Iraqi Kurdistan Region Tishk International University TIU Faculty

Iraqi Kurdistan Region Tishk International University (TIU) Faculty of Engineering Department of Petroleum and Mining (PAME) Erbil Applied Geophysics Lecture Notes By Dr. Fadhil Ali Ghaeb Fourth Semester 2018/2019 Text Books: 1 Keary P. and Brooks, M. (1986, 1991): An Introduction to Geophysical Exploration. 2 Reynolds, J. M. (1997): An Introduction to Applied and Environmental Geophysics. 3 Dobrin, M. (1974, 1983): An Introduction to Geophysical Prospecting. 2018/2019 1

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2018/2019 Geophysics The science of geophysics applies the principles of physics to the study of the Earth. Geophysical investigations of the interior of the Earth involve taking measurements at or near the Earth’s surface that are influenced by the internal distribution of physical properties. Analysis of these measurements can reveal how the physical properties of the Earth’s interior vary vertically and laterally. By working at different scales, geophysical methods may be applied to a wide range of investigations from studies of the entire Earth to exploration of a localized region of the upper crust for engineering or other purposes. In the geophysical exploration methods (also referred to as geophysical surveying) discussed in this course, measurements within geographically restricted areas are used to determine the distributions of physical properties at depths that reflect the local subsurface geology 3

The survey methods Geophysical surveying methods are divided into those that make use of natural fields of the Earth (passive methods) and those that require the input into the ground of artificially generated energy (active methods). The first, utilizes the gravitational, magnetic, electrical and electromagnetic fields of the Earth itself. The second involves the generation of local electrical or electromagnetic fields that may be used analogously to natural fields, or, in the most important single group of geophysical surveying methods, the generation of seismic waves whose propagation velocities and transmission paths through the subsurface are mapped to provide information on the distribution of geological boundaries at depth. Generally, natural field methods can provide information on Earth properties to significantly greater depths and are logistically more simple to carry out than artificial source methods. The latter, however, are capable of producing a more detailed and better resolved picture of the subsurface geology. 2018/2019 4

Applied Geophysics Comprises the following subjects: 1 Determination of the thickness of the crust (which is important in hydrocarbon exploration. 2 Study of shallow structures for engineering site investigations. 3 Exploration for ground water and for minerals and other economic resources. 4 Trying to locate narrow mine shafts or other forms of buried cavities. 5 The mapping of archaeological remains. 6 Locating buried pipes and cables. More than one geophysical method are often used to solve geological problems 2018/2019 5

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Geology and Geophysics: Geology involves the study of the earth by direct observations on rocks either from surface exposures or from boreholes and the deduction of its structures, composition and historical evolution by analysis of such observations. Geophysics involves the study of the inaccessible earth by means of physical measurements, usually on or above the ground surface. It also includes interpretation of the measurements in terms of subsurface structures and phenomena. Hence, Geophysics is the third dimension of geoplogy 2018/2019 7

? ? ? Surface geology to be interpreted for subsurface picture. Many types of structures can be imagined by geologists. Geophysics can end the argument 2018/2019 8

Physical Properties of Rocks • The physical properties of rocks as used in different geophysical methods are: Density Gravity method Magnetic susceptibility Magnetic method Elasticity Seismic method Electrical resistively or conductivity Electrical and electromagnetic methods Radioactivity Radiometric method Thermal conductivity Geothermal method 2018/2019 9

Geophysical surveying applications Application Appropriate survey methods* Exploration for fossil fuels (oil, gas, coal) Exploration for metalliferous mineral deposits SP, IP, R Exploration for bulk mineral deposits (sand gravel) Exploration for underground water supplies Engineering/construction site investigation Archaeological investigations S, G, M, (EM) M, E, S, (E), (G) E, S, (G), (Rd) E, S, Rd. (G), (M) Rd, E, EM, M, (S) --------------------------------------------------* G, gravity; M, magnetic; S, seismic; E, electrical resistivity; SP, selfpotential; IP, induced polarization; EM, electromagnetic; R, radiometric; Rd, ground-penetrating radar. Subsidiary methods in brackets. 2018/2019 10

Gravity Method General Review • The basic concept underlying gravity surveying is the variation of the Earth gravitational field caused by lateral variation of subsurface rock densities. In other words, a given rock body whose density is different from its surrounding medium (i. e. geological anomaly) produces a corresponding disturbance (gravity anomaly) in the Earth gravity filed. The form and amplitude of the created anomaly depend on the subsurface geological anomaly such as a salt dome, granite intrusion, buried valley, folded or faulted beds. • Gravity surveying involves measurements of the changes in gravitational acceleration at points over a given area distributed randomly or in the form of a grid. The observation data are then subjected to a series of corrections and some processes in order to reduce them to gravity values measured relative to a datum plane in such a way that all gravity values are related to variations in the sub datum. 2018/2019 11

