Refraction Seismology. Chapter :: 6

Transcription

1 Refraction Seismology Chapter :: 6

2 Snell s Law & Critical Refraction Because seismic sources radiate waes in all directions Some ray must hit interface at exactly the critical angle, i c This critically oriented ray will then trael along the interface between the two layers If more oblique than critical, all wae energy is reflected The reflected energy is useful too! E.g. Chapter 7 sin i sin i sin i c sin 2 2 sin 90 i c 2 2 i c arcsin 2

3 Critical Refraction and Wae Fronts When a ray meets a new layer at the critical angle The ray traels along the interface What layer is it in? Rays, aren t real, so consider the wae fronts Wae fronts trael in both layers Wae front in top continues on the same trajectory Wae front in Bottom has to be perpendicular to the ray But the layers hae different elocities This sets up waelets and head waes

4 Huygens s Principle Recall that rays are not real They are just an easy way to understand and quantify waes Wae fronts are what is really happening But what causes wae fronts? Huygens s waelets explains Each point along a material is acts like a point source of waes Like a pebble dropped into water

5 Huygens s Waelets Huygens (a 7 th century Dutch physicist) realized that: When any particle oscillates it is a tiny source of waes So, eery point on a wae front acts as a small source that generates waes The waes hae circular (spherical) wae fronts and are called waelets Waelets constructiely interact (reinforcement) to produce the wae front Has important implications for diffraction and critical refraction Final Wae Front New Wae Front Waelets Trough Planar wae front

6 Waelets and Diffraction If waelets didn t occur, we wouldn t be able to hear around corners. Light doesn t trael around corners ery well because of its ery high frequency If only there were waelets then I could hear you What Up Dr. Kate??

7 Waelets and Diffraction Because of waelets, a wae front that encounters an obstacle: Will trael through the open space The wae front after the barrier diffracts, or bends into an area that is predicted to be a shadow by ray theory. But what about critical refraction?? (jaa animation) Final Wae Front Wasuuuup! Waelets New Wae Front What Up Dr. Kate??

8 Waelets and Head Waes The wae front just aboe the interface produces a continual stream of critically refracted rays The wae front just below the interface does the same These stream of critically refracted rays form waelets The waelets combine to form head waes The head waes propagate up to the surface and can be recorded. The recorded rays are called the refracted rays

9 Potential Paths in a Refraction Surey When doing a seismic refraction surey, a recorded ray can come from three main paths The direct ray The reflected ray The refracted ray Because these rays trael different distances and at different speeds, they arrie at different times The direct ray and the refracted ray arrie in different order depending on distance from source and the elocity structure Shot Point (i.e. the Source) Direct Ray Receier Layer Layer 2 i c i c 2

10 The Time-Distance (t-x) Diagram Think about: What would a fast elocity look like on this plot? Why is direct ray a straight line? Why must the direct ray plot start at the origin (0,0)? Why is refracted ray straight line? Why does refracted ray not start at origin? Why does reflected ray start at origin? Why is reflected ray asymptotic with direct ray?

11 Time (t) The Direct Ray The Direct Ray Arrial Time: Simply a linear function of the seismic elocity and the shot point to receier distance t direct x Shot Point Direct Ray Distance (x) Receier Layer Layer 2 2

12 Time (t) The Reflected Ray The Reflected Ray Arrial Time: is neer a first arrial Plots as a cured path on t-x diagram Asymptotic with direct ray Y-intercept (time) gies thickness Why do we not use this to estimate layer thickness? 2h Shot Point Distance (x) Receier Layer Layer 2 2

13 Time (t) The Refracted Ray The Refracted Ray Arrial Time: t x 2 2h Plots as a linear path on t-x diagram Part traels in upper layer (constant) Part traels in lower layer (function of x) Only arries after critical distance critical distance cross oer distance Is first arrial only after cross oer distance Traels long enough in the faster layer 2h Distance (x) i c i c i c i c Layer Layer 2 2

14 Making a t-x Diagram Refracted Ray Arrial Time, t t x 2 2h or t xsin i c 2h cosi c Y-intercept to find thickness, h 2 = /slope = /slope

15 Refraction What is it Good For? Seismic refraction sureys reeal two main pieces of information Velocity structure Used to infer rock type Depth to interface Lithology change Water table

16 Seismic refraction can detect multiple layers The elocities are easily found from the slopes on the t-x diagram Multiple Layers

17 Multiple Layers: Refracted Ray Trael Times Seismic refraction can detect multiple layers Each subsequent refracted ray has a different trael time equation st Refracted Ray (top of layer 2) t = x 2 + 2h nd Refracted Ray (top of layer 3) t 2 = x 3 + 2h h rd Refracted Ray (top of layer 4) t 3 = x 4 + 2h h h And so on for subsequent layers

