Lecture 6 - Geophysics PDF

Lecture 6 Geophysics GEOPHYSICS  a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis Sub-discipline of geophysics  Global geophysics structure of t...

Lecture 6 Geophysics GEOPHYSICS  a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis Sub-discipline of geophysics  Global geophysics structure of the Earth  Exploration geophysics petroleum geophysics - structures that trap oil mining geophysics - detection of ore bodies groundwater studies - depths, thicknesses  Geotechnical & environmental geophysics site investigations - mechanical properties and depth contaminant studies - detection, flow direction archeological investigation Objective of geophysics  to locate or detect the presence of subsurface structures or bodies and determine their size, shape, depth, and physical properties (i.e. physical parameters) Geophysical Anomaly  A geophysical anomaly is detected when a survey encounters some geometric perturbation in the distribution of a particular physical property in the rocks.  Gravity anomalies arise due to lateral perturbations in rock density, magnetic ones are caused by lateral changes in rock magnetization, and seismic anomalies indicate variations in acoustic impedance. SIGNAL + NOISE Signal = objective of the survey; due to the causative or target body Signal - Signal+ Noise Noise = anything else measured but which may not contain useful information S/N ratio is of outmost concern in geophysical surveys. Noise www.guruprasad.net Nature of Field Natural – utilizes natural fields of the earth (e.g. gravity, magnetic, spontaneous potential) Artificial – involves generating a field using an artificial source (e.g. seismic reflection and refraction, electrical resistivity, induced polarization) Magnetic potential http~://.:a.y,,·ikj1,tdit1.orgi,-.·iki.' t'i k:VH'i_Solr11uid_corn,ct2.s,,g Vibrator Truck Recofding Truck (Energy Source) Geophone Geophysical Noise Disturbance Field Noise  Natural - fluctuating measurements (e.g. lightning strokes, magnetic storms, earthquakes, typhoons)  Artificial – man-made structures (e.g. powerlines, buried metal pipes, metallic objects on the ground) Remedy: (natural) discontinue measurements; (artificial) stay away from sources of noise  Geologic Noise – variable thickness of overburden, presence of noneconomical minerals in the overburden or overlying layers Remedy: mathematical corrections Mode of applicability     Ground – best applied to flat or gently undulating terrain Airborne – for large or heavily forested areas Marine – for offshore investigations Borehole – records one or more physical properties as a function of depth Table 1.1 eoph)~C'.il m~thcxh. Method Measured ,parameter Operati\e ph) ical propert <;c smic Tra\i cl ti mes of rell ected/re fra cted Densi and elastic moduli, \\ hich determine the prop.'!gation velocity of se1sm1c \V"d\'eS se1sm1c wa\lcs Spa tial variations in the strength oi the gravitational field oi the E.lrth Densi • Spa ial , riations in the strength of the geomagnetic field 1\1agnetic susccptibilit)' and rem nence Resistivi Eanh resistance Electncal conductivit • Induced polarization Polariz.ation vohages or frequen ·depend nt ground rcsisranc Electrical capacitance Sc Ii-potential Electrical po<ential Electrical conductivity Electromagnetic Response to clectromagnc.: ic radiation Electrical onduccivity, nd inductance R.idar Trav ,1 ,im - of r •necred radar pulses Gravi • Electric.al Table 1.l Gcophpic.il mn·()1og .i.pplicJ.tio ru. Application Appropriate survey me'Chod • Exploration fo r fossil fuels (oil, gas, coal) Exploration fo r metaltiferous mirneral depo5its Exploration fo r bulk mineral deposits (sand and gravel) Exp!oration fo r undergrournd water supplies Erngineering/constructron site investiga tion Archaeological investigatiorns S. G, M, iEM1 * M, Eh,\ E, SP, IP, R S, I E), ~GJ E,. S, tGJ, lRdJ E, S, Rd. \G,, MJ Rd, E, E.i\1, 1\\, tS} g1r.1¥1ty; magn.c-tic; seismic; r.idiomctric: R.d. gmuad-penttr.iriag r.id.J.r. Subudi:lr}' mC'thods G . M , S , . E. d c c t r i c a . 1 ~ is t ii,, · i t y ; S1elf-potc111ti.u: lbr.ickcts_ S P , i n I P . i n d uc i e d polariutiio n: EJ\t d«-m:im;igpc-tic: R. Physical Properties  Density – mass per unit volume  Magnetic susceptibility – degree to which a substance may be magnetized; k = I/H k = magnetic susceptibility; I = intensity of magnetization; H = magnetic field  Elasticity – deformation that vanish upon removal of the stresses; elastic moduli (Young’s modulus, bulk modulus, shear modulus, etc.)  Conductivity – ability of a material to conduct electrical current UNITS USED  Magnetics  magnetic susceptibility: dimensionless  magnetic field strength: Gauss = 10^-4 T; Gamma = nT  Gravity  density: kg/m3; g/cm3  gravitational field strength: mgal = 10^-3 cm/s^2  Seismic velocity: m/sec; km/sec; m/msec  Electrical  resistivity: ohm-meters  conductivity: mho/m = Siemens/m Gravity Survey Principle  Spatial variations in the earth’s gravitational field are caused by lateral variations in rock density.  In gravity surveying, subsurface geology is investigated on the basis of variations in the Earth’s gravitational field arising from differences of density between subsurface rocks.  