The corrected and processed field data is then interpreted to what they mean in geology. This gravity to geology process (interpretation) forms the ultimate objective of any gravity survey project. Applications of Gravity method: Primary; hydrocarbon exploration, regional geological studies. Secondary; explorations for: mineral deposit, Site investigations, hydrogeology, karsts, geodesy, isostasy, archaeology and volcanic monitoring. 2018/2019 12

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The Earth’s Shape The Ellipsoid the Earth is approximately ellipsoidal rather than being perfectly spherical along the mean sea level surface. This model is called the reference or normal ellipsoid. It is a theoretical surface. Up to date information The equatorial radius (a) = 6378. 160 km The polar radius (b) = 6356. 775 km The difference (a b) = 21. 385 km The flattening factor (a b)/a = 1/298. 25 The angular Rotation Speed (ω) = 7. 292 *10 5 radian/sec (About 460 meters per second) 2018/2019 14

The Geoid It is the Ellepsoid surface affected by mass distribution beneath the datum level. It is global with the plumb line vertical at any point on its surface. The difference between Geoid and Ellipsoidal surfaces is called Warp which indicates the presence of either excess or deficiency in mass. Warp is an anomaly. 2018/2019 Excess mass Deficiency in mass 15

Explanation A: A theoretical model of the earth having vertical variations in density leading to the Ellipsoidal model. B: An actual Earth having vertical and horizontal variations in density leading to Geoid model. 2018/2019 16

The Universal Law of Gravitation Isaac Newton (1643 1727) formulated the universal law of gravitation which evaluates the attraction force F that exists between two particles of masses m 1 and m 2 located at distance r apart. The constant G, called the Universal Gravitational Constant, was experimentally determined and found to be of the value: G = 6. 673 x 10 -8 (cm 3. gm 1. sec 2) or, G = 6. 673 x 10 11 (m 3. kg 1. sec 2) 2018/2019 cgs and SI units ? 17

Newton's second law of motion states that any body of mass (m) under the effect of attraction force (F) (say it is the force of attraction of the Earth mass M with a radius R ) moves with acceleration (a) where: F = ma G m. M /r 2 = ma or = mg Acceleration a is called (gravity g ), then g = G M/R 2 in our course acceleration is called gravity The units of g that are in common use in gravity exploration are: 1 gal = 1 centimeter /sec 2 1 milligal = (1/1000) gal 1 microgal = (1/1000 000) gal Another acceleration unit, the International Standard (SI) gravity unit (g. u. ), is also used. One g. u. is equal to 1 micrometer/sec 2. Hence, 1 g. u. = 1 micrometer/sec 2 1 milligal = 10 g. u. 2018/2019 18

Note that The acceleration is simply called gravity (g) and it is measured during the gravity survey. According to the relation g = G M/R 2 , g is proportional to two variables only; they are density and distance so gravity changes on a horizontal plane (datum plane) in a small district should be due to changes in density beneath datum only. If the earth was perfectly sphere and having a homogeneous density, gravity value will not change any where on its surface. Anomaly explanation Gravimeter (1) will measure (g) due to the attraction of the Earth Excess whilemass gravimeter (2) measures the (g) of the Earth plus (g) due to the excess mass present. The anomaly will be positive. In the case of a cavity instead of mass there will be an efficiency in mass so giving rise to a negative anomaly relatively. 2018/2019 Gravimeter (1) Gravimeter (2) Excess mass Center of the Earth 19

Measurements of Gravity Absolute gravity Determination of the acceleration due to gravity in absolute terms requires very careful experimental procedures and is normally only undertaken under laboratory conditions. Two methods of measurement are used, namely the falling body and swinging pendulum methods. A mass falling from a rest position of height (h) will cover the distance h during time lapse (t) according to the equation: h = (1 / 2) g t 2 2018/2019 h 20

A swinging pendulum is defined as an instrument consisting of a freely swinging mass which is suspended from a fixed point. The pendulum swinging period T is the function of the pendulum constants and the earth gravity (g). For the well known simple pendulum, swinging with small amplitude, the period (T) is given by the function: where L is the length of the string (considered to be weightless) which connects a point mass to a suspension point. 2018/2019 21

Relative gravity measurements Because it is difficult to design precise portable absolute measuring instruments, gravity is measured relatively (relative to a reference station called Base Station), these stations are or are not tied to primary base stations (primary base stations have absolute gravity values). Devices which measure relative gravity values are called Gravimeters. They are accurate balances measure gravity in different points on the surface to show the variation in gravity, hence the variation in density. A net of International Base Stations (primary) are present in all countries. They are called International Gravity Standardization Network; IGSN 71. The number 71 is due to the year 1971 at when the international formula was established (subject will be given later). 2018/2019 22

The principle of a gravimeter is a spring of initial length s has been stretched by an amount ds as a result of an increase in gravity dg increaseing the weight of the suspended mass m. The extension of the spring is proportional to the extending force (Hooke’s Law), thus m ∆ g = k ∆s and ∆s = (m/k) ∆g where k is the elastic spring constant and ∆s must be measured to a precision of 1 : 108 in instruments suitable for gravity surveying on land. (1) All gravimeters depend upon this principle. Based on that, many types of gravimeters are now present such (2) as those which are shown in the next page. 2018/2019 23

