Geology 228 Applied Geophysics Lecture 4. Seismic Refraction (Reynolds, Ch. 4-6)

Transcription

1 Geology 8 Applied Geophysics Lecture 4 Seismic Refraction (Reynolds, Ch. 4-6)

2 Seismic Methods Some fundamentals of seismic waes One dimensional wae equation the solution of a plane wae in unbounded uniform medium amplitude, phase, frequency, wae number, wae length,... Huygens Principle and some simulations Waefront and ray: from physical wae to geometric wae Seismic refraction Field examples

3 Seismic Refraction Snell s law Incident angle, reflection angle, refraction angle Reflection coefficient, transmission coefficient Energy distribution Seismic refraction for a single horizontal layer Seismic refraction for multiple horizontal layers Seismic refraction for a single dipping layer Seismic refraction tomography Field examples

4 Wae energy is dissipating in the media. There are three major ways in energy dissipation, or attenuation. They are Geometry spreading (total energy conseration) Intrinsic absorption caused by material imperfection (conersion to other types) Diffraction caused by material heterogeneity (reflection, refraction, reerberation, etc.)

5 Seismic fundamentals Some fundamentals of seismic waes One dimensional wae equation Solution of a plane wae in unbounded uniform medium Amplitude, and phase Frequency, and period Wae number, and wae length

6 A simplified case for the wae equation is the plane wae propagating in direction, say the x-direction. In this case, the wae equation can be written as u x u t (3.) One solution for a plane wae propagating in an unbounded, uniform medium can be expressed as u u0 cos( ω t + kx) (3.) This plane wae can be iewed as the wae generated by a plane source occupying the entire yz-plane to generate wae propagation in the x-direction. In this equation, u 0 is the amplitude, ω is the angular frequency; k is called the wae number. We will show the relationship of k with respect to angular frequency ω by demonstrating Eqn (3.) does satisfy the -D wae equation (3.). Taking the secondary deriatie of u with respect to space, here the x-coordinate, is u x k u 0 cos( ωt + kx) and putting the second deriatie of u with respect to time on the right hand side of Eqn (3.) gies u ω u0 cos( ωt + kx) t comparing the last equation leads to ω k

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8 In time domain ω T πf f f f T ω π In space domain π k π λ λ k They are linked through the propagation elocity ω k λ T

9 A seismic wae field moie Uniform medium D point source impulse time function a rich frequency content

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12 Huygens Principle In a wae field, all points with the same phase construct a wae front; Huygens Principle: Each point on a particular wae front can be treated as a new source To illustrate this point let s consider the following case.

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15 More complicated case to show the relationship between waefront and ray 3 layer model 3>> 3:: 9:4:3

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19 Ray is the outward normal at each point of the waefront

20 Rays in a two-layer model: the elocity in the upper layer increases linearly from km/sec, oer a thickness of 0 km (gradient 0.5/km/sec/km). The elocity in the lower layer increases linearly from km/sec, oer a thickness of 4 km (gradient 0.5 km/sec/km).

21 Snell s law, Reflection coefficient, and Transmission coefficient

22 Refraction from multiple horizontal layers

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25 The refracted wae is the wae energy traels below the interface at the elocity on the second layer, but trael horizontally along the interface, then trael back to the geophone receier planted on the surface. The refracted wae can only be receied after the critical distance x crit. To learn what is the critical distance, we hae to know what is the critical angle i crit first. First we need introduce the Snell s law. sin i sin i

26 Snell s law sin i sin i At the critical incident angle, there is no transmitted energy radiated in the second layer, so the refraction angle is 90 degrees, so we hae sin i then sin( π / sin i crit )

27 So that we can define the critical angle i crit as sin i or i crit crit and the critical distance x crit is x crit h h [( tan i ( [( ( h ) crit ] h ) ) / ] / sin i cosi arcsin( crit crit )

28 When a plane wae impinging at a flat interface, both reflection and transmission occur. The quantitatie description of the reflection and transmission relies on the reflection coefficient and transmission coefficient. The Reflection Coefficient R and the Transmission Coefficient T are, respectiely, defined as R T A A A A reflect incident transm incident

29 It can be demonstrated that the coefficients R and T are associated with the combination of the acoustic impedance. Acoustic impedance is defined as the product of the density and the elocity, I.e., Z ρ. The reflection coefficient R in a general case is R ( Z ( Z / / Z Z ) ) + ( n ( n ) tan ) tan α α i i where n ( / ) and α i is the angle of incidence of the wae ray.