Causative body - which is a rock unit of different density from its surroundings. A causative body represents a subsurface zone of anomalous mass and causes a localized perturbation in the gravitational field known as a gravity anomaly  Prerequisite for gravity anomaly: lateral density contrast Gravity Survey Density variations Based on rock types: Sedimentary rocks exhibit the greatest range of density variation (mineral composition, cementation, porosity, pore fluid type) Density of igneous rocks is controlled primarily by the silica content. Gravity Survey Physical property Shale 2.00 - 2.65 Serpentine 2.20 Sandstone 2.20 - 2.70 Quartz 2.65 Granite 2.65 - 2.75 Olivine 3.30 Gabbro 2.85-3.10 Pyrite 5.00 Quartzite 2.60 - 2.70 Magnetite 5.10 Schist 2.60 - 3.00 Sphalerite 4.00 Amphibolite 2.70 - 3.20 Gold 19 Gravity Survey Basic Theory The basis of the gravity survey method is Newton’s Law of Gravitation, which states that the force of attraction F between two masses m1 and m2, whose dimensions are small with respect to the distance r between them, where G is the Gravitational Constant (6.67 x 10^-11 m^3 kg^-1 s^-2). F = Gml m? ..... Gravity Survey Basic Theory Consider the gravitational attraction of a spherical, non-rotating, homogeneous Earth of mass M and radius R on a small mass m on its surface. It is relatively simple to show that the mass of a sphere acts as though it were concentrated at the centre of the sphere and by substitution in equation Force is related to mass by an acceleration and the term g = GM/R^2 is known as the gravitational acceleration or, simply, gravity. The weight of the mass is given by mg. Gravity Survey Basic Theory On such an Earth, gravity would be constant. However, the Earth’s ellipsoidal shape, rotation, irregular surface relief and internal mass distribution cause gravity to vary over its surface. The gravitational field is most usefully defined in terms of the gravitational potential U: U=- GM - r Gravity Survey Basic Theory U= -GMm r Where, U = Gravitational potent ial energy G = Universal gravitational constant M = Mass of the earth m = mass of the body r = Distance of t he body from t he center of the earth u- GM r Gravity Survey l Gravity meter or gravimeter  Directly measures small differences in the strength of gravity s l  Gravimeters are basically spring balances carrying a constant mass.Variations in the weight of the mass caused by variations in gravity cause the length of the spring to vary and give a measure of the change in gravity. mg Accuracy of instrument: 0.1 mgal Most commonly used: LaCoste & Romberg Scintrex Unit of gravity is the milligal (1 mgal = 10^-3 gal = 10^-3cm s^-2), equivalent to 10 gu. m (g + 6g) Fig. 6.1 Principle of stable gravimeter operatio n. (Hooke's Law), thus ,n8g = k8s and s: us = -m us:g k here k is the elastic spring constant. Gravity Survey Gravity Reduction or Reduction to the Geoid. 1. Drift Correction Correction for instrumental drift is based on repeated readings at a base station at recorded times throughout the day. Cl C -0 Ill ....QJ ....Q) t E -~ .... I..'.) l l -----------,---------d t Time Fig. 6.10 A gravimeter drift curve constructed from repeated reaclings at a fixed location. The drift correction to be subtracted for a reading taken at time tis d. Gravity Survey 2. Latitude Correction  Variations with latitude result from the oblate spheroid shape of the earth  Gravity is greater at the poles than at the equator International Gravity Formula – formulated by Clairaut in 1743 to account for the variation of gravity with latitude g = go (1 + sin2 -  sin22) g = the predicted value of gravity at latitude  go = gravity at sea level at the equator and  And  = Constants dependent on the shape and speed of rotation of the Earth.  = latitude (go = 9 780 318 gu,  = 0.0053024,  = 0.0000059); “In combination, the equatorial bulge and the effects of the surface centrifugal force due to rotation mean that sealevel effective gravity increases from about 9.780 m/s2 at the Equator to about 9.832 m/s2 at the poles, so an object will weigh about 0.5% more at the poles than at the Equator.” Gravity Survey 3. Elevation Correction (by 3 steps)  Free-air Correction  Correction for the decrease in gravity with height in free air resulting from increased distance from the centre of the Earth, according to Newton’s Law. To reduce to datum an observation taken at height h.  The FAC is positive for an observation point above datum to correct for the decrease in gravity with elevation.  The free-air correction accounts solely for variation in the distance of the observation point from the centre of the Earth; no account is taken of the gravitational effect of the rock present between the observation point and datum. FAC = 3.086h gu (h in rn etres) Gravity Survey 3. Elevation Correction (by 3 steps)  Bouguer Correction  Removes the effect that FAC neglects by approximating the rock layer beneath the observation point to an infinite horizontal slab with a thickness equal to the elevation of the observation above datum. If p is the density of the rock, from equation  On land the Bouguer correction must be subtracted, as the gravitational attraction of the rock between observation point and datum must be removed from the observed gravity value.  The Bouguer correction of sea surface observations is positive to account for the lack of rock between surface and sea bed. The correction is equivalent to the replacement of the water layer by material of a specified rock density pr. BC= 21tCph = 0.4191ph gu (h in m e tres, pin Mg m - 3 ) where z is the water depth and Pw the density of water. - . - Gravity Survey 3. Elevation Correction (by 3 steps)  Terrain Correction  The free-air and Bouguer corrections are often applied together as the combined elevation correction.  