Commercial types of Gravimeters La. Cost & Romberge EG CG 5 Autograv 2018/2019 24

Gravity surveying It involves measuring the gravity values at defined locations (the survey station-points or stations) which are distributed throughout the survey area. In addition, other measurements data must be made available. These are the supporting data which principally include location coordinates (longitudes, latitudes and elevations) and times at which readings are taken. These data are necessary for computing the gravity anomaly in a later processing stage. A land gravity survey is normally conducted through two operation phases. These are; establishment of the base station network and documenting the gravity readings at all of the station points in the survey area. A location map with an adequate scale must be first made available 2018/2019 25

A base-station is a point located within, or near, the survey area. Its gravity value and position is precisely known. The base station serves two purposes. First, the gravity value at the base station is used as a reference value for computing gravity at all of the survey-points. In addition to that, the tidal effect and the drift behavior of the measuringgravimeter can be determined. St. Time go(SD) coordinates Remarks XYZ BS 8: 05 5684. 32 ----1 8: 18 5688. 66 ----2 8: 31 5679. 25 ----3 8: 39 5978. 65 ----4 8: 49 5992. 24 ----5 9: 00 5983. 28 ----6 9: 25 5894. 36 ----BS 9: 35 5684. 63 ----7 10: 00 5882. 95 ----- Field Procedure 2018/2019 26

Factors Affecting Gravity Factors can be subdivided into two categories: those that give rise to temporal variations and those that give rise to spatial variations in the gravity. A. Temporal Based Variations These are changes in the observed acceleration that are time dependent. In other words, these factors cause variations in acceleration that would be observed even if we didn't move our gravimeter. Instrument Drift Changes in the observed acceleration caused by changes in the response of the gravimeter over time. Tidal Affects Changes in the observed acceleration caused by the gravitational attraction of the sun and moon. 2018/2019 27

B. Spatial Based Variations are changes in the observed gravity that are space dependent (i. e. gravity change from place to place), but not related to geology. Latitude Variations – Changes caused by the ellipsoidal shape and the rotation of the earth. Elevation Variations Changes in the observed acceleration caused by differences in the elevations of the observation points. Bouguer Effects Changes in the observed acceleration caused by the extra mass underlying observation points at higher elevations. Topographic Effects Changes in the observed acceleration related to topography near the observation point. 2018/2019 28

Gravity reductions It is necessary to correct each observation point for all variations in the Earth’s gravitational field (discussed before) which do not result from the differences of density in the underlying rocks. Solid dots are measurements at base station in different times (g) reading Drift correction Correction for instrumental drift is based on repeated readings at a base station at recorded times throughout the day. The meter reading is plotted against time and drift is assumed to be linear between consecutive base readings. The drift correction at time t is d, which is subtracted from the observed value. d Base line arbitrary t 2018/2019 time 29

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Latitude correction Gravity varies with latitude because of the non spherical shape of the Earth and because the angular velocity of a point on the Earth’s surface decreases from a maximum at the equator to zero at the poles. The variation in angular velocity with latitude around the Earth represented by vectors whose lengths are proportional to angular velocity (and center fugal force). Points near the equator are farther from the centre of mass of the Earth than those near the poles, causing gravity to increase from the equator to the poles. Gravity at the poles exceeds gravity at the equator by some 5186 m. Gal, with the north-south gravity gradient at latitude Φ being (∆gΦ) = 0. 812 sin 2 Φ m. Gal. km-1. This value is either added or subtracted depending upon the location of the observation point relative to base station. (1% of the value 5186 is due to center fugal force). 2018/2019 31

This gradient is calculated by differentiating the (Clauriat) formula mentioned before. [gØ = g 0(1+C 1 sin 2Ø C 2 sin 2 2Ø)] Where gØ is theoretical value at a latitude Ø, g 0 is theoretical gravity value at equatorial sea level (=978. 0318 Gal), C 1 and C 2 are constants (0. 0053024 and 0. 0000059 respectively). These numbers were matter of Change during past because Of scientific progress. This gradient relation ∆gΦ could be used for purposes of latitude corrections in local surveys where Ø is the latitude angle of base station. Example: A station 100 m north of base station in Erbil City (lat. ~36 N), its correction value, which will be subtracted from the observed reading, is: 0. 1 x [0. 812 sin 2(36)] = ? m. Gal 2018/2019 32

Free Air Correction: Accounts for the height difference between the gravity station and a certain datum level. Gravity decreases with height because the gravitational acceleration is proportional to 1/ r 2. Therefore the free air effect is added to the gravity value of a certain station if it is above datum and subtracted if below. No accounts are taken for rock density F. A. C. =0. 3086 m. Galx. Height difference(∆h) ∆h is the elevation difference between the station which is to be corrected and the datum level 2018/2019 33

