Refraction seismic Method

Transcription

1 Refraction seismic Method Field techniques Inversion for refractor velocity, depth, and dip Delay time Interpretation Basic-formula methods Delay-time methods Wavefront reconstruction methods Reading: Sheriff and Geldart, Chapter 11

2 Field techniques In-line shooting May shoot segments (e.g., C-D, D-E, E-F, etc. below) in order to economize Depending on the target, longer or shorter profiles, with or without recording at shorter offsets

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 and a (refractor velocity and dip). Different intercept times. T R determine h d and h u (interface depths). t p u = sin i c p d = sin i c 2z u cosi c 2z d cosi c S slope= p 1 = 1 R x

4 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 d = sini c Up-dip: (faster). From the two reversed apparent velocities, i c and a are determined: i c =sin V 1 1, V d V u = sin i c i c =sin 1 V u. i c = 1 2 sin 1 V d sin 1 V u, = 1 2 sin 1 V d sin 1 V u. From i c, the refractor velocity is: = sini c.

5 Determination of Refractor Depth From the intercept times, t d and t u, refractor depth is determined: h d = t d 2 cosi c, h u = t u 2cosi c. S x R h d i c A B i c h u a (dip) >

6 Delay time (the basis for most refraction interpretation techniques) 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/. t S Delay = SA BA = h s Note that = /sini c cosi c h s tan i c = h s cosi c 1 sin 2 i c = h s cosi c. Thus, the source and receiver delay times are: t S, R Delay = h s, r cosi c. S h/cosi c and t SR =t S Delay t R Delay SR. R x h s B i c X A htani c h r >

7 Basic-formula interpretation (The ABC method) New! Uses reversed shots Combine the refraction times recorded along A-C, B-C, and A-B: A C B t AC t CB t AB 2t DelayC = 2h C cosi c Therefore: h C 2 cosi c t AC t CB t AB. Note the typical time-to-depth conversion factor: cosi c = 1 sin 2 i c = 2 2.

8 Delay-time methods Barry's method New! Uses shots recorded in the same direction Note that the ABC formula applies to the reduced (or intercept ) times, with any value of reduction velocity V R assumed: t int =t x V R t int AC t int CB t int AB 2t Delay C = 2h cosi C c S 1 S 2 G 1 G 2 A B C Thus the shot delay at C is: t Delay C 1 t int 2 CB t AC int int t AB And geophone delay at B: t Delay( B) =t int CB t Delay (C ) 1 ( t int 2 CB t int int AC + t AB )

9 Delay-time methods Barry's method New! 1) Plot the time-reduced travel times. 2) Calculate the geophone delay times. 3) Plot the delay times at the offset geophone positions. 4) Adjust until the lines from reversed profiles are parallel.

10 Delay-time methods Wyrobek's method New! 1) Plot the time-reduced travel times. 2) Calculate the geophone delay times. 3) Plot the delay times at the offset geophone positions. 4) Adjust until the lines from reversed profiles are parallel. A series of unreversed profiles is used For each geophone the various shots form an equivalent of a reversed profile. The delay times are combined into a composite delay-time curve With properly adjusted, the composite delay times match the half-intercept times

11 Plus-Minus Method (Hagedoorn) Assume that we have recorded two headwaves in the opposite directions, and have estimated the velocity of the overburden,. How can we map the refracting interface? S 1 D(x) S 2 T R t t S1 D t S2 D S 1 D S 2 x Solution: Profile S 1 S 2 : t S 1 D = x t S 1 t D ; Profile S 2 S 1 : t =S 1 S 2 x S 2 D t V S 2 t D. 2 Form PLUS travel-time: t PLUS =t S1 D t S 2 D = S 1 S 2 t S1 t S 2 2t D =t S 1 S 2 2t D. Hence: t D = 1 2 t PLUS t S1 S 2. To determine i c (and depth), still need to find.

12 Plus-Minus Method (Continued) To determine : Form MINUS travel-time: this is a constant! t MINUS =t S 1 D t S 2 D= 2x S 1 S 2 t s1 t s2. Hence: slope[t MINUS x]= 2. The slope is usually estimated by using the Least Squares method. Drawback of this method averaging over the precritical region. S 1 D(x) S 2 T R t t S1 D t S2 D S 1 D S 2 x

13 Generalized Reciprocal Method (GRM) 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 velocity analysis function; 2) Corresponding to the most detail of the refractor. XY t S 1 D S 2 t S2 D T R t S1 D The velocity analysis function: S 1 D XY S 2 x t V = 1 2 t S 1 D t S 2 D t S 1 S 2, should be linear, slope = 1/ ; The time-depth function: t D = 1 2 t S 1 Dt S 2 D t S 1 S 2 XY. this is related to the desired image: h D = t D 2 2

14 Wavefront reconstruction methods New! Head-wave wavefronts can be propagated back into the subsurface...

15 Wavefront reconstruction methods New!... and combined to form an image of the refractor: Refractor is the locus of (x,z) points such that: t Forward x, zt Reversed x, z=t Reciprocal Note the similarity with the PLUS- MINUS method! Head wave from source A Head wave from source B Line on which t A + t B = const