The Bouguer correction makes the assumption that the topography around the gravity station is flat.  Account for topographic relief in the vicinity of the gravity station. This correction is always positive Fig. 6.12 (a)The free-air correctio n for an observation at a height ft above datum. (b) The Bouguer correction. T he shaded region corresponds to a sJab ofrock of thickness h extending to infinity in both horizontal directions. (c) The terrain correction. Gravity Survey 4. Tidal Correction  Gravity measured at a fixed location varies with time because of periodic variation in the gravitational effects of the Sun and Moon associated with their orbital motions, and correction must be made for this variation in a high precision survey.  The periodic gravity variations caused by the combined effects of Sun and Moon are known as tidal variations. They have a maximum amplitude of some 3 gu and a minimum period of about 12 h. Gravity Survey 5. Eötvös correction • The Eötvös correction (EC) is applied to gravity measurements taken on a moving vehicle such as a ship or an aircraft. Depending on the direction of travel, vehicular motion will generate a centripetal acceleration which either reinforces or opposes gravity. The correction required is EC = 75.03V sin acos<fa + 0.04154V2 gu • where V is the speed of the vehicle in knots, a the heading and the latitude of the observation. In midlatitudes the Eötvös correction is about +75 gu for each knot of E to W motion so that speed and heading must be accurately known. Gravity Survey  The Bouguer anomaly forms the basis for the interpretation of gravity data on land.  In marine surveys Bouguer anomalies are conventionally computed for inshore and shallow water areas as the Bouguer correction removes the local gravitational effects associated with local changes in water depth.  Moreover, the computation of the Bouguer anomaly in such areas allows direct comparison of gravity anomalies offshore and onshore and permits the combination of land and marine data into gravity contour maps. These may be used, for example, in tracing geological features across coastlines.  The Bouguer anomaly is not appropriate for deeper water surveys, however, as in such areas the application of a Bouguer correction is an artificial device that leads to very large positive Bouguer anomaly values without significantly enhancing local gravity features of geological origin.  Consequently, the free-air anomaly is frequently used for interpretation in such areas. Moreover, the FAA provides a broad assessment of the degree of isostatic compensation of an area The free-air anonialy (FAA) and B ouguer anomaly (BA) may now be defined BA= gobs - g¢ + PAC + BC+ T C(+ EC) (6.13) Gravity Survey Applications • Investigation of large- and medium-scale geological structures and ancient suture zones • Location of sedimentary basins and possible hydrocarbon traps • Hydrogeological investigations to determine the geometry of potential aquifers • Engineering and geotechnical applications for the location of cavities and voids • Exploration of mineral resources (e.g. chromitite, massive sulfide deposits) Seismic Survey Principle • Seismic waves propagate through the Earth’s interior. The travel times, of waves that return to the surface after refraction or reflection at geological boundaries, are measured. Seismic Survey Stress and Strain I I E]astic field Ductile 1field Fracture po~nt I I I I I / I I I I . . 1 I Yie lld I I point I I I I I I I I I I I I I I I I I / I I Straiin Fig~l~ 1 A typical stress-strain curve-for a.s.olid body. Seismic Survey Stress and Strain 1, p 1, --------------------- --, - (a) rI I (b) ,f ~ f -<if- 1 I I '-- ~-------------------- I --, - - -.r ,.,:: ~___ ( '° I I I I I I I: ----t,.- F I I -----I I ~ I I: I: I -, - I ,P f! I:' i,, p - - - - -'~ _J I 1, I + ~l : lo ngitud inal stress FIA E= 'E (c), , , a - - - - I. I I , J , I - r I I I I I I :: _J ' + Af shear stress t shear strain t an ', : ____.. f I I I I L µ= ,: I F-+-: J , (d) I I J I I I ,: vol um e strain Avi v : - --...' I K= longitudinal strain 111/l volum e stress P ! lo ngitudinal st:riess FIA a ~= longit udinal strain llll l I Fig. 3.2 T he dastic moduli. (a)Young' s modulus E. (b) Bulk modulus K. (c) Shear modulusµ. (d).AJ..-ial modulus 'I'- r( no lateral strain) : :, : - Seismic Survey Seismic Wave Seismic waves are parcels of elastic strain energy that propagate outwards from a seismic source such as an earthquake or an explosion. Sources suitable for seismic surveying usually generate short-lived wave trains, known as pulses, that typically contain a wide range of frequencies, Seismic Survey Body waves can propagate through the internal volume of an elastic solid and may be of two types.  Compressional waves, the longitudinal, primary or P-waves of earthquake seismology, propagate by compressional and dilational uniaxial strains in the direction of wave travel. Particle motion associated with the passage of a compressional wave involves oscillation, about a fixed point, in the direction of wave propagation.  Shear waves, the transverse, secondary or Swaves of earthquake seismology, propagate by a pure shear strain in a direction perpendicular to the direction of wave travel. Individual particle motions involve oscillation, about a fixed point, in a plane at right angles to the direction of wave propagation {a) P-wave . . 