∆g = (2 g 0/R) h = constant x h = 0. 3086 m. Gal/m = 0. 094 m. Gal/ft At station A the effect is added while at B it is subtracted…. . Why? A topography * ∆h Datum ∆h * B 2018/2019 34

Bouguer Correction: Accounts for the effect of the attraction of rock materials between the station and datum levels, by approximating them into an infinite horizontal slab. This slab has a thickness equal to the elevation difference between the station and datum level with a homogeneous density, it is called Bouguer Slab. Ground surface h is the Bouguer slab thickness having a density ρ B Rock materials A h Datum Level C 2018/2019 h 35

At station B the gravity is increased relative to datum because of the slab. The gravity effect is equal to 2πρGh, this is called the Bouguer Correction. Density used here is the average density of surface rocks while h is thickness. In the case of station B the effect is subtracted, in station C the effect is added while in station A there is no Bouguer effect ……Why? B. C. = 0. 04191ρh (h in meters) = 0. 1277 ρh (h in feet) Since the FAC and BC are both proportional to elevation above (or below) datum, it is usual to combine them into a simple Elevation Correction (EC). EC = FAC – BC or = BC – FAC = 0. 3086 h – 0. 041981ρh = [(03086 – 0. 04191ρ)h] m. Gal/m = [(0. 09406 – 0. 01277ρ)h] m. Gal/ft Hence the correction for the station B in the above figure will be: g = g. O – (0. 09406 – 0. 01277ρ)h Where g. O is the observed value. 2018/2019 36

Typical mean values and ranges of density for some common rock types 2018/2019 37

Terrain (Topographic) Correction: It accounts for the errors caused by assuming the materials between the station and datum as a slab in Bouguer correction since those materials are neither homogeneous nor of constant thickness. In applying the slab correction to observation point B, we remove the effect of the mass surrounded by the rectangle. Note, however, that in applying this correction in the presence of a valley to the left of point B, we have accounted for too much mass because the valley actually contains no material. Thus, a small adjustment must be added back into our Bouguer corrected gravity to account for the mass that was removed as part of the valley and, therefore, actually didn't exist. 2018/2019 38

Principle of (always) adding the effect of Terrain correction is illustrated below. Pendulum normal, towards earth's center Pendulum deflected towards (excess) mass or away from the (deficiency) in mass; in both cases it leads to reduce gravity value. Hill valley 2018/2019 39

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Bouguer Anomaly The end product of gravity data corrections is the Bouguer Anomaly (B. A. ), which should correlates only with lateral variations in density of the upper parts of the crust and which are of most interest to applied geophysicists and geologists. The B. A. is the difference between the observed gravity value (go) adjusted by the algebraic sum of all the necessary corrections, and that at a certain base station (gbase) ∆gb = go +∑ (all corrections) gbase = (go – gbase) + [∆ Drift C. + ∆ (FAC – BC) +/ ∆LC + ∆TC] = B. A. (see Reynolds, page 70 71) 2018/2019 41

Important: Gravity values in stations are either relative to an arbitrary value in a locally established base station and the Bouguer values are found using the formula: B. A = g station – g base station + Corrections ……(as mentioned before) Or they are related to a base station that its absolute value is known using the formula: B. A. = ga – gØ + (FAC BC+TC)… where ga is the absolute value at the station (relative to a base station of known absolute value) and gØ is theoretical value at the station calculated using the international formula. [gØ = g 0(1+C 1 sin 2Ø C 2 sin 2 2Ø)] Hence the latitude of stations should be known. 2018/2019 42

Although for any given body, a unique gravity field is predicted, a single gravity anomaly may be explained by an infinite number of different bodies, e. g. , spheres and point masses. Because of this dilemma, it is most important use constraints from surface outcrop, boreholes, mines and other geophysical methods. The value of gravity data is dependent on how much other information is available. 2018/2019 depth The problem of ambiguity Any of the four bodies may produce the gravity anomaly shown at the top. 43

Regional and Residual Gravity The Bouguer map is the sum of gravity effects resulting from density changes (geological anomalies) existing in the subsurface medium of the surveyed area. These changes, expressed by the gravity anomalies, are produced from lateral changes in density. The amplitude of the anomaly is function of both the density difference (density contrast) and the depth of the responsible geological structure. In fact, the anomaly amplitude gets larger with the increase of density contrast and with the decrease of the depth of the anomalous body. For a given anomalous mass, the amplitude of the gravity anomaly, its smoothness and width are governed by depth of the mass. As the depth increases, the resulting gravity anomaly gets wider, weaker, and smoother. 2018/2019 44

There may be a gentle trend in the gravity data, reflecting a long wavelength gravity anomaly attributable to deep seated crustal features; this is known as a regional anomaly. Shorter wavelength anomalies arising from shal lowergeological features are suprimposed on the regional anomaly, and it is these anomalies that are often to be isolated for further analysis. Separation of the regional from the Bouguer anomaly will leave a residual anomaly. The deeper the body the broader the anomaly. The interpreter may wish to emphasize some anomalies and suppress others, e. g. , shallow anomalies are important to mineral exploration, and deep anomalies are important for oil exploration. One survey’s signal is another’s noise. The effects of shallow bodies may be considered to be near surface noise, and the effects of deep bodies, known as the regional, may be caused by large scale geologic bodies, variations in basement density or isostatic roots. These must be removed to enable local anomalies to be interpreted. The problem lies in separating out the two effects, and it is not strictly possible to do this without afecting what is left. 2018/2019 45

