Sismik Yorumlama Sismik Yorumlama - 1a GEOL 335.3 Refraction Seismic Method Intercept times and apparent velocities; Critical and crossover distances; Hidden layers; Determination of the refractor velocity and depth; The case of dipping refractor: Hagedoorn plus-minus method; Generalized Reciprocal Method ('refraction migration'); Travel-time continuation. Reading: Reynolds, Chapter 5 Telford et al., Sections 4.7.9, 4.9 Sheriff and Geldart, Chapter 4.GEOL 335.3 Two-layer problem One reflection and one refraction x critical S i c i V 1 V 2 >V 1 Direct Headwave Refracted Reflected x t x crossover Direct Reflected: Head pre-critical post-critical t= t 0 x V 2 = t 0 x p 2 t= x V 1 = x p 1 t 0 At pre-critical offsets, record direct wave and reflection In post-critical domain, record direct wave, refraction, and reflection h 1GEOL 335.3 Travel-time relations Two-horizontal-layer problem For a head wave: For a reflection: this is also sin i intercept time, t 0GEOL 335.3 Multiple-layer case (Horizontal layering) p is the same critical ray parameter; t 0 is accumulating across the layers:GEOL 335.3 Dipping Refractor Case shooting down dip S i c V 1 V 2 >V 1 h d R x a (dip) i c h u A B R' xsina x(cosa-sina tani c ) xsina /cosi c sini c would change to '-' for up-dip shootingGEOL 335.3 Refraction Interpretation Reversed travel times One needs reversed recording (in opposite directions) for resolution of dips. The reciprocal times, T R , must be the the same for reversed shots. Dipping refractor is indicated by: Different apparent velocities (=1/p, TTC slopes) in the two directions; determine V 2 and a (refractor velocity and dip). Different intercept times. determine h d and h u (interface depths). S x t R T R 2z d cosi c V 1 2z u cosi c V 1 slope= p 1 = 1 V 1 p u = sin i c V 1 p d = sin i c V 1GEOL 335.3 Determination of Refractor Velocity and Dip Apparent velocity is V app = 1/p, where p is the ray parameter (i.e., slope of the travel-time curve). Apparent velocities are measured directly from the observed TTCs; V app = V refractor only in the case of a horizontal layering. For a dipping refractor: Down dip: (slower than V 1 ); Up-dip: (faster). From the two reversed apparent velocities, i c and a are determined: V d = V 1 sin i c V u = V 1 sin i c i c = 1 2 sin 1 V 1 V d sin 1 V 1 V u , i c = sin 1 V 1 V u. i c = sin 1 V 1 V d , = 1 2 sin 1 V 1 V d sin 1 V 1 V u . From i c , the refractor velocity is: V 2 = V 1 sin i c .GEOL 335.3 Determination of Refractor Depth From the intercept times, t d and t u , refractor depth is determined: h d = V 1 t d 2 cos i c , h u = V 1 t u 2 cos i c . S i c V 1 V 2 >V 1 h d R x a (dip) i c h u A BGEOL 335.3 Apparent Velocity Relation to wavefronts Apparent velocity, V app, is the velocity at which the wavefront sweeps across the geophone spread. Because the wavefront also propagates upward, V app, ‡ V true : A C q B wavefront Propagation direction Apparent propagation direction AC= BC sin V app = V sin . 2 extreme cases: q = 0: V app = ¥ ; q = 90 : V app = V true . GEOL 335.3 Delay time Consider a nearly horizontal, shallow interface with strong velocity contrast (a typical case for weathering layer). In this case, we can separate the times associated with the source and receiver vicinities: t SR = t SX + t XR . Relate the time t SX to a time along the refractor, t BX : t SX = t SA – t BA + t BX = t S Delay +x/V 2 . S i c V 1 V 2 >V 1 h s x B A X R h/cosi c htani c t S Delay = SA V 1 BA V 2 = h s V 1 cos i c h s tan i c V 2 = h s V 1 cos i c 1 sin 2 i c = h s cosi c V 1. Note that V 2 =V 1 /sini c Thus, source and receiver delay times are: t S , R Delay = h s , r cosi c V 1. t SR = t S Delay t R Delay SR V 2. and h rGEOL 335.3 Plus-Minus Method (Weathering correction; Hagedoorn) Assume that we have recorded two headwaves in opposite directions, and have estimated the velocity of overburden, V 1. How can we map the refracting interface? S 1 V 1 D(x) S 2 S 1 x t S 2 T R t S1 D t S2 D D Solution: Profile S 1 ? S 2 : Profile S 2 ? S 1 : Form PLUS travel-time: t S 1 D = x V 2 t S 1 t D ; t S 2 D = SR x V 2 t S 2 t D. t PLUS = t S 1 D t S 2 D = SR V 2 t S 1 t S 2 2t D = t S 1 S 2 2t D. t D = 1 2 t PLUS t S 1 S 2 . Hence: To determine i c (and depth), still need to find V 2 .GEOL 335.3 Plus-Minus