1fflliirn·111i L {b) $-wave Dilatat ions _J Seismic Survey Surface waves - can propagate along the boundary of the solid.  Rayleigh waves propagate along a free surface, or along the boundary between two dissimilar solid media, the associated particle motions being elliptical in a plane perpendicular to the surface and containing the direction of propagation. The orbital particle motion is in the opposite sense to the circular particle motion associated with an oscillatory water wave, and is therefore sometimes described as retrograde.  If the surface is layered and the surface layer shear wave velocity is lower than that of the underlying layer, a second set of surface waves is generated. Love waves are polarized shear waves with a particle motion parallel to the free surface and perpendicular to the direction of wave propagation Pa rtl c le ~ Wave pro pa gatlon {a) -- ;::- _,.,.ti~, ff~""• <~::;:: t:'. .-1" a .......... - - ~ I I "1 _v ")..._ r-\-...J _I I I I (b) ® _f I I I I I .... ...,, _,,., ,. t i I. . .~ ~ --0--'::i- _. - I I I t-- H ~ ,,,,m : :>~/... i-i::: I f I I Seismic Survey Seismic wave velocity of rocks The following empirical findings of velocity studies are noteworthy: 1. Compressional wave velocity increases with confining pressure (very rapidly over the first 100MPa). 2. Sandstone and shale velocities show a systematic increase with depth of burial and with age, due to the combined effects of progressive compaction and cementation. 3. For a wide range of sedimentary rocks the compressional wave velocity is related to density, The densities of inaccessible subsurface layers may be predicted if their velocity is known from seismic surveys. 4. The presence of gas in sedimentary rocks reduces the elastic moduli, Poisson’s ratio and the v /v ratio. v /v ratios greater than 2.0 are characteristic of unconsolidated sand, whilst values less than 2.0 may indicate either a consolidated sandstone or a gasfilled unconsolidated sand. The potential value of v in detecting gas-filled sediments accounts for the current interest in shear wave seismic surveying p s p s s Seismic Survey Reflected S Incident P Law of reflection: angle of reflection = angle of incidence Law of refraction (Snell’s Law): sin I/sin r = V1/V2 Refracted S klcldent Ray Reflected Ray Medium 1: R&tractlve ttctex • n1 Medium 2; R&tractlve tldex • n 2 Snell's law Seismic Survey K = bulk modulus (“incompressibility”)  = shear modulus  = density p Seismic Survey Seismic Sources  Explosives  Non-explosives a. Air gun, buffalo guns and rifles. – compressed air is released in the form of high-pressure bubble b. Water Gun - are an adaptation of air guns to avoid the bubble pulse problem c. Vibroseis, Marine Vibroseis – truck-mounted vibrators (50000 – 60000 pound output) d. Weight drop – ~10kg weight dropped from a height of ~3-4m; depth of penetration: ~10 – 50 meters e. Hammer – depth of penetration: 10 – 20m (refraction); 40 – 50m (reflection) f. Sparkers are devices for converting electrical energy into acoustic energy. The sparker pulse is generated by the discharge of a large capacitor bank directly into the sea water through an array of electrodes towed in a frame behind the survey vessel g. Boomers comprise a rigid aluminium plate attached below a heavy-duty electrical coil by a spring-loaded mounting. Seismic Survey Seismic Sources Echo - - - - - sou nders - - - - Pingers - - - - - - - - - - Boomers - - - - - - - - Spa rke rs Air guns Vibroseis - - - - - - - Qua rry blasts - - - - - - Earthquake body waves - - - - - - - Earthqua ke surface waves -------~-----~-----~-----~-----~-----~-----~----~---------· 10-1 ,os 10-2 1 t 01 102 104 Frequency (Hlz) (log scale) IFig. 3.14 The seismic/acoustic spectrum. Seismic Survey Seismic detectors • Geophones - a device that converts ground movement (velocity) into voltage, which may be recorded at a recording station. The deviation of this measured voltage from the base line is called the seismic response and is analyzed for structure of the earth : • Hydrophones - a microphone designed to be used underwater for recording or listening to underwater sound. Most hydrophones are based on a piezoelectric transducer that generates electricity when subjected to a pressure change. Seismic Survey Noise in Seismic Survey Uncontrolled ground motion - traffic traveling down a road, running engines and equipment, and people walking. Other sources that you might not consider include wind, aircraft, and thunder Electronic noise - dirty or loose connections between the geophones and the cable or the cable and the recording system Seismic Survey The Seismic Reflection Method: A dynamic geophysical technique of generating a sound wave at a source and recording the time it takes for components of that seismic energy to return to the surface and be recorded by receivers Ground Penetrating Radar: Utilizes similar theory, but the source is electromagnetic waves • So, what are the main take-home differences between these two seismic techniques? Refraction Resolves gross crustal velocities critical refraction requires large v gradient X=5-10x the depth of interest Processing is relatively easy Reflection Resolves fine subsurface details requires a change in v or density X=1x the depth of interest Processing can be very CPU intensive Refraction vs. Reflection Seismic Reflection : The Basics • In the simplest sense seismic reflection is echo sounding. • Echoes come from layers in the Earth, not fish or the sea floor • E.g. a ship sends out a seismic pulse • The pulse is reflected back to a receiver on the ship’s bottom after some time has passed • The various arrivals can be used to map out subsurface “reflectors” or layers sea floor (b) ... ◄1--- time! distance 1. 