This (separation) may be performed graphically by sketching in a linear or curvilinear field by eye. Such a method is biased by the interpreter, but this is not necessarily disadvantageous as geological knowledge can be incorporated into the selection of the regional field. m. Gal Bouguer anomaly Estimated regional Residual distance Bouguer profile, estimated regional and residual Whether it is a profile or a contour map, the graphical smoothing technique is basically dependent on personal judgment. For this reason, the computed regional and residual variations may differ from one interpreter to another. The extent of difference depends on the degree of complexity of the given Bouguer gravity data and on the interpreter individual skill. 2018/2019 Bouguer anomaly map, regional and residual 46

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Bouguer Residual 2018/2019 Regional 48

Interpretation of Gravity Data: The aim of any gravity prospecting is to translate the geophysical data obtained after corrections into geology, which means size, shape and the depth of the subsurface structures that give rise to gravity anomaly. It is necessary before carrying out interpretation to differentiate between two dimensional and three dimensional anomalies. Two dimensional anomalies are elongated in one horizontal direction so that the anomaly length in this direction is at least twice the anomaly width. Such anomalies may be interpreted in terms of structures which theoretically extend to infinity in the elongate direction by using profiles at right angles to the strike. Three dimensional anomalies may have any shape and are considerably more difficult to interpret quantitatively. Bouguer maps are tested in two stages; qualitative and quantitative. 2018/2019 49

Qualitative interpretation involves the description of the Bouguer anomaly map or profile and their transformed regional, residual, second vertical derivative…etc. . The description involves the dimension, trend, amplitude, gradient, shape, location relative to study area, relative density and possible geologic source after integrations with any other information. General aspects for qualitative interpretation: 1 Surface geological information should be collected as much as possible. These Information is; rock types, major structural trends, jointing, faulting, folding…etc. 2 Maps such as topographic, geologic, gravity…etc. are better to be of one scale for the purpose of overlays and correlations. 3 Divide the map into sectors to describe. 4 Correlate sectors with geology. 5 Delineate anomalies that should be quantitatively interpreted. 2018/2019 50

2018/2019 g 1 2 3 Depth Quantitative Interpretation: Direct interpretation provides, direct parameters of the gravity anomalies and information on the anomalous body which is largely independent of the true shape of the body. Various methods are discussed below. You should know that Gravity anomalies decay with the inverse square of the distance from their source so that anomalies caused by deep structures are of lower amplitude and greater extent than those caused by shallow sources. This wavenumber–amplitude relationship to depth may be quantified to compute tge maximum depth (or limiting depth) at which the top of the anoma lous body could be situated. 1 2 3 51

Direct quantitative interpretation It is the direct use of the anomaly parameters. The original data are analyzed to produce an interpretation. Certain geologic structures can be approximated to models with known geometric forms. For example, a buried cavity may be represented by a sphere, a salt dome by a vertical cylinder, a basic igneous dyke by an inclined sheet or prism, etc. 2018/2019 52

Some methods of direct interpretation Limiting depth It refers to the maximum depth at which the top of a body could lie. (a) Half-width method. If the anomaly is three dimensional If two dimensional body (b) Gradient–amplitude ratio method. This method requires the computation of the maximum anomaly amplitude (Amax ) and the maximum horizontal gravity gradient (A/ max ) If three dimensional body 2018/2019 If two dimensional body 53

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Shape of two and three dimensional bodies on maps 3 D anomaly 2018/2019 55

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(c)For a step model anomaly (i. e. fault) also the half width with the maximum gravity value could be used. A section across the fault (a fault is a sudden change in gravity value on both sides of the fault line g 3/4Δgmax 1/2Δgmax Z Z t Fault shape on a map The horizontal distance Z is approximately equal to the depth to center of the slab having a thickness t. This thickness could be calculated using the Bouguer slab formula (t = 0. 04191σ /Δgmax); σ is density contrast. 2018/2019 57

Calculation of gravity anomalies using the above methods should be regarded as a first step in the interpretation process. There are other, more sophisticated, and commonly computerized methods of gravity anomaly analysis. Indirect interpretation In indirect interpretation, the causative body of a gravity anomaly is simulated by a model whose theoretical anomaly can be computed using formulas which some of them are diven in previous slides , and the shape of the model is altered until the computed anomaly closely matches the observed anomaly. Altering models should be in consistence with the geology of the area. 2018/2019 58

Steps are: 2018/2019 59

Gravity anomaly due to a two dimensional vertical Column (prism): Gravity anomaly due to a series of vertical columns: gz r 1 b r 2 2018/2019 Summing all columns 60

