isostatic equilibrium • Find the geoid near you by going to http://www.ngs.noaa.gov/cgibin/GEOID_STUFF/geoid03_prompt1.prl Byerlee’s Law • Defines failure criteria for movement along a fault plane. • Movement depends on overcoming frictional resistance. • σ < 200 MPa σ = 0.85σ • 200 MPa<σ <2000MPa σ = 50 MPa + 0.6σ n s n n From Earth Structure (2004) s n Bulk Modulus (K) www.ux1.eiu.edu/.../10FldRst/Images/bulk.gif -measures a substance's resistance to uniform compression -defined as the pressure increase needed to effect a given relative decrease in volume - is the reciprocal of a substances compressibility(β) which is the measure of the relative volume change of a fluid or solid as a response to a pressure (or mean stress) K=1/β Plane Stress σ3 σ2 σ 1 http://maps.unomaha.edu/Maher/GEOL3300/week4/ellipse.j peg -a state of plane stress exists when one of the three principal stresses is zero σ1≥σ2>0 σ3=0 -the other two stresses are nonzero and act on the same plane creating plane stress Uniaxial Stress • When only one principal stress is acting on a body within the earth’s crust. • Example: – s1 ≠ 0, s2 = s3 = 0 • This is a rare occurrence. LITHOSTATIC AND DEVIATORIC STRESS •Lithostatic Stress= Equal pressure from all directions •Deviatoric Stress= Unequal pressure in different directions -Three different Deviatoric Stress types Tension • Boudinage Compression • Folds http://myweb.cwpost.liu. edu/vdivener/notes/stre ss-strain.htm •Affects textures and structures Shear • Fractures Flexural Rigidity • “Is the resistance to bending (flexure) of a material” • For instance, in regards to the lithosphere: “is the uppermost rheologic layer of the earth. . .behaves rigidly on geologic timescales. If you place a load on it, the lithosphere either supports the load or bends – it does not simply flow out of the way.” Marshak, Stephen, and Ben A. van hoc hw href hoc hm g ( m hm oc hoc w hw ) strength point load (weight) = g (href w oc hoc ) large load Discovered by Pierre Bouguer in the 1700s the difference between what gravity is at a particular location(absolute observed gravity) and what gravity is supposed to be at that location(theoretical gravity value). Bouguer anomaly = theoretical gravity value absolute observed gravity value.