2. 3. 4. Seismic Reflection Caveats The vertical scale on seismic reflection profiles is time, not depth • Velocity varies with depth, so time cannot be easily converted to depth Reflections may not come from directly below the source • Reflections occur perpendicular to the interface. Receivers / Geophones / Seismometers cannot directly detect this. There may be multiple reflections off of single interfaces • Called multiples There are other caveats, but we’ll deal with these later Non-Vertical Reflection  Reflected rays travel back to the source following a path perpendicular to the interface • The receiver will record an arrival time that is too short and a dip that is too shallow recorded position Multiples • On their return to the surface… • Reflected rays can also reflect back down and then later be reflected back up • This causes a single reflector to potentially produce several “multiples” •• Short path (less (lcs"' reflections) multiples n1ultip]cs are arc usually u. ually stronger •• These artifacts a11ifacts can be removed ren,oved by migration n1igratio11 multiples T 1 f " primary reflection 1 ', ' I ' ' ~ 'f I ,J ~' ', Velocity Determination Using Normal Moveout • To deduce the velocity structure, multiple receivers are needed so that most rays do not travel vertically • For a horizontal reflector… • The shortest path is the vertical one • Rays that reach receivers to each side travel increasingly longer distances -X R+X s ... ... \ This Th is is the Fixed Fi ·cd 1\1cthod Source Method V1 There are arc also other methods: n1ethods: e.g. the Common Midpoint lid g oint l\1ethod Method V2 i l I / h1 A V '-....,,....--, X 2 Velocity Determination Using Normal Moveout • Normal Moveout = The later time of arrival of the reflected rays at receivers offset from the source for a horizontal reflector. • On a t-x diagram, the Normal Moveout (NMO) produces a hyperbola. Q) E ·,.::::; 0 distance (x) 0 X Velocity Determination Using Normal Moveout • Using the Fixed Source Method, we can estimate seismic velocity x2 t t  2 v1 2 • These parameters are read off of the t-x diagram • If layer thickness is large compared to receiver offset… x But But where \\ here does docs this v1  conic from?? froin?? ✓2t0 t come X -X V1 V2 i l R+X • h1 A V '-....,,---/ X 2 2 0 Velocity Determination Using Normal Moveout (“TWTT”) • t0 = vertical “two-way travel time” (book calls it “TWT”) • Measured along SV t0  2h1 v1 • t = total two-way travel time to receiver R (at distance = X) • Use triangle SVA: • Travel time, t, is 2*SA/v1 X I -X V1 V2 i l  x 2 h1    2 2 t  t0  t   v1 h1 A V '-....,,---/ X 2 R+X • 2 This isn’t isn ·t This helpful because we \Ve don’t don ·1 know kno,v v, 11 or h11 Velocities From Normal Moveout • Given some basic geometry and data from the t-x diagram, we can do some mathematical magic… • Given: • Square both sides: 2 t  t0  t   v1 • Do some algebra… t 2  t0  t  2 • Expand '  x h12    2 2 2  4  2  x   4  2 x 2    2 h1     2  h1    v1  4   2   v1  Replace 2h1/v1 with t0 t  t0  t  2 2 2  2h1  4h 4x 4h x x2 x2 2   2  t0  2   2   2   v 4v1 v v1 v1 v1  v1  2 1 2 1 t02  2t0 t  t 2  t02  2 2 1 2 1 2 2 x v12 Almost A ln,ost there... there ... Now we \\C know knO\V all of or these the c terms tenn: from fi·on1 t-x graph gldpll except cxct:pl v1·1, 1, so we "'e can solve soh e this!! thi~! ! Velocities From Normal Moveout • From previous page… 2 x 2t0 t  t 2  2 v1 • If the receiver offsets are small compared to the layer thickness (this is common) x2 • Then Δt will be small…and thus Δt2 ≈ 0 • Rearrange to solve for v1 **The The bad bad news… news ... This Thi process is only on]y for the first layer / topmost topn1ost reflector. re flcctor. We must n1nst account for tor refraction in the the subsequent subsequent layers… ]ayers ... v1  t  t  t0  x 2t0 t 2v12t0 Look at the t-x diagram. diagra1n. This Thi- makes n1ake . sense ~ense right? to ---0 distance (x) 0 X Multiple Horizontal Layers • If multiple reflectors are encountered • This is almost always the case • The preceding formulas still work, however: • We must keep track of the t-axis intercepts (t1,0, t2,0, etc…) for each interface • We must also account for refraction through the various interfaces • If we do this, we can still use the previous process • The previous equations will then yield RMS velocities. • What are RMS velocities? • We’ll look at this later… Multiple Horizontal Layers • When multiple reflectors are encountered, multiple NMO hyperbolas are produced • The shallowest reflector arrives first at t1,0 • Each reflector’s TWTT for vertical reflection (t1,0, t2,0, t3,0, etc…) and NMO (Δt) can be read off of the graph. • We can then easily calculate the one-way travel times in each layer, τn surface V1 I I I I I • 1 I I I ,;. Q) E ·.;:; I l I I -..... f3,o I + f2,o I I ' I I ' t 1,0 ' ' 2r1 I I I ' I I I I I I I I V3 JM -- --- --------- --~ 2r2 I I I V2 2r3 reflector of interest distance (x) I I I I I I I I I RMS Velocity • Root-Mean-Square (RMS) Velocity: A