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Seismic Method (Applied Seismology) In seismic surveying, seismic waves are created by a controlled source and propagate through the subsurface. Some waves will return to the surface after refraction or reflection at geological boundaries within the subsurface. Instruments distributed along the surface detect the ground motion caused by these returning waves and hence measure the arrival times of the waves at different ranges from the source. These travel times may be converted into depth values and, hence, the distribution of subsurface geological interfaces may be systematically mapped. 2018/2019 62

Applications: Seismic methods are widely applied to exploration problems involving the detection and mapping of subsurface boundaries of, normally, simple geometry. They also identify significant physical properties of each sub surface unit. The methods are particularly well suited to the mapping of layered sedimentary sequences and are therefore widely used in the search for oil and gas. The methods are also used, on a smaller scale, for the mapping of near surface sediment layers, the location of the water table and, in an engineering context, site investigation of foundation conditions including the determination of depth to bedrock. Seismic surveying can be carried out on land or at sea and is used extensively in offshore geological surveys and the exploration for offshore resources. 2018/2019 63

Stress and strain When external forces are applied to a body, balanced internal forces are set up within it. Stress is a measure of the intensity of these balanced internal forces. The stress acting on an area of any surface within the body may be resolved into a component of normal stress perpendicular to the surface and a component of shearing stress in the plane of the surface. 2018/2019 64

A body subjected to stress undergoes a change of shape and/or size known as strain. Up to a certain limiting value of stress, known as the yield strength of a material, the strain is directly proportional to the applied stress (Hooke’s Law). This elastic strain is reversible so that removal of stress leads to a removal of strain. If the yield strength is exceeded the strain becomes non linear and partly irreversible (i. e. permanent strain results), and this is known as plastic or ductile strain. If the stress is increased still further the body fails by fracture. A typical stress–strain curve is illustrated in the next figure. 2018/2019 Stress The linear relationship between stress and strain in the elastic field is specified for any material by its various elastic moduli, each of which expresses the ratio of a particular type of stress to the resultant strain. Elastic field Ductile field Fracture point Yield point permanent strain Strain 65

The elastic moduli are: (a)Young’ s modulus E. (b) Bulk modulus K. (c) Shear modulus m. (d) Axial modulus and (e) Piosson’s ratio. (e) σ = (Δy/y) / (Δx/x) = Contraction / Extension Δx Δy 2018/2019 66

Seismic (Elastic) waves 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. Except in the immediate vicinity of the source, the strains associated with the passage of a seismic pulse are minute and may be assumed to be elastic. On this assumption the propagation velocities of seismic pulses are determined by the elastic moduli and densities of the materials When the Earth is rapidly displaced or distorted at some point, the energy imparted into the Earth by the source of the distortion can be transmitted in the form of elastic waves. A wave is a disturbance that propagates through, or on the surface of, a medium. Elastic waves satisfy this condition and also propagate through the medium without causing permanent deformation of any point in the medium. Elastic waves are fairly common. For example, sound propagates through the air as elastic waves and water waves propagate across the surface of a pond as elastic waves. 2018/2019 67

Wave Characteristics 4 1 2 Distance or Time 3 1: Amplitude 2; Wave Height 3: Period or Wavelength 4: Crest Q/ what is the wavelength of a wave signal which has a period of 10 sec. and velocity 1500 m/s. you know that Velocity = Freq. x Wavelength Frequency= 1/ Period Velocity = Freq. x Wavelength 2018/2019 68

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There are two groups of seismic waves, body waves and surface waves. Body waves P Waves (or primary waves) are associated with compressive deformation (compression). They travel through all states of matter (liquid, solid and gas), are the fastest of the three seismic waves and range in speed from 6 km/sec (granite) to 7 km/sec (gabbro) in crustal rocks. P waves dramatically increase in velocity the deeper they penetrate into the Earth. The reason is that seismic waves travel faster through more dense materials. S-waves (or secondary waves) are associated with shear. They are significantly slower than P-waves (commonly 4 -5 km/sec) and can only pass through solid materials. When they encounter rock with liquid properties (e. g. , magma), they simply die out. This is an important thing to remember because it will be one of the facts that allow us to resolve the Earth's interior. 2018/2019 70

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Two types of S waves: 1 - SH 2 -SV Some relations: Vp = (K/ρ)1/2 = [(K + 4/3µ/ρ)]1/2 Vs = (µ/ρ)1/2 Vp/Vs = [2(1 σ)/(1 2σ] 1/2 2018/2019 Vp ~ 1. 7 Vs 72

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Surface waves Waves that do not penetrate into the subsurface media are known as surface waves. They decay rapidly with depth and travel at the free surface of a semi-infinite media. Rayleigh wave (also called Ground Roll) Travels along the free surface of the earth with amplitudes that decrease exponentially with depth; Particle motion is in an elliptical sense in a vertical plane with respect to the surface. Rayleigh waves travel only through a solid medium. VR = 0. 92 Vs 2018/2019 Retrograde movement of particles 74