Method (Continued) S 1 V 1 D(x) S 2 S 1 x t S 2 T R t S1 D t S2 D D To determine V 2 : Form MINUS travel-time: t MINUS = t S 1 D t S 2 D = 2x V 2 SR V 2 t s 1 t s 2 . slope t MINUS x = 2 V 2 . Hence: The slope is usually estimated by using the Least Squares method. Drawback of this method – averaging over the pre-critical region. this is a constant!GEOL 335.3 Generalized Reciprocal Method (GRM) S 1 V 1 D S 2 S 1 x t S 2 T R t S1 D t S2 D D The velocity analysis function: Introduces offsets ('XY') in travel-time readings in the forward and reverse shots; so that the imaging is targeted on a compact interface region. Proceeds as the plus-minus method; Determines the 'optimal' XY: 1) Corresponding to the most linear time-depth function; 2) Corresponding to the most detail of the refractor. XY XY t D = 1 2 t S 1 D t S 2 D t S 1 S 2 XY V 2 . t V = 1 2 t S 1 D t S 2 D t S 1 S 2 , should be linear, slope = 1/V 2 ; The time-depth function: this is related to the desired image: h D = t D V 1 V 2 V 2 2 V 1 2GEOL 335.3 Phantoming Refraction imaging methods work within the region sampled by head waves, that is, beyond critical distances from the shots; In order to extend this coverage to the shot points, phantoming can be used: Head wave arrivals are extended using time-shifted picks from other shots; However, this can be done only when horizontal structural variations are small. x t Phantom arrivalsGEOL 335.3 Hidden-Layer Problem Velocity contrasts may not manifest themselves in refraction (first-arrival) travel times. Three typical cases: Low-velocity layers; Relatively thin layers on top of a strong velocity contrast; Short travel-time branch may be missed with sparse geophone coverage.1 Applied Geophysics – Refraction I Seismic methods:Refraction I Refraction reading: Sharma p158 - 186 Applied Geophysics – Refraction I Pre-Critical incidence Snell’s Law: p V r V R V i P P P P P P = = = 2 1 1 sin sin sin where p is the ray parameter and is constant along each ray. Reflection and refraction Reflection and transmission coefficients for a specific impedance contrast 2 Applied Geophysics – Refraction I Critical incidence When r P = 90° i P = i C the critical angle 2 1 sin P P C V V i = The critically refracted energy travels along the velocity interface at V 2 continually refracting energy back into the upper medium at an angle i C a head wave Reflection and transmission coefficients for a specific impedance contrast Applied Geophysics – Refraction I Reflection and transmission coefficients for a specific impedance contrast Post-Critical incidence The angle of incidence > i C No transmission, just reflection3 Applied Geophysics – Refraction I Horizontal interface Traveltime equations 1 V x T = 1 2 2 1 2 2 1 2 2 1 1 1 ' 2 tan 2 cos 2 V V V V h V x T V i h x i V h T T T T T c c BD DD SB - + = - + = + + = Direct wave: Head wave: T = ax + b slope: 1/V 2 intercept: gives h 1 Head wave Applied Geophysics – Refraction I Horizontal interface Crossover distance, x co Where the direct and head wave cross. Their travel times are equal: Another approach to obtaining layer thickness 1 2 1 2 1 1 2 2 1 2 2 1 2 1 2 2 V V V V h x V V V V h V x V x co co co - + = - + =4 Applied Geophysics – Refraction I Horizontal interface Reflections The critical reflection is the closest head wave arrival. At shorter offsets there are low amplitude reflections (used in reflection seismology). At greater offsets there are wide-angle reflections. Applied Geophysics – Refraction I Three-layer model 1 2 3 2 1 V DG V CD V BC V AB V SA T SG + + + + = Traveltime 3 2 1 1 2 2 1 1 1 tan 2 tan 2 cos 2 cos 2 V z z x V z V z T c c SG ? ? ? ? - - + + = 2 3 2 2 2 3 2 1 3 2 1 2 3 1 3 2 2 V V V V z V V V V z V x T SG - + - + = With some manipulation 1. Determine V 1 , V 2 , V 3 from slopes 2. Determine z 1 from 1 st intercept 3. Determine z 2 from 2 nd intercept5 Applied Geophysics – Refraction I 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 1 2 2 1 2 2 1 2 2 V V V V h V x T - + = n n j j n j n j V x V V V V h T + ? ? ? ? ? ? ? ? - = ? - = 1 1 2 2 2 Head wave from top of layer 2: Head wave from top of layer 3: Head wave from top of layer n: 2 3 2 2 2 3 2 1 3 2 1 2 3 1 3 2 2 V V V V h V V V V h V x T - + - + = Applied Geophysics – Refraction I Horizontal vs. vertical