weighted average across nlayers that factors out the differences in travel time spent in layers of differing velocity i1 vi2 i n vrms    n 1 τr;i = the one-way travel time ti1ne for vertical reflection in in ii1th11 layer th layer vi1 = the interlayer velocity of of the i;rh i 1 i surtace l l •1 I I v, '• I I I I I I l I l Cl) ~ I I t3,o 21'3 + I I I I I I I I I t2,o :} : M ----- --- ------ --~ 2 Z'2 f 1.0 2r 1 reflector of interest distance (x) x 2t1, 0 t v1  For a simple two layer model… • • • • x Get velocity of first layer using NMO equations vrm s  2t 2, 0 t Get RMS Velocity down to 2nd layer from NMO eq’s Solve for the second interlayer velocity n 2 2 2 v     v v  i i i 1 1 1 2 2  Use the various tn,o values vrms   n 1   2   2hn  To get thicknesses i 1 i t n , 0  t n 1, 0  vn 6 I I I I I I I I I I I I , ' ---....---.. . -~ . _____________ J Two-Layer Example reflector of interest distance (x) Al For an n-layer model… N-Layer Example ttBB = the TWTT TWT·r to (botton1) • You could follow the previous procedure for each layer the deeper (bottom) reflector • If you only want to know a certain interlayer velocity • Only need to know the information for the reflectors directly above and below the layer of interest. 2 2 • Dix Formula :: ttr= vrm shallo,vcr T = the TWTT to the shallower s. B t n  vrm s.T t n 1 vlayer  (top) reflector t B  tT  ✓  surface V1 V2 I I I I I II •1 I I I ,+ I I I I .,_ Ql E :.:; t3,o 2f3 :} : M -- --------- --- --~ ,+ t2,o I I I I 2r2 I I I f1,0 { { { V3  I I 2r1 reflector of interest distance (x) N-Layer Example t n , 0  t n 1, 0  To Find Layer Thicknesses… 2hn vn • Use the intercepts and calculated velocities to Rearrange and solve for hhn0 calculate thicknesses of each layer  t n , 0  t n 1, 0   hn  vlayer  2   surface V1 V2 I I I I I II •1 I I I ,+ I I I I .,_ Ql E :.:; t3,o 2f3 :} : M -- --------- --- --~ ,+ t2,o I I I I 2r2 I I I f1,0 { { { V3 - I I 2r1 reflector of interest distance (x) Seismic Survey The Seismic Reflection Method: Limitations  relatively high cost of surveying – equipment, logistics and crew involved during surveying (land survey may consist of about 20 people)  computer intensive – size of seismic data generated during surveys is quite large and processing requires large data storage space  data processing involves several steps (filtering, deconvolution, migration, etc.) before a “clean” seismic section can be obtained The Seismic Reflection Method: Applications  Search for hydrocarbons (onshore and offshore)  High resolution studies of shallow geology (e.g. Quaternary sedimentary sequences, detailed mapping of concealed bedrock surfaces, etc)  Crustal and lithospheric studies (e.g. crustal structure of oceanic areas, studies of continental crust and uppermost mantle) Seismic Refraction Survey Wavelets and Head Waves • The wave front just above the interface produces a continual stream of critically refracted rays • The wave front just below the interface does the same • These stream of critically refracted rays form wavelets • The wavelets combine to form head waves • The head waves propagate up to the surface and can be recorded. • The recorded rays are called the refracted rays (a) s (b) Potential Paths in a Refraction Survey • When doing a seismic refraction survey, a recorded ray can come from three main paths • The direct ray • The reflected ray • The refracted ray • Because these rays travel different distances and at different speeds, they arrive at different times • The direct ray and the refracted ray arrive in different order depending on distance from source and the velocity structure Shot S.,ot Point Point (i.e. the Source) ic Receiver Direct Direct Ray Ray ic Layer Layer 1I Layer layer 2 WHY ARE TBrSE RAYS STRAIGHT LINES? v1 v2 The Time-Distance (t-x) Diagram Think about: • What would a fast velocity look like on this plot? • Why is direct ray a straight line? • Why must the direct ray plot start at the origin (0,0)? • Why is refracted ray straight line? • Why does refracted ray not start at origin? • Why does reflected ray start at origin? • Why is reflected ray asymptotic with direct ray? ---..... --E <D :;::::: - 2h1 V1 tInt ~ ~<:)~ \'o-~ G- &\(?; I I gl -~I~' (U ._g ·;::: I (.) 0 distance (x) s ' I I C' D' E' distance (x) UNDERSTANDING TB& T•X DIAGRAM IS ICBYIII The Direct Ray • Simply a linear function of the seismic velocity and the shot point to receiver distance t direct Sliot Point Shot ....A Layer Layer 1I Layer layer 2 Time (t) • The Direct Ray Arrival Time: x  v1 Direct Direct Ray Ray Distance Distance (x) R (ci,er Receiver I\ v1 v2 The Reflected Ray • The Reflected Ray Arrival Time: Time (t) • is never a first arrival • Plots as a curved path on t-x diagram • Asymptotic with direct ray • Y-intercept (time) gives thickness 2 h1 v1 • Why do we not use this to estimate layer thickness? Sliot Point ~oint Shot Distance Distance (x) R (ci,er Receiver Layer Layer 11 v V11 Layer I ayer 2 v v2 The Refracted Ray t • The Refracted Ray Arrival Time: x 1 1  2h1  2 2 v2 v1 v2 • Plots as a linear path on t-x diagram • Part travels in upper layer (constant) • Part travels in lower layer (function of x) • Travels long enough in the faster layer cross over distance Time (t) • Only arrives after critical distance • Is first arrival only after cross over distance critical cntical distance di~tanct.: 2h1 "CRITICAL D ISTANCE" No REFRACTED RAYS ic Layer Layer 1I Layer layer 2 ic 1 1  2 2 v1 v2 Distance Dist n c (x) ic ic v1 v2 Making a t-x Diagram Refracted Ray Arrival AtTival Time, Tin1e t t  1 1 x x sin ic 2h1 cos ic or  2h1  t   2 2 v2 v1 v2 v1 v1 (b) Y-intercept find thickness, }'-intercept to find thick11<!