Gravity Method - Chapter 3

CHAPTER 3 GRAVITY METHOD Introduction • Measurements of the gravitational field at a series of different locations over an area of interest. • The objective in exploration work is to associate variations with differences in the distribution of densities and hence rock types. • Dense and solid roc...

CHAPTER 3 GRAVITY METHOD Introduction • Measurements of the gravitational field at a series of different locations over an area of interest. • The objective in exploration work is to associate variations with differences in the distribution of densities and hence rock types. • Dense and solid rocks have higher gravity accelerations • Dense rock (anticline), ρ↑ → g ↑ • Salt dome, ρ↓ → g↓ Introduction Introduction • Most of the gravity survey for petroleum exploration is design for reconnaisance study in large area and unexplored. • advantages → faster and cheaper. Theory of Gravity • Need to understand on fundamental concept of physics related to gravitational force, gravitational acceleration and gravitational potential. a) Gravitational force - based on Newton law’s (universal law of gravitation) • - states that the mutual attractive force between two point masses, m1 and m2, is proportional to one over the square of the distance between them : Theory of Gravity F = G(m1.m2)/r2 where, F = force of attraction (dyne) G = universal gravitational constant (6.67 x10-8 dyne.cm2/g2) r = distance between m1 and m2 (cm) Theory of Gravity b) Gravitational acceleration - Acceleration on the mass m2 due to attraction of m1 (law of mutual attraction) is given as: a = F/m2 • Combining Newton's second law with his law of mutual attraction, the gravitational acceleration on the mass m2 can be shown to be equal to the mass of attracting object, m1, over the squared distance between the center of the two masses, r. g = G m1/r2 Theory of Gravity • Or we can combine them to obtain the gravitational acceleration at the surface of the Earth: g = GM/R2 • Variations in g: Theory of Gravity c) Gravitational potential • The gravitational potential, U, due to a point mass m, at a distance r from m, is the work done by the gravitational force in moving a unit mass from infinity to a position r from m. • Gravitational potential: U = Gm1 dr/r2 = Gm1/R • U is a scalar field which makes it easier to work with. Theory of Gravity The picture can't be displayed. QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Theory of Gravity - Units for gravity (g): - SI unit SI for g : m/s2 – rarely used - 1 cm/s2 = 1 Gal (for Galileo) = 0.01 m/s2 - milliGal or mGal = 10-3 Gal – typical unit for field studies - or gravity unit (gu) 1 gu = 0.1 mgal Theory of Gravity • Normal value of g at the surface of the Earth: gE = 9.8 m/s2 = 980 cm/s2 =980 Gal = 980,000 mGal = 9800 x 103gu • In exploration survey, measuring of very small gravitational acceleration values  milligal (mGal) Gravitational Acceleration • Factors that Affect the Gravitational Acceleration: 1. Latitude 2. Elevation 3. Topographic effects 4. Tidal affects 5. Variation in rock density in subsurface Gravitational Acceleration • Changes in the observed acceleration caused by the ellipsoidal shape and the rotation of the earth • Gravity differences for equator and pole is 5 gal or 0.5% from average g (~ 980 gals). • Elevation variations - 0.1 gal or ~ 0.01%. • In gravity exploration, factor (5) is important but has the smallest affects - 10 mgal (~ 0.001%). • Common elevation to which all of the observations are corrected to is usually referred to as the datum elevation or Geoid . Gravitational Acceleration & Corrections • Geoid – mean sea level is an equipotential surface. • Reference Spheroid – all points on the Earth surface have equal gravity value • g value at spheroid is given by formula (Geodetic Ref system, 1967): gφ = go (1 + α sin2 φ + β sin2 2φ) go = g at equator = 978.0318 gals φ = latitude α = 0.0053024 β = -0.0000059 Gravity Corrections 1) latitude correction - the value of gravity increases with the geographical latitude. - latitude correction value is negative if away from equator: LC = dgL /ds = 1/Re (dgL /dφ) ≈ 1/Req (dgL /dφ) ds = horizontal distance (N – S) Re = Earth radius at latitude φ Req = Earth radius at equator Penurunan Graviti QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Gravity Corrections 2) elevation variation corrections - can be divided into 2: i) free-air correction, FAC - g values decrease with elevation or distance from the center of the Earth g ∞ 1/r2 - for free-air correction FAC = dgFA /dRe = -2GMe/Re3 ≈ -2g/Req ≈ - 0.9406 mgal/ft ≈ - 0.3086 mgal/m Penurunan Graviti QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Gravity Corrections ii) Bouguer correction (BC)/ slab effects - accounts for rock thickness between current and