velocity contrasts A three-horizontal layer model can produce the same traveltime curve as a single horizontal layer over a vertical velocity contact 1/V 1 1/V 2 1/V 3 1/V 1 1/V 2a 1/V 2b Head wave continues into 2b6 Applied Geophysics – Refraction I Horizontal vs. vertical velocity contrasts Use a long-offset shot • Leave the geophones fixed and move shot to greater offset In horizontal layers case the shape of the traveltime curve is unchanged, just shifted in space. In vertical velocity contrast case the crossover distance remains fixed but is time shifted. Applied Geophysics – Refraction I Mapping vertical contacts Small offsets A vertical step causes an offset on the traveltime curve 1 2 1 2 2 1 2 V V V TV z t - ? = • Diffractions link the two head wave curves • Depth, z1, is calculated from the intercept in the usual way • The relation of velocity to the slope remains unchanged • The offset can be calculated from the time offset, ?T7 Applied Geophysics – Refraction I Mapping vertical contacts Infinite/large offsets For infinite/large vertical offsets there is no secondary head wave Three segments • Direct wave • Head wave • Diffracted wave Will have the velocity close to the direct wave Reverse the line • Shooting to the same string of geophones from the other end • Two traveltime segments: direct and head wave Head wave generated from energy entering the high velocity layer at the vertical interface Applied Geophysics – Refraction I Dipping layers Dipping layers still produce head waves but the traveltimes are affected by the dip Shooting up-dip: the velocity appears greater Shooting down-dip: the velocity is reduced8 Applied Geophysics – Refraction I Reversing lines For horizontal layers the traveltime curves are symmetrical For dipping layers layer velocities appear different for each end – the dip and true velocity can be determined from the up- dip and down-dip velocities …shooting to a line of geophones from both ends Applied Geophysics – Refraction I Dipping layer traveltime Down-dip 1 2 1 ' V DS V CD V SC T d + + = [] 2 1 tan ) ( cos V i h h x i V h h T c d u c d u d + - + + = With trigonometric transformations, an exercise for the class: Down-dip traveltime 1 1 cos 2 ) sin( V i h V i x T c d c d + + = ? Up-dip traveltime 1 1 cos 2 ) sin( V i h V i x T c u c u + - = ? …where is V 2 dependence? ) sin( 1 ? + = c d i V V Down-dip apparent velocity ) sin( 1 ? - = c u i V V Up-dip apparent velocity9 Applied Geophysics – Refraction I Dipping layer traveltime ) sin( 1 ? + = c d i V V Given ) sin( 1 ? - = c u i V V We can solve for: ? ? ? ? ? ? + = ? ? ? ? ? ? - = - - - - u d c u d V V V V i V V V V 1 1 1 1 2 1 1 1 1 1 2 1 sin sin sin sin ? Finally, the intercept times can be used to determine the perpendicular distance to the reflector: 2 1 sin V V i c = V 2 then obtained from: 1 cos 2 V i h T c d id = 1 cos 2 V i h T c u iu = Applied Geophysics – Refraction I Dipping layer Example Direct arrivals Velocities from slopes: 1780 m/s and 2250 m/s average: 2015 m/s Head waves Up-dip velocity, V u = 3200 m/s Down-dip velocity, V d = 2870 m/s Using ? ? ? ? ? ? + = ? ? ? ? ? ? - = - - - - u d c u d V V V V i V V V V 1 1 1 1 2 1 1 1 1 1 2 1 sin sin sin sin ? we obtain: ? = 2.8 ° i c = 42 °10 Applied Geophysics – Refraction I Dipping layer 2 1 sin V V i c = Now obtain V 2 from V 2 = 3000 m/s To determine the perpendicular depths, h u and h d , use h u = 155 m and h d = 95 m 1 cos 2 V i h T c d id = 1 cos 2 V i h T c u iu = Example1 Applied Geophysics – Refraction II Seismic methods:Refraction II Refraction reading: Sharma p158 - 186 Advanced interpretation Applied Geophysics – Refraction II 594 Schedule Tue Oct 28 th Refraction II (Hwk handed out) Thu Oct 30 th Refraction III and Seismic Review: bring questions Fri Oct 31 st Hwk to Stuart (if to be returned before exam) Tue Nov 4 th Resistivity I Thu Nov 6 th Seismic Exam Tue Nov 11 th Resistivity II …2 Applied Geophysics – Refraction II Real Earth “flat” layers Although the interfaces between real Earth layers are not perfectly flat, head waves still travel along them Analysis methods: Best-fit straight line through the points provides some kind of average layer thickness and velocity though the error may be unacceptable Special analysis techniques: Phantom arrivals