\S, h h,1 0.8 I l I 0.7 I 0.34 S 1 vv,2 = - 1/slope I /"lope u Q) (/) 0.6 -- 0.5 E - 0.4 ·,.::; 0 / / -, Q) (/) 0.3 / Q) E ·.;=: v1 = 1/slope LOO LOO lO OLOC>LOOLO O LOO LOO ...- .,.... C\I C\I C") Cl') ..::t- ..::t- LO LO CD C.O t--- t- CO geophone distance (m) / / I I 0.2 0.28 s 0.1 0000000000000000 , 500 m /2 Q) I 0.42 S 250 m 200 400 distance (m) 600 800 Table 6.1 Seismic velocities for rocks Rock type Refraction…What is it Good For? • Seismic refraction surveys reveal two main pieces of information • Velocity structure • Used to infer rock type • Depth to interface • Lithology change • Water table Unconsolidated sediments clay sand, dry sand, saturated Sedimentary rocks anhydrite chalk coal dolomite limestone shale salt sandstone Igneous and metamorphic rocks basalt granite gabbro slate ultramafic rocks Other air natural gas ice water oil vP (km/sec) 1.0- 2.5 0.2-1.0 1.5-2.0 6.0 2.1-4.5 1.7-3.4 4.0-7.0 3.9- 6.2 2.0-5.S 4.6 2.0-5.0 5.3- 6.5 4.7-6.0 6.5-7.0 3.5-4.4 7.5-8.5 0.3 0.43 3.4 1.4-1.5 1.3- 1.4 Ranges of velocities, wh ich are from a variety of sources, are approximate. Multiple Layers • Seismic refraction can detect multiple layers • The velocities are easily found from the slopes on the t-x diagram t;n13 --.,_ (1) E :;:::; tint 2 -- --- - - - --- _,,..,- 1 V4 V3 _,,..,- -- V2 _,,..,- ti nt1 V1 distance (x} (b) s' I / C1i c2' C3• Multiple Layers • The layer thicknesses are not as easy to find • Recall… fint3 - ...... ..__. (1) E :;::; tint2 x sin ic 2h1 cos ic t  v1 v1 --- --- ---- 1 V4 V3 - -- V2 distance (x) tint1  2h1 cos ic1 v1 Solve Sohc for h11… ... ➔ h1  v1tint1 2 cos ic1 Now, plug in No\v, plug in h1 h 1 and and solve solve the the remaining rc111aining layers layers one one at at aa time… tin1c ... tint 2  2h1 cos ic1 v1  2h2 cos ic2 v2 BEWARE!!! h'111,~ h'122,, are arc layer thicknesses, lhicknes cs, not depth to lo interfaces. interface·. So, depth to bottom botto1n of of layer layt:r 3 /top top of of layer 4 = = h11 ++ hI,2 + h3~ Multiple Layers • The layer thicknesses are not as easy to find • Recall… fint 3 -- --- - - - - - - - --- Q) ._§ f int2 x 1 1 t   2h1  2 2 v2 v1 v2 tint1  2h1 ' distance (x ) 1 1  2 2 v1 v2 Solve Sohe for h11… ... ➔ h1  t 1 1 2 2 2 v1 v2  t v v 2 2 2 21 v1 v2 Now, NO\\ plug plug in in h1 h 1 and and solve so]vc the the remaining re•11aining layers layers one one at at aa time… t1n1c ... tint 2  2h1 1 1 1 1   2 h  2 2 2 2 2 v1 v2 v2 v3 BEWARE!!! h'111,~ h'122,, are arc layer thicknesses, lhicknes cs, not depth to lo interfaces. interface·. So, depth to bottom botto1n of of layer layt:r 3 /top top of of layer 4 = = h11+ hI,22+ h3~ 2 2 • Only works if each successive layer has increasing velocity • Cannot detect a low velocity layer • May not detect thin layers • Requires multiple (survey) lines • Make certain interfaces are horizontal • Determine actual dip direction not just apparent dip Caveats of Refraction Applications of seismic refraction method 1. Foundation studies on construction sites – to map bedrock surface 2. Engineering applications – to estimate bulk and shear moduli from P- and S-wave velocities 3. Exploration for underground water supplies in sedimentary sequences in conjunction with electrical resistivity 4. Regional investigation of the internal structure and thickness of the earth’s crust – thickness of continental and oceanic crusts •ELECTRICAL RESISTIVITY Principle The basic principle behind electrical methods is the injection of current into the ground using a pair of electrodes. This current causes a potential difference in the ground which is measured by a separate pair of electrodes. Ohm’s Law: V/I= R or R=V/I I = current in a conducting body V = potential difference between two surfaces R = resistance between the surfaces Resistance, Voltage, & Current • An analogy… To get current to flow you must provide a push… The “push” is called a potential difference or voltage – Symbol: p.d. V or ΔV (V [=] volts) The “flow” is called the current – Symbol: I (I = amperes / amps • – Apply a known potential difference (measured with voltmeter) to a circuit with a resistive material of known length and cross-sectional area. • – Then measure the current (with ammeter) • – This gives the resistance, R How Do We Measure resistivity? • Voltage is measured by a voltmeter • Current is measured by an ammeter Measuring Resistivity The resistivity of the subsurface depends upon: – The presence of certain metallic ores • Especially metallic ores – The temperature of the subsurface • Geothermal energy! – The presence of archeological features • Graves, fire pits, post holes, etc… – Amount of groundwater present • Amount of dissolved salts • Presence of contaminants • % Porosity and Permeability Table 12.1 Resistivities of some rocks and minerals Rocks, minerals, ores Resistivity (ohm-m) Sediments chalk clay gravel limestone marl quartzite shale sand sandstone 50-150* 1-100 100-5000 so-101 1-100 10- 108 10- 1000 500-5000 1-108 Igneous and metamorphicrocks basalt gabbro granite marbl,e schist slate 10-101 1000-106 100-106 100-108 10-104 100-107 c Minerals and ores s,:ver g apl ii te, ",a,,i oe 01, galena (PbS) magnetite ore splhalerite (ZnS) pyrite chalcopyrite quartz rock salt 1.6 X 10·; 10◄- 10~ 10-3-102 > 1-105 10 3- 106 1X 100 1 X 10-5- 0.3 1010-2 X 1014 10-10 13 Waters and effect of water and salt content pure water 1 x 106 natural waters 1- 101 sea water 0.2 20% salt sx 10-2 granite, 0% water 1010 granite, 0.19% water 1 x 106 granite, 0.31 %water 4 x 10 3 *Values or ranges, which havecome from several sources, are only approximate. Rock & Mineral Resistivities Resistivity variations Ill ,o 001 MASSIVE I 000 100 10 000 1. Common rock-forming minerals are poor conductors. WUTH£R!O LAYER 2. Most oxides are intermediate conductors. GL ACIAl SE01t,' £NYS 3. Very roughly, igneous rocks have the highest resistivity and sediments the lowest. 