30 For normal incidence, the reflection coefficient is R Z Z for αi + Z Z 0 and the transmission coefficient is T ZZ for αi Z + Z 0

31 Recall that the energy of wae motion is proportional to the amplitude, so for the reflection energy coefficient we hae E R ( Z ( Z Z ) ) for α i + Z and the transmission energy coefficient is E 4Z Z ( Z + Z T for α i ) These relations are applicable for the case of the incidence angel less than 5 degrees. Apparently, we hae E R + E T 0 0

32 Seismic refraction Seismic refraction only consider the first arrials - so simple and easy to use The detection depth is about /4 to /0 of your geophone spread

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35 Seismic Refraction oscilloscope ASTM D 5777 Note: V p < V p Determine depth to rock layer, z R Source (Plate) t t Vertical Geophones t3 t4 z R x x x3 x4 Soil: V p Rock: V p

36 t x Xcross A piece of real data

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38 The trael time to each geophone for the direct wae in the first layer is simply t direct x

39 The trael time for the reflected wae for a -layer model can be deried as follows. Start with the ray path and the knowledge of Snell s law we hae 4 4 ) ( ) ( ) ( h x t h x t h x t reflect reflect reflect + + +

40 The second equation in the last slide can be reformatted as ) ( + h x h t h x t reflect reflect The second equation is in a standard format for expressing a hyperbola cure. t x

41 Another important concept is the cross-oer distance Xcross. At Xcross, the refracted wae starts to take oer to be the first arrie at a point.

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43 The ray path and the trael time for the refracted wae for a -layer model can be deried as SB BC t refract + + CR

44 At the crossoer distance x cross the trael times to the point are the same for the direct wae and the refracted wae, so we hae / / / ) ( )] )( [( ) ( ) ( x h h h x h x x h x x t t cross cross cross cross cross cross refract direct + + +

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46 Seismic Refraction Trael Time (seconds) z x c Horizontal Soil Layer oer Rock V V c p p V p + V V p 350 m/s p x c 5.0 m V p 4880 m/s Depth to Rock: z c 5.65 m t alues x alues Distance From Source (meters)

47 Trael times for the direct, reflected, and refracted waes for a -layer model 4 h x t h x t x t refract reflect direct + +

48 n n n n n n n k n k k k n n n k n k k k n T x t h T h h T ) ( ) ( ) ( cos ] cos [ cos θ θ θ For multiple layers, the thickness of each layer for n> can be calculated from

49 For example, for the first 3 layers we hae / cos )] cos cos ( [ ] cos cos cos [ cos ] cos [ ] cos cos [ ) ( cos θ θ θ θ θ θ θ θ θ θ θ h h T h h h h T h T h h h T T h h T

50 Procedure to get the stratigraphic structure from the refraction x-t plot :, from the slope get the elocity in each layer;, from the elocity to get the critical angle of the k-th interface sinθ k ( n+ ) k n 3, get the interception time T n ; 4, get the thickness h n.