Delay time Plus-minus Applied Geophysics – Refraction II Phantom arrivals Undulating surface • Cannot extrapolate the head wave arrival time curve back to the intercept • How do we determine layer thickness beneath the shot, S?3 Applied Geophysics – Refraction II Phantom arrivals 1. Shoot a long-offset shot, S L 2. The head wave traveltime curves for both shots will be parallel, offset by time ?T 3. Subtract ?T from the S L arrivals to generate fictitious 2 nd layer arrivals close to S – the phantom arrivals 4. The intercept point at S can then be determined: T i 5. Use the usual formula to determine perpendicular layer thickness beneath S 1 2 2 1 2 2 2 V V V V h T s i - = Applied Geophysics – Refraction II Separation of delay times Delay time is the difference between the slant path traveltime (AB) and the traveltime along the refractor beneath (A’B) Delay time below shotpoint S: 1 2 2 1 2 2 2 1 2 1 tan cos ' V V V V h T V i h i V h T V B A V AB T A S c A c A S S - = ? - = ? - = ? 1 2 2 1 2 2 V V V V h T D D - = ? Likewise, beneath D: The delay time is related to the perpendicular depth beneath the geophone. If we know the delay time, V 1 and V 2 then we can calculate the depth. 4 Applied Geophysics – Refraction II Separation of delay times Determining the delay time beneath a geophone, ?T D : Total traveltime ABFG: ' 2 S S t T T V L T ? + ? + = Total traveltime ABCD: D S SD T T V x T ? + ? + = 2 Total traveltime GFED: D S D S T T V x L T ? + ? + - = ' 2 ' Adding the equations for T SD and T S’D and using the equation for T t we obtain an equation for ?T D : 2 ' t D S SD D T T T T - + = ? determine ?T D from a reversed refraction line “plus” Applied Geophysics – Refraction II Separation of delay times Determining velocity, V 1 V 2 : Direct arrival slope = 1/V 1 Subtracting the equations for T SD and T S’D we obtain the equation: ' 2 2 ' 2 S S D S SD T T V L V x T T ? - ? + - = - “minus” y = ax + b •P l o t t i n g ( T SD -T S’D ) against x the slope is 2/V 2 • Variations in the slope reflect lateral variations in velocity5 Applied Geophysics – Refraction II The plus-minus method Given the delay time ?T D , (from the “plus”) and the velocities V 1 (from direct arrival) and V 2 (from the “minus) We can calculate the perpendicular depth: 1 2 2 1 2 2 V V V V h T D D - = ? Note: we need to see refracted arrivals from both forward and reverse shots (three geophones only in figure) Use long offset shots to collect necessary data for all geophones Applied Geophysics – Refraction II The plus-minus method Assumptions and approximations 1. The relief on the refractor must be small compared to the depth 2. Geometric relations assume a small refractor dip (dip < 10 deg) 3. Refractor assumed to be planar between the two points of emergence to a given geophone (ie between C and E) So that ?T D is equal when shooting from both sides6 Applied Geophysics – Refraction II Generalized reciprocal method The plus-minus method assumes a planar interface and shallow dip between C and E The generalized reciprocal approach uses two geophones, X and Y, recording refracted arrivals originating from the same point on the refractor avoiding these assumptions Applied Geophysics – Refraction II Generalized reciprocal method Define two functions: 1. Velocity analysis function, T V 2 AB BX AY V T T T T + - = This is the traveltime from A to H 2. Time-depth function, T G ( ) 2 ' V XY T T T T AB BX AY G - - + = This is the traveltime along EX or FY minus the traveltime of the projection of GX or GY along the refractor interface i.e. the traveltime along the GH V’ is the apparent refractor velocity determined from T V7 Applied Geophysics – Refraction II Generalized reciprocal method Procedure: Velocity analysis function, T V •C a l c u l a t e T V as a function of offset AG for a variety of XY distances • The optimal XY is when E and F converge on H • Optimal XY is identified by the smoothest T V curve • Refractor velocity V’ is the reciprocal of the slope of T V • Can determine variations in V’ along the length of the profile T V Offset AG Applied Geophysics – Refraction II Generalized reciprocal method Procedure: Time-depth function, T G •C a l c u l a t e T G as a function of offset AG for a variety of XY distances • Optimal XY is identified by