4. Resistivities also vary with the porosity of the rock and the salinity of the contained water. SULFtO(S ~ --r- ----r- - --r-- ~ IGNCOUS ANO MtTAMORPHIC ROCKS GRAPHITE --~~-~=( (IGNEOUS ROCKS SAPROLITE MAflC fELSIC l MOTTlfO ZONC SHll;~O UNWUTHCAfO ROC "- I 0UAICRU$T CMETAMORPHIC ROCKS) I I CU YS ,AO IILLS SH ALES SANOS TO'lE CONO~OMeAATf seo1ueN-TAR'I' ROCK LIGNITE, COAL OO~OMITE, LIMCSTONli I $AI.T WAT ER 100 000 10 000 ~ I 000 PCRMAfRO f RESH WATER WATE R. AOUIFeRS 100 I ICt SlA 10 01 0,01 CONOUCTIVIT'I' (mS1111) Physical property General Rules of Thumb For Resistivity Highest R Igneous rocks Why? Only a minor component of pore water Metamorphic rocksWhy? Hydrous minerals and fabrics Sedimentary rocksWhy? Abundant pore space and fluids Lowest R Clay: super low resistivity General Rules of Thumb For Resistivity Highest R Older rocks Why? More time to fill in fractures and pore space Younger rocks Why? Abundant fractures and/or pore space Lowest R Electrical resistivity meter FIELD EQUIPMENTS Source - current supply provides voltages from 100 to >500 volts; Receiver – potential electrodes detect the small potential difference and relays it to the receiver console where it is measured 1. Mapping/profiling/traversing – to determine the gross resistivity features of a prospect and its surrounding region 2. Vertical electrical sounding – to determine the vertical resistivity structure at a set of stations Data acquisition Resistivity arrays 1. Wenner spread – most commonly used; electrodes are uniformly spaced 2. Schlumberger spread – current electrodes are spaced much farther apart than the potential electrodes 3. Dipole-dipole spread – a denotes constant separation between the electrodes, and the distance between B and M can be increased to be an integral multiple n of a REIIITIVITY SURVEY USING THE WENNER ARRAY Electrlcal Resistivity Meosue C CUlllllff II.ICTaD8 / Principle I Source urren MeoS\le \t ltOQe Schlumberger Profile Ground Penetrating Radar Principle High frequency EM waves are sent into the ground through a transmitter antenna  subsurface structures cause some of the wave energy to be reflected back to the surface, the rest penetrate deeper  reflected wave energy is detected by a receiver antenna Reflections due to responses at interfaces of materials with different electrical properties The depth range of GPR is limited by the electrical conductivity of the ground, the transmitted center frequency and the radiated power. GPR antennas can be hand-towed or vehicle-towed control unit registers the reflections against two-way travel time in nanoseconds and then amplifies the signals. r- ....... ,;-~ R d Wv s ~ ~ I Object Basic GPR Principal Data acquisition ' - ,,,, ~ D ta Col ct1 n • Depth of investigation is generally up to depths of 30 meters a. Higher frequency (900 and 500 MHz) antennas – can penetrate 5-15 ft of soil; resolution is 0.5 – 2 inches b. Lower frequency (300 and 80 MHz) antennas – can attain depths of 30 to 80 feet; resolution is 0.5 – 3 feet) Borehole logging Borehole geophysical investigations provide excellent vertical-profile information on the lithology, flow components (production zones), structure, permeability, porosity, and water quality of the ground-water system. Involves lowering a probe or sonde down a borehole which allows measurement of a physical property of the surrounding rock or soil. Principle Sonde or probe – cylindrical metal tube which houses the instrumentation needed for borehole logging Data acquisition Alhntlll --- - - - - - - Data acquisition Sule Method Property measured Caliper Borehole diameter Resistance of formation, fluids in formation and borehole Single-po int reason fluids Resistivity of t he formation w it h addit ional data, t rue Normal resist ivity resistivity and can be calculated Bulk apparent conductivity o f t he formation of t he formation Electromagnetic Induction and pore fluid surrounds t he boreho le Electr ical resistivity of borehole fluid from which specific Fluid resist ivity conductance is calculated Fu ild temperature electromagnetic and Temperature of borehole fl uid; differential temperature D irect ion and magnitude of vertical flow w it hin t he borehole spinner flowmeter Logging methods Camera V isual fish-eye view and side looking view of borehole A coust ic T eleviewer A mplit ude and travel t ime of the reflected acoustic signal Deviation Azimuthal directio n and the inclination of the borehole 1. 2. 3. 4. Hydrocarbon exploration Hydrogeological exploration Mapping stratigraphic boundaries Mapping contaminant plumes Applications of borehole logging References Selected References Lowrie, W. (2007). Fundamentals of Geophysics Second Edition. United States of America by Cambridge University Press, New York.