18 The layer thicknesses are not as easy to find Recall layer thickness: Multiple Layers t = x 2 + 2h Use y-intercept of best fit line t int = 2h Then sole for h t 2 = x 3 + 2h 2 nd Refracted Ray Trael Time Equation h Use y-intercept of best fit line t int2 = 2h h Then sole for h 2 But BEWARE: h, h2, are layer thicknesses, not depth to interfaces. So, depth to bottom of layer 2 (top of layer 3) = h + h2

19 Caeats of Refraction Only works if each successie layer has increasing elocity Cannot detect a low elocity layer May not detect thin layers Requires multiple (surey) lines Make certain interfaces are horizontal Determine actual dip direction not just apparent dip

20 A dipping interface produces a pattern that looks just like a horizontal interface! Velocities are called apparent elocities What do we do? Dipping Interfaces What if the critically refracted interface is not horizontal? In this case, elocity of lower layer is underestimated

21 Shoot lines forward and reersed If dip is small (< 5 o ) you can take aerage slope The intercepts will be different at both ends Implies different thickness Dipping Interfaces To determine if interfaces are dipping Beware: the calculated thicknesses will be perpendicular to the interface, not ertical

22 If you shoot down-dip Slopes on t-x diagram are too steep Underestimates elocity May underestimate layer thickness Conerse is true if you shoot up-dip In both cases the calculated direct ray elocity is the same. The intercepts t int will also be different at both ends of surey Dipping Interfaces

23 The Hidden Layer There are two cases where a seismic interface will not be reealed by a refraction surey. The Hidden Layer (book calls it Hidden Layer Proper ) The Low Velocity Layer This one is straightforward, so we will look at it first.

24 If a layer has a lower elocity than the one aboe There can be no critical refraction The Low Velocity Layer The refracted rays are bent towards the normal There will be no refracted segment on the t-x diagram The t-x diagram to the right will be interpreted as Two layers Depth to layer 3 and Thickness of layer will be exaggerated

25 Causes: Sand below clay The Low Velocity Layer Sedimentary rock below igneous rock (sometimes) sandstone below limestone How Can you Know? Consult geologic data! Boreholes / Logs Geologic sections Geologic maps

26 The Hidden Layer Recall that the refracted ray eentually oertakes the direct ray (cross oer distance). The second refracted ray may oertake the direct ray first if: The second layer is thin The third layer has a much faster elocity Show Maple Animations

27 Geophone Spacing / Resolution Often near surface layers hae ery low elocities E.g. soil, subsoil, weathered top layers of rock These layers are likely of little interest But due to low elocities, time spent in them may be significant To correctly interpret data these layers must be detected Decrease geophone spacing near source This problem is an example of?

28 Undulating Interfaces Undulating interfaces produce non-linear t-x diagrams There are techniques that can deal with this delay times & plus minus method We won t coer these techniques

29 Detecting Offsets Offsets are detected as discontinuities in the t-x diagram Offset because the interface is deeper and D E receies no refracted rays.

30 Fan Shooting Discontinuous targets can be mapped using radial transects: called Fan Shooting A form of seismic tomography

31 Ray Tracing All seismic refraction techniques discussed thus far are inerse methods One can also fit seismic data to forward models using Snell s law, geometry, and a computer Initial structure is guessed and then the computer uses statistical ersions of guess and check to fit the data. Model generates synthetic seismograms, which are compared to the real seismograms

32 Surey Types The simplest (and cheapest) type of surey is called a hammer seismic surey A sledgehammer is whacked into a steel plate Impact switch tells time=0 First arrials are read digitally or inferred from seismogram Because swinging a hammer is free, only one geophone is needed More can be used, but single geophones must be along a linear transect

33 Surey Types The maximum workable distance depends on: The sensitiity of the system The strength of the sledgehammer whacks The amount of noise Wind shakes trees, etc Cars, footsteps, HVAC, traffic, etc Sureys may be done at night to minimize noise

34 Surey Types Often the signal to noise ratio is ery poor: Stacking is often used to help delineate first arrials General rule of thumb: Geophone array should be about 0x the depth to interface 00 meters is the typical upper limit on length of hammer seismic transect So hammer seismics are best for shallow interfaces (< 0 m)

35 Explosion seismics Other Surey Types Offers a much stronger signal Can detect deeper features Often inoles water explosions (much cheaper) Geophones / Seismometers are often linked wirelessly (RF / radio waes) Marine Sureys Sometimes use explosies, compressed air, high oltage charges, or many other types. Usually use hydrophones Respond to pressure changes (p-waes) Sureying is often done while the ship is moing, so ery long transects can be done at a lower cost