the roughest T G curve • Calculate average velocity from surface to refractor • Calculate the depth from T G and the average velocity T G Offset AG ' 2 ' 2 V T XY XY V V G + = 2 2 ' ' V V V V T h G - =8 Applied Geophysics – Refraction II Experiment design Geophones: often use the same geophones as in reflection work – constraint is the frequency of the geophones Frequency: refraction studies may be constrained to lower frequencies due to longer ray lengths (10Hz vs. 100Hz for reflection) Profile length: typically 5 to 10 times the depth of the refractor to ensure head wave as first arrival Shot points: Typically five for each geophone array • One at each end: uppermost velocity plus reversed line • One at center: to determine uppermost layer velocity • Two long offset shots: to determine phantom arrivals and reverse line Applied Geophysics – Refraction II Low velocity layers Limitations • They are completely invisible to the refraction method • They will cause miss-interpretation of the depth of lower lying layers • Lower layers appear deeper than they are The intercept of the refraction from layer 3 will be dependent on the thickness and velocity in layer 29 Applied Geophysics – Refraction II Hidden layers Limitations • If a layer is thin it may never produce a first arrival • Lower layers always appear too shallow as a layer has been missed Either the direct or refraction from a lower (much higher velocity layer) is always first Applied Geophysics – Refraction II Velocity and rock strength Relating velocity to rock strength allows site classification based on refraction studies 1. Elastic moduli: Poisson’s ratio ) ( 2 2 2 2 2 2 S P S P V V V V - - = ? • Tells us about the elastic strength of the material • Important for building foundations etc • Determined from knowledge of V P and V S – need shear sources and horizontal geophones for V S 2. Degree of jointing •J o i n t i n g l o w e r s s e i s m i c velocity • Degree of jointing can be estimated from velocity for a known rock type 10 Applied Geophysics – Refraction II Velocity and rock strength Relating velocity to rock strength allows site classification based on refraction studies 3. Rippability • Jointing is also a factor in the rippability of a rock • Seismic velocity can therefore be used to determine the methods necessary to excavate an area 1 Applied Geophysics – Refraction III Seismic methods:Refraction III Refraction reading: Sharma p158 - 186 Examples and limitations Applied Geophysics – Refraction III Generalized reciprocal method The plus-minus method assumes a planar interface and shallow dip between C and E The generalized reciprocal approach uses two geophones, X and Y, recording refracted arrivals originating from the same point on the refractor avoiding these assumptions2 Applied Geophysics – Refraction III Generalized reciprocal method Define two functions: 1. Velocity analysis function, T V 2 AB BX AY V T T T T + - = This is the traveltime from A to H 2. Time-depth function, T G ( ) 2 ' V XY T T T T AB BX AY G - - + = This is the traveltime along EX or FY minus the traveltime of the projection of GX or GY along the refractor interface i.e. the traveltime along the GH V’ is the apparent refractor velocity determined from T V Applied Geophysics – Refraction III Generalized reciprocal method Procedure: Velocity analysis function, T V •C a l c u l a t e T V as a function of offset AG for a variety of XY distances • The optimal XY is when E and F converge on H • Optimal XY is identified by the smoothest T V curve • Refractor velocity V’ is the reciprocal of the slope of T V • Can determine variations in V’ along the length of the profile T V Offset AG3 Applied Geophysics – Refraction III Generalized reciprocal method Procedure: Time-depth function, T G •C a l c u l a t e T G as a function of offset AG for a variety of XY distances • Optimal XY is identified by the roughest T G curve • Calculate average velocity from surface to refractor • Calculate the depth from T G and the average velocity T G Offset AG ' 2 ' 2 V T XY XY V V G + = 2 2 ' ' V V V V T h G - = Applied Geophysics – Refraction III Rockhead determination for waste disposal site Example Refraction study to determine if a permit should be issued for a waste disposal site Site description: • Isolated site adjacent to a river. • Basalt basement rock outcrops adjacent to site on far side from the river. • Basal believed to underlie entire site. • Overburden is alluvium and windblown sand Refraction deployment: • Sledge hammer ineffective due to high attenuation of loose surface sand. Used explosives • Series of geophone arrays used to form one long array across the site • For each array use one short and one long offset shot at each end plus a mid-spread shot4 Applied Geophysics – Refraction III Rockhead determination for waste disposal site Example Forward shots Long offset shot • No direct arrivals as no geophones close enough • Arrives earlier due to shallower refractor depth beneath long offset shot Direct arrivals provide overburden velocities along profiles Near parallel arrivals tell us there is near-constant lower layer velocity How many layers? Applied Geophysics – Refraction III Rockhead determination for waste disposal site Example Reversed shots Forward shots5 Applied Geophysics – Refraction III Rockhead determination for waste disposal site Example Phantoming • Used to generate a refraction arrival time much longer that it is possible to collect • Could be used to determine intercept, or • In preparation for reciprocal method Near-constant velocity refractor Increased velocity or reduced depth? (Data also interpolated between each geophone to increase range of possible XY distances) Applied Geophysics – Refraction III Rockhead determination for waste disposal site Example Velocity analysis: •T V calculated for a range of XY values • Optimal XY: 0 feet (The smoothest curve) T V6 Applied Geophysics – Refraction III Rockhead determination for waste disposal site Example Refractor velocity determination • Velocity is 1/slope of optimal T V plot • Decided on three refractor velocities as data fitted well with three straight line segments Applied Geophysics – Refraction III Rockhead determination for waste disposal site Example T G Time-depth plot • To determine depth of refractor beneath each geophone point • Again, optimal XY is zero offset: the roughest curve on the T G plot •U s i n g T G , the refractor and overburden velocity we can calculate the depth of the refractor beneath each geophone7 Applied Geophysics – Refraction III Rockhead determination for waste disposal site Example Refractor depth profile •U s i n g T G , the refractor and overburden velocity, we can calculate the depth of the refractor beneath each geophone • Note it is the distance of the refractor from the geophone so draw circles • Refractor surface is tangent to all the circles Ground surface Refractor - basalt Applied Geophysics – Refraction III Archeological investigations Examples Locating the vallum Adjacent to Vindobala Fort on Hadrian’s Wall • Want to locate the buried vallum for possible excavation and preservation • Vallum: a flat bottomed ditch (!)8 Applied Geophysics – Refraction III Archeological investigations Examples P-wave refraction lines • Sledge hammer source •2 m g e o p h o n e s p a c i n g • 50m lines reversed S-wave refraction lines • Rubber maul hammer striking horizontally on a vertical plate • 2m horizontal geophone spacing From Sharma: “The stand was orientated perpendicular to the seismic line, so the S-waves propagating along the line were horizontally polarized in the transverse direction for being detected by transversely orientated geophones.” Applied Geophysics – Refraction III Archeological investigations Examples Depth profiles used to identify the location of the vallum Difference in P and S results give some indication of uncertainty9 Applied Geophysics – Refraction III GPR survey lines spaced 0.5 m apart Injection well ERT borehole NC Line NC Line EC Line EC Line 0 2.5 5 m Boundary of backgroundsurveys Boundary of surveys during injection Line 18 Air sparging: Testing effectiveness Applied Geophysics – Refraction III Figure 6 – (a) Velocity model for background refraction data along line EC. (b) Velocity model for background refraction data along line (NC). (c) Ray density for the velocity image of the background refraction data collected along line EC shown in (a). Areas that are black have a ray density less than unity. Vertical black arrows and white triangles represent