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Love wave Occurs only where a medium with a low S wave velocity overlies a layer with a higher S wave velocity; particle motion is at right angles to the wave propagation but parallel to the surface. They look like SH waves and not detected by geophone…. (why? ) 2018/2019 76

Seismic wave velocities of rocks By virtue of their various compositions, textures (e. g. grain shape and degree of sorting), porosities and contained pore fluids, rocks differ in their elastic moduli and densities and, hence, in their seismic velocities. Information on the compressional and shear wave velocities, Vp and Vs, of rock layers encountered by seismic surveys is important for two main reasons: firstly, it is necessary for the conversion of seismic wave travel times into depths; secondly, it provides an indication of the lithology of a rock or, in some cases, the nature of the pore fluids contained within it. It can be shown that in homogeneous, isotropic media the velocities of P and S waves through the media are given by the expressions shown to the right. 2018/2019 77

Velocity in some materials S wave Velocity (m/s) 3500 2000 2800 -3000 3200 700 -2800 -3000 80 -400 320 -880 400 -1000 600 -1000 2018/2019 P wave Velocity (m/s) 332 1400 -1500 1300 -1400 6100 3600 5500 -5900 6400 1400 -4300 5900 -6100 200 -1000 800 -2200 1000 -2500 1500 -2500 Material Air Water Petroleum Steel Concrete Granite Basalt Sandstone Limestone Sand (Unsaturated) Sand (Saturated) Clay Glacial Till (Saturated) 78

Velocity in rocks is affected by: 1 Texture (grain shape and sorting) 2 Porosity 3 Pore fluids 4 Density Water saturated rocks have different elastic wave velocities compared with gas saturated rocks. In porous rocks the nature of the materials within the pores strongly influences the elastic wave velocity. Seismic velocities can be used to estimate porosity using the time average equation. Velocity is measured: 1/V=Ǿ/Vf + (1 Ǿ)/Vm 1 In laboratories (from cylindrical where V p wave velocity for a rock specimens) Ǿ fractional porosity 2 Acoustic logs Vf acoustic velocity in the pore fluid 3 Up hole shooting Vm acoustic velocity in the rock 4 Schmidt hammer system 5 On land seismic surveying (T X diagram) 2018/2019 79

Reflection and transmission of normally incident seismic rays Consider a compressional ray of amplitude A 0 normally incident on an interface between two media of differing velocity and density. A transmitted ray of amplitude A 2 travels on through the interface in the same direction as the incident ray and a reflected ray of amplitude A 1 returns back along the path of the incident ray. The total energy of the transmitted and reflected rays must equal the energy of the incident ray. The relative proportions of energy transmitted and reflected are determined by the contrast in acoustic impedance Z across the interface. The acoustic impedance of a rock is the product of its density (ρ) and its wave velocity (v); that is, The harder a rock, the higher is its acoustic impedance, while the smaller the contrast in acoustic impedance across a rock interface the greater is the proportion of energy transmitted through the interface. 2018/2019 80

Reflected and transmitted rays associated with a ray normally incident on an interface of acoustic impedance contrast. The reflection coefficient R is a numerical measure of the effect of an interface on wave propagation, and is calculated as the ratio of the amplitude A 1 of the reflected ray to the amplitude A 0 of the incident ray 2018/2019 81

where ρ1, v 1, Z 1 and r 2, v 2, Z 2 are the density, P wave velocity and acoustic impedance values in the first and second layers, respectively. From this equation it follows that 1 ≤ R ≥ +1. A negative value of R signifies a phase change of (180°) in the reflected ray. The transmission coefficient T is the ratio of the amplitude A 2 of the transmitted ray to the amplitude A 0 of the incident ray T = A 2 / A 0 0 ≤ T≤ 2 Reflection and transmission coefficients are some times expressed in terms of energy rather than wave amplitude 2018/2019 82

Important 2018/2019 83

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Typical Reflection Coefficients 2018/2019 85

Reflection and refraction of obliquely incident rays When a P-wave ray is obliquely incident on an interface of acoustic impedance contrast, reflected and transmitted P wave rays are generated as in the case of normal incidence. Additionally, some of the incident compressional energy is converted into reflected and transmitted S wave rays Reflected and refracted P- and S-wave rays generated by a P-wave ray obliquely incident on an interface of acoustic impedance contrast. A general relation (sin i / V)p =[(sin i / V)pr = (sini / V)sr]refleced =[(sini / V)pt = (sini / V)st]transmitted 2018/2019 86

Snell’s Law of Refraction applies equally to the optical and seismic cases. Snell defined the ray parameter p = sini /v, where i is the angle of inclination of the ray in a layer in which it is travelling with a velocity v. The generalized form of Snell’s Law states that, along any one ray, the ray parameter remains a constant. For the refracted P wave ray shown here OR Note that if v 2 > v 1 the ray is refracted away from the normal to the interface. Snell’s Law also applies to the reflected ray, from which it follows that the angle of reflection equals the angle of incidence • The incident, reflected and refracted rays and the normal at the point of incidence all lie in the same plane. 2018/2019 87