base station elevation - treat the rock as an infinite horizontal slab: BC = dgB /dRe = 2πGρ mgal/ft = 0.01277 ρ mgal/ft = 0.000419 ρ mgal/m Gravity Penurunan Corrections Graviti QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Gravity Corrections - if rock density, ρ = 2.67g/cm3 dgB /dRe = 0.034 mgal/ft 3) Terrain correction (TC) - when BC is inadequate, also use terrain correction. • - terrain correction consider a topographic irregularity. Changes in the observed acceleration related to topography near the observation point. • - there are several TC approaches; rectangular grid (template) and Hammer segments. Penurunan Graviti Gravity Corrections hill QuickTime™ and a valley TIFF (LZW) decompressor are needed to see this picture. Penurunan Graviti Gravity Corrections QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Gravity Corrections - both need topographic map (shows the different in elevation between station and surrounding). - most common using template - gravity for each sector can be calculated: dgT = Gρө{(ro-ri) + (ri2+z2)½ – (ro2+z2)½} where, ө = sector angle z = |es - ea| , es = sector elevation es = mean elevation ro , ri = outer and inner radius Gravity Corrections - if ρ = 2.67g/cm3 dgT = 5.35 x 10-3ө{(ro-ri) + (ri2+z2)½ – (ro2+z2)½} 4) Eotvos correction (EC) - EC used to measure gravity on moving vehicle such as ship. EC = 75.03Vsinα cosφ + 0.04154V2 gu where, V = ship speed (knots) α = direction φ = latitude Gravity Corrections 5) Tidal correction • - Changes in the observed acceleration caused by the gravitational attraction of the sun and moon. Normally to be included in the drift correction. • Instrument drift - Changes in the observed acceleration caused by changes in the response of the gravimeter over time. Gravity Corrections Tidal & drift corrections: a field procedure • - to establish a base station - A reference station that is used to establish additional stations in relation thereto. Gravity Corrections • Let now consider an example of how we would apply this drift and tidal correction strategy to the acquisition of an exploration data set. • Establish the location of one or more gravity base stations. • Establish the locations of the gravity stations. • After some time period, usually after 1 hour, we return to the base station. • The procedure is generally referred to as a looping procedure. Gravity Corrections • For example, the value of the temporally varying component of the gravity field at the time we occupied station 159 is computed using the expressions given below: Gravity Corrections Bouguer Gravity - when all correction have been done, corrected gravity value or Bouguer gravity, gB for station is available: gB = gobs ± dgL + dgFA – dgB + dgT = gobs ± dgL + 0.094h – (0.01277h-T)ρ Free-air Anomaly • For regional gravity study, gravity anomaly is the difference between observed gravity, gobs at any point and theoretical gravity, gr values. • If free-air anomaly is only considered in gobs value, is called free-air anomaly, ΔgFA ΔgFA = gobs ± dgL + dgFA – gr • Free-air anomaly, ΔgFA mostly used for offshore and continental shelf survey. Free-air Anomaly QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Bouguer Anomaly • The corrected gravity diff. between a station and a base in land measurements is called the Bouguer anomaly, ΔgB : ΔgB = gB - gr ΔgB = gobs ± dgL + dgFA - dgB + dgT – gr ΔgB = gobs ± dgL + 0.094h – (0.01277h)ρ – gr • For smaller scale engineering/environmental survey: – Not tied to absolute gravity – Use corrections with accuracy necessary Gravity Measurement Density Variations of Earth Materials • The densities associated with various earth materials are shown below: Material Density (gm/cm3) Air ~0 Water 1 Sediments 1.7-2.3 Sandstone 2.0-2.6 Shale 2.0-2.7 Limestone 2.5-2.8 Granite 2.5-2.8 Basalts 2.7-3.1 Metamorphic Rocks 2.6-3.0 Density Variations of Earth Materials • Consider the variation in gravitational acceleration that would be observed over a simple model. • Assume due to the presence of a small ore body. • Let the ore body have a spherical shape. Gravity Measurement & Equipment • Measuring g: • •   Absolute and relative: variations in g on the order 1 mGal need to measure g to better than 1 part in 1 million use instruments sensitive to relative changes in g Gravity Measurement & Equipment • Absolute Gravity: Gravity Measurement & Equipment • Relative gravity: • Mass on spring measurements. Two types: • 1. Stable Gravimeter. Ex: Askania, Gulf dan Norgaard • Change in g --> change in spring length. • Δg = -k ΔL/m Gravity Measurement & Equipment • 2. Unstable gravimeter or astatic. • Suitable choice of mass, spring constant and geometry makes the system unstable and very sensitive to changes in g. • Ex: LaCoste-Romberg and Worden gravity