the shot and geophone locations, 0 5 10 15 20 25 0.0 1.0 2.0 3.0 Distance (m) Depth (m) 51 01 52 02 53 03 54 0 Ray Density 0 5 10 15 20 25 0.0 1.0 2.0 3.0 Distance (m) Depth (m) 0 5 10 15 20 25 0.0 1.0 2.0 3.0 Distance (m) Depth (m) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Velocity (m/ms) W E N S W10 Applied Geophysics – Refraction III 0 5 10 15 20 25 0.0 1.0 2.0 3.0 Distance (m) Depth (m) Figure 7 –Difference in velocity between injection and background refraction images collected along (a) line EC, and (b) line NC. The regions that are black have a ray-path density less than unity in either the background or injection images, and thus are not constrained by the data. 0 5 10 15 20 25 0.0 1.0 2.0 3.0 Distance (m) Depth (m) -0.10 -0.05 0.00 0.05 0.10 Velocity Difference (m/ms) Applied Geophysics – Refraction III Quarry survey Examples Identifying location and thickness of sand and gravel deposits Gravel Sand Chalk11 Applied Geophysics – Refraction III Crustal structure of the Alps Examples Applied Geophysics – Refraction III Crustal structure of the Alps Examples Note the strong postcritical reflections (PmP) • Suggests large velocity contrast across the Moho 1 Physics and chemistry of the Earth’s interior – Seismic refraction Seismic refraction Controlled source seismology: Reading: Fowler p119-130 Physics and chemistry of the Earth’s interior – Seismic refraction Seismic methods and scale Global seismology (earthquakes) • Provides information on global earth structure and large scale velocity anomalies (100’s to 1000’s km) • Difficult to image smaller scale structure, particularly away from earthquake source regions Controlled source seismology • Allows higher resolution studies (meters to 100’s km) • Can carry out experiments away from tectonic regions2 Physics and chemistry of the Earth’s interior – Seismic refraction Controlled source seismology • Set out a line or array of geophones • Input a pulse of energy into the ground • Record the arrival times to interpret velocity structure Seismic refraction • Used to study large scale crustal layering: thickness and velocity Seismic reflection • “Imaging” of subsurface reflectors • Difficult to determine accurate velocities and depths reflection refraction Physics and chemistry of the Earth’s interior – Seismic refraction Reflection and refraction Seismic rays obey Snell’s Law (just like in optics) The angle of incidence equals the angle of reflection, and the angle of transmission is related to the angle of incidence through the velocity ratio. 2 2 1 1 1 sin sin sin ? ? ? e e i = = Note: the transmitted energy is refracted ? 1 ? 23 Physics and chemistry of the Earth’s interior – Seismic refraction Reflection and refraction Seismic rays obey Snell’s Law (just like in optics) The angle of incidence equals the angle of reflection, and the angle of transmission is related to the angle of incidence through the velocity ratio. But a conversion from P to S or vice versa can also occur. Still, the angles are determined by the velocity ratios. where p is the ray parameter and is constant along each ray. ? 1 ß 1 ? 2 ß 2 p f f e e i = = = = = 2 2 1 1 2 2 1 1 1 sin sin sin sin sin ß ß ? ? ? Physics and chemistry of the Earth’s interior – Seismic refraction Reflection and refraction You can see: a direct wave, reflected and transmitted waves, plus multiples…4 Physics and chemistry of the Earth’s interior – Seismic refraction Critical incidence when ? 2 > ? 1 , e 2 > i we can increase i P until e 2 = 90° When e 2 = 90° i = i C the critical angle 2 2 1 sin sin ? ? e i = 2 1 sin ? ? = C i ? 1 ? 2 The critically refracted energy travels along the velocity interface at ? 