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Critical refraction When the velocity is higher in the underlying layer there is a particular angle of incidence, known as the critical angle ( ic or θc), for which the angle of refraction is 90°. This gives rise to a critically refracted ray that travels along the interface at the higher velocity v 2 2018/2019 89

Seismic data acquisition The essential instrumental requirements are to generate a seismic pulse with a suitable source. detect the seismic waves in the ground with a suitable transducer. record and display seismic wave forms on a suitable seismograph. For details See Reynolds, 1997 2018/2019 90 90

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Geophones Conversion of the ground motion to an electrical signal requires a transducer which is sensitive to some component of the ground motion, and can record the required range of frequencies and amplitudes without distortion. Geophones are of several designs, but the most common is the moving-coil geophone. 2018/2019 93

Seismic recording systems (seismograms) 1. The recording must be timed accurately relative to the seismic source. 2. Seismograms must be recorded with multiple transducers simultaneously, so that the speed and direction of travel of seismic waves can be interpreted. 3. The electrical signals must be stored for future use. Ground surface 2018/2019 94

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Seismic reflection surveying The essence of the seismic reflection technique is to measure the time taken for a seismic wave to travel from a source down into the ground where it is reflected back to the surface and then detected at a receiver. The time is known as the two way travel time (TWTT). The most important problem in seismic reflection surveying is the translation of TWTT to depth. While travel times are measured, the one parameter, that most affects the conversation of to depth is seismic velocity. ➔ two unknowns (depth + velocity) 2018/2019 96

Single horizontal reflector The basic geometry of the reflected ray path is shown in the figure (a) Section through a single horizontal layer showing the geometry of reflected ray paths and (b) time–distance curve for reflected rays from a horizontal reflector. ΔT= normal moveout (NMO). 2018/2019 97

The equation for the travel time t of the reflected ray from a shot point to a detector at a horizontal offset, or shot–detector separation, x is given by the ratio of the travel path length to the velocity. Reflection time t is measured at an offset distance Can be written as Two unknown values which are related to the subsurface structure, z and V. The graph of travel time of reflected rays plotted against offset distance (the time– distance curve) is a hyperbola whose axis of symmetry is the time axis 2018/2019 98

Substituting x = 0 in the above equation, the travel time t 0 of a vertically reflected ray is obtained: This is the intercept on the time axis of the time–distance curve By simple substitution If t 2 is plotted against x 2, the graph will produce a straight line of slope 1/V 2. The intercept on the time axis will also give the vertical two way time, t 0, from which the depth to the reflector can be found. T 2 Slope = 1/V 2 T 02 x 2 2018/2019 99

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Dipping reflector In the case of a dipping reflector the value of dip enters the time–distance equation as an additional unknown. The equation is derived similarly to that for horizontal layers by considering the ray path length divided by the velocity: Consider two receivers at equal offsets x updip and downdip from a central shot point. Because of the dip of the reflector, the reflected ray paths are of different length and the two rays will therefore have different travel times. 2018/2019 101

Dip moveout DTd is defined as the difference in travel times tx and t x of rays reflected from the dipping interface to receivers at equal and opposite offsets x and 2018/2019 102

The shot gather The initial display of seismic profile data is normally in groups of seismic traces recorded from a common shot, known as common shot point gathers or, simply, shot gathers. The seismic detectors (e. g. geophones) may be distrib uted on either side of the shot, or only on one side. Shot–detector configurations used in multichannel seismic reflection profiling. (a) Split spread, or straddle spread. (b) Single- ended or on-end spread. 2018/2019 103

This is called a seismic trace reflected waves Direct waves Geophone 2018/2019 104

The number of times the same point on a reflector is sampled as the fold of coverage. For example: Four shot against four geophone locations give four fold coverage when moving the array one distance forward. See the following figure…. . . 2018/2019 105

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Given the Source receiver layout and corresponding ray paths for a common depth point spread, shown in (a), the resulting seismic traces are illustrated in (b), uncorrected (on the right), (corrected on the left) – note how the reflection events are aligned – and the final stacked trace. 2018/2019 NMO correction 107

Seismic refraction surveying The seismic refraction surveying method uses seismic energy that returns to the surface after traveling through the ground along refracted ray paths. The most commonly derived geophysical parameter is the seismic velocity of the layers present. A number of geotechnical parameters can also be derived from seismic velocity. In addition to the more conventional engineering applications of foundation studies for dams and major buildings, seismic refraction is increasingly being used in hydrogeological investigations to determine saturated aquifer thickness, weathered fault zones. 2018/2019 108

Geometry of refracted ray paths 2018/2019 109

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Multiple layered models For multiple layered models we can apply the same process to determine layer thickness and velocity sequentially from the top layer to the bottom Head wave from top of layer 2: Head wave from top of layer 3: Head wave from top of layer n: 2018/2019 112

The end for academic year 2018 2019 Hopping A good luck for all students 2018/2019 113