meter. Gravity Measurement & Equipment • LaCoste-Romberg gravity meter. Gravity Measurement & Equipment • Worden Gravity Meter Gravity Measurement & Equipment • Modern gravimeters are capable of measuring changes in the Earth's gravitational acceleration down to 1 part in 100 million. • This translates to a precision of about 0.01 mgal. Such a precision can be obtained only under optimal conditions when the recommended field procedures are carefully followed. Field Determination of Density • Why do we need rock density? • Nettleton method: density profile. • Other methods: • The same problem can be formulated mathematically and solved by least squares • Borehole logging. Gravity Surveying • • • • • • • • • Survey design considerations: Uniform grid – for easier interpretation Station spacing: s < h h is the depth of the body of interest Absolute and relative station locations are needed …how accurate? Typical station spacing: Regional geologic studies: km to 10s of km Local structure/Engineering/Environmental: 10s to 100s m Near surface e.g. archeology: few meters Local and Regional Gravity Anomalies • Let's consider a slightly more complicated model for the geology in this problem. • Assume that the ore body is spherical in shape and is buried in sedimentary rocks having a uniform density. • Let's now assume that the sedimentary rocks in which the ore body resides are underlain by a denser Granitic basement that dips to the right. Local and Regional Gravity Anomalies • Notice that the observed gravity profile is dominated by a trend indicating decreasing gravitational acceleration from left to right. • This trend is the result of the dipping basement interface. Unfortunately, we're not interested in mapping the basement interface in this problem; rather, we have designed the gravity survey to identify the location of the buried ore body. • The gravitational anomaly caused by the ore body is indicated by the small hump at the center of the gravity profile. Local and Regional Gravity Anomalies • If we knew what the gravitational acceleration caused by the basement was, we could remove it from our observations and isolate the anomaly caused by the ore body. • This could be done simply by subtracting the gravitational acceleration caused by the basement contact from the observed gravitational acceleration caused by the ore body and the basement interface. • The gravitational acceleration produced by these large-scale features is referred to as the Regional Gravity Anomaly. • That portion of the observed gravitational acceleration associated with the ore body is referred to as the Local or the Residual Gravity Anomaly. Local and Regional Gravity Anomalies • The effects of burial depth on the recorded gravity anomaly, consider three cylinders all having the same source dimensions and density contrast with varying depths of burial. • For this example, the cylinders are assumed to be less dense than the surrounding rocks. Local and Regional Gravity Anomalies • Separating Local and Regional Gravity Anomalies. • Graphical Estimates - These estimates are based on simply plotting the observations, sketching the interpreter's estimate of the regional gravity anomaly, and subtracting the regional gravity anomaly estimate from the raw observations to generate an estimate of the local gravity anomaly. • Computer Approach Isolating gravity anomalies • Small geological features near the surface cause small wavelength anomalies. • Large scale structures at greater depth cause longer wavelength anomalies. Isolating gravity anomalies • Enhance the anomalies of interest. Isolating gravity anomalies • Survey ∆g minus regional trend Isolating gravity anomalies • Survey ∆g regional trend minus high frequency noise Isolating gravity anomalies • 1. Regional trend removal: high-pass filter • 2. Noise filter: low-pass filter • • • bandpast filter Strong regional dip, deflected by oil-filled anticline, Oklahoma Overview Analysis and interpretation • Buried sphere vertical column Analysis and interpretation Example: Salt dome •    •    •  Anomaly: Near circular Δgmax ~ 16 mGal x1/2 ~ 3700 m Assume spherical salt body: Depth to center ~ 4800 m Assume Δρ -250 kg/m3: Radius ~ 3800 m Depth to top of salt: 4800-3800 = 1000 m Example: Mapping basin depth Mapping basin depth Tutorial 3 1. 2. Stat. Time Dist. (m) Elev. (m) Reading BS 0805 0 0 2934.2 1 0835 20 10.37 2931.3 2 0844 40 12.62 2930.6 3 0855 60 15.32 2930.4 4 0903 80 19.40 2927.2 BS 0918 0 0 2934.9 Base reading Drift corr’d anom. (gu) LC (gu) FAC (gu) BC (gu) 0 2934.49 -12.10 0 -0.16 32.00 -11.73 Free air anom (gu) Boug. anom. (gu) 0 0 19.74 8.01 0 0 Built a graph and determine the value of drift correction Determine gravity anomalies and built a graph of gravity anomaly (Δg) corrected against height