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52 True elocity in the second layer: ( + u d )

53 Homework Exercise: refraction oer a layer model Xs (m) Ys (m) Xr (m) Yr (m) T (sec) Time (sec) Seismic Trael Time (sec)

54 Seismic Refraction Sureys Measure: propagation of elastic wae through layers of the Earth Results: depth structure and elocities of elastic waes Equipment: 48-channel portable StrataView Distance (m) Shots Geophones

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59 Intercept Time Method Procedure: - First arrials pick up. - Plot trael time ersus distance - Calculate depths to layer interfaces: Z Z T T V V + V Z V V 3 V V 3 V V V V 3 3 V TRAVEL TIME (ms) T T /V /V /V3 Xc Xc DISTANCE (m)

60 Delay Time Method SIPwin Program First arrials pick up Layer assignment Create depth-elocity model

61 Intercept Time Method X-T plot of EE' Trael Time (ms) Offset (m) Trael time- Distance plot of line EE (top) and DD (bottom) X-T plot of DD' Trael time(ms) Offset (m)

62 Depth(m) m/s 963 m/s 495 m/s Distance (m)

63 DEPTH(m) m/s 600 m/s m/s DISTANCE (m)

64 Seismic Refraction Results Profile Parallel to the Tennis Courts

65 The Project In central Japan, a 300m long mountain tunnel was planned to be built in a Tertiary mudstone area. The rock condition was found to be quite different from the result of prior inestigation, and the cutting face collapsed after construction was started. A High Resolution Seismic Refraction analysis is applied to ealuate the rock condition of a non-excaated section in detail. The principal objectie of the HRSR analysis was to detect the distribution and extent of weathered rock at the nonexcaated section in order to modify the tunnel design and ensure construction safety. Result and Interpretation The existing data used in the HRSR analysis were collected at receier interals of 0m and maximum exploration depth of 50m. The figure shows the final elocity model and construction record. It can be seen that the collapsed zones correspond to the lower elocity areas (the green zones in the figure) relatie to the surrounding area. This result of the HRSR analysis allowed precise prediction of the weathered rock zone and was ery useful for modifying the tunnel design and ensuring construction safety at the non-excaated section.

66 Example of Geotechnical Applications

67 Seismic refraction tomography example: Locating DNAPL Traps in a Complex Shallow Aquifer, Hill Air force Base, Utah Project of Dept of Geophysics, Rice Uniersity Reference: Zelt, C. A., "Lateral elocity resolution from 3-D seismic refraction data," Geophys. J. Int., 35 (998): /emsp000/605.html

68 Seismic refraction tomography example: Locating DNAPL Traps in a Complex Shallow Aquifer, Hill Air force Base, Utah Project of Dept of Geophysics, Rice Uniersity Reference: Zelt, C. A., "Lateral elocity resolution from 3-D seismic refraction data," Geophys. J. Int., 35 (998): /emsp000/605.html

69 Map of the depth to the confining clay layer that underlies the area is based on geologic information collected at the site from monitoring wells and soil tests. Each data point is indicated with a blue dot. The map was constructed by interpolation between the data points. DNAPLs collect in the deep depression running through the center of the map. This area is the focus of the seismic imaging effort. The location of the three profiles from the -D surey are shown. The pipe is part of the remediation facilities.

70 First-arrial picks from the Line slide hammer data plotted as a function of receier position. There are 473 picks from 6 shots. The picks from 3 shots hae been colored to highlight the time-offset characteristics of the data; the position of the corresponding shots is indicated by the large colored circles on the distance axis.

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72 Top: Final -D elocity model for the Line sledge hammer data. Bottom: Raypaths through the final model for the Line sledge hammer data.

73 Final -D elocity model for the Line combined rifle and shotgun data. Contour interal is 00 m/s; the 500, 000 and 500 m/s black contours are labeled. The known water table depth in the channel is indicated by the brown arrows. The pink dot indicates the depth (3. m) to the clay aquiclude from a well at 5 m distance.

74 Relatie difference between the final model for the slide hammer data and the -D starting model. The approximate position of the channel inferred from the reflection images is indicated aboe, and the depth to the water table is also indicated. There is a good correlation between the low-elocity region in the tomographic model and the extent of the channel and its depth. Note the large elocity perturbations from the starting model, up to 65% in magnitude.