2 continually refracting energy back into the upper medium at an angle i C a head wave Physics and chemistry of the Earth’s interior – Seismic refraction Head wave • Occurs due to a low to high velocity interface • Energy travels along the boundary at the higher velocity • Energy is continually refracted back into the upper medium at an angle i C • Provides constraints on the boundary depth e.g. Moho depth5 Physics and chemistry of the Earth’s interior – Seismic refraction Head wave You can see: a head wave, trapped surface wave, diving body wave Physics and chemistry of the Earth’s interior – Seismic refraction Two-layered model Energy from the source can reach the receiver via several paths: 1. Direct wave Energy traveling through the top layer, traveltime: A straight line passing through the origin 1 ? x t = xR S6 Physics and chemistry of the Earth’s interior – Seismic refraction Two-layered model 1. Direct wave 2. Reflected wave Energy reflecting off the velocity interface, traveltime: 1 1 ? ? CR SC t + = 4 2 2 1 x z CR SC + = = 4 2 2 2 1 1 x z t + = ? where so 2 2 1 2 2 1 4 x z t + = ? or The equation of a hyperbolae xR S Physics and chemistry of the Earth’s interior – Seismic refraction Two-layered model xR S 1 1 1 ? ? ? BR AB SA t + + = 2 2 2 2 1 1 1 1 2 ? ? ? ? x z t + - = bx a t + = ie. the equation of a straight line 1. Direct wave 2. Reflected wave 3. Head wave or refracted wave Energy refracting across the interface, traveling along the underside and then back up to the surface, traveltime: with some algebra where the slope of the line is and the intercept is 2 1 ? 2 2 2 1 1 1 1 2 ? ? ? - z7 Physics and chemistry of the Earth’s interior – Seismic refraction Determining model parameters • ? 1 determined from the slope of the direct arrival (straight line passing through the origin) • ? 2 determined from the slope of the head wave (straight line first arrival beyond x cross ) • Layer thickness z 1 determined from the intercept of the head wave (already knowing ? 1 and ? 2 ) Two-layered model xR S Physics and chemistry of the Earth’s interior – Seismic refraction 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 2 2 2 2 1 1 1 1 2 ? ? ? ? x z t + - = 3 2 3 2 2 2 2 2 3 2 1 1 1 1 2 1 2 ? ? ? ? ? ? ? x z z t + - + - = m m j m j j j x z t ? ? ? ? + ? ? ? ? ? ? ? ? - = ? - = 1 1 2 2 1 2 Head wave from base of layer 2: Head wave from base of layer 3: Head wave from base of layer m:8 Physics and chemistry of the Earth’s interior – Seismic refraction Some problems This analysis works for horizontal flat layers each of which produces a head wave with first arrivals in some distance window This is not the case for: Hidden layers do not produce first arrivals Low velocity layers do not produce a head wave (need a velocity increase) Non-horizontal layers? Physics and chemistry of the Earth’s interior – Seismic refraction Dipping layers Dipping layers still produce head waves but the traveltimes are affected by the dip Shooting up-dip: the velocity appears greater Shooting down-dip: the velocity is reduced9 Physics and chemistry of the Earth’s interior – Seismic refraction Reversing lines For horizontal layers the traveltime curves are symmetrical For dipping layers layer velocities appear different for each end – the dip and true velocity can be determined from the up- dip and down-dip velocities …shooting to a line of geophones from both ends Physics and chemistry of the Earth’s interior – Seismic refraction Real Earth “flat” layers Although the interfaces between real Earth layers are not perfectly flat, head waves still travel along them Analysis methods: Best-fit straight line through the points provides an average layer thickness and velocity Model the data by creating a velocity model and calculating the arrival times: Forward modeling Trade-off between layer thickness and velocity variations Ambiguity!10 Physics and chemistry of the Earth’s interior – Seismic refraction Crustal structure of the Alps Fowler Fig 9.20 Reduced traveltime Pg PmP Pn crust mantle Physics and chemistry of the Earth’s interior – Seismic refraction Amplitudes reflected and transmitted The amplitude of the reflected, transmitted and converted phases can be calculated as a function of the incidence angle using Zoeppritz’s equations. Reflection and transmission coefficients for a specific impedance contrast 11 Physics and chemistry of the Earth’s interior – Seismic refraction Summary Controlled source seismology • Provides for high resolution studies (crustal and smaller scale) • Possible is non-tectonic region • Reflection and refraction seismic techniques Reflection and refraction at an interface • Snell’s Law allows calculation of ray trajectories • The ray parameter is constant along a ray • Incidence at the critical angle results in a head wave Refraction (Wide-angle) studies • Provide layer velocity and thickness – crustal structure