Geology 56606660 Applied Geophysics 2 Feb 2018 Last

Geology 5660/6660 Applied Geophysics 2 Feb 2018 Last time: Refraction in Non-Ideal Media: • Limitations of the Refraction Method: Do not get returns from low velocity layers Can alias or miss entirely thin layers Deeper layer thicknesses are overestimated for the first case; underestimated for the second • Velocity changes within layers can be distinguished by similar slopes (forward & reversed) over same locales • Change in thickness change in intercept time • Single step change in thickness h: In t-x plot, similar slopes before & after shift in intercept (with opposite sign forward vs reversed) Read for Mon 5 Feb: Burger 149 -167 (§ 4 -4. 1) © A. R. Lowry 2018

Geology 5660/6660 Applied Geophysics Last time cont’d: Refraction Plus-Minus: • Plus-Minus Method for arbitrarily changing h: where m– is slope of a plot of t 1 i–t 2 i vs xi for SP 1, 2 and geophones i

The Reflection Seismic Method: Consider a single horizontal layer over a half-space, with layer thickness h 1 and velocity V 1: x/2 V 1 h 1 The travel-time for a reflected wave to a geophone at a distance x from the shot is given by:

The Reflection Seismic Method: The travel-time for a reflection corresponds to the equation of a hyperbola. If we re-write: Hyperbola: intercept = b; asymptote m = b/a water shale gas sand shale This implies an intercept at 2 h 1/V 1 and asymptotes with slope ± 1/V 1 ±x/V 1

Some quick observations: h 1 = 15 m V 1 = 1500 m/s h 1 = 45 m V 1 = 1500 m/s Changing only depth of the layer changes intercept of the hyperbola but not the slope or intercept of the asymptotes, so a reflection from a shallower interface appears more “pointy”

h 1 = 45 m V 1 = 1500 m/s h 1 = 45 m V 1 = 4000 m/s Changing velocity of the layer changes intercept of the hyperbola and the slope of the asymptotes, so a reflection in a layer with higher velocity arrives sooner and appears more “flat”

Normal Move-Out (NMO) is the difference in reflection travel times at distance x relative to the travel time at the intercept (x = 0), i. e. , NMO emphasizes changes in curvature of the hyperbola (i. e. , it is greater for shallower depth of reflection and for lower velocity of the layer). The reason we accord special status to NMO is that we will need to correct for move-out if we want to use the reflection energy to image the subsurface as a seismic section…

Distance water Two-Way Travel Time shale gas sand shale

Shifting the seismic reflection amplitude to where it would be (in two-way travel-time) for zero-offset produces an image… Note that this approach is VERY different from the model of velocity structure we generate from the refraction method!

Reflection from a second layer interface over half-space: x/2 V 1 V 2 h 1 h 2 Can derive using Snell’s law but easier to consider that: • For x = 0, intercept of hyperbola • For x , asymptotic to the layer 2 refraction

Equation for the hyperbola then is After some algebra we have And you might see where this could start to get complicated for 3, 4, … layers This is part of why industry seismic reflection processing historically did not go after full seismic velocity analysis but instead took shortcuts to imaging of structures…

A Dipping Reflector: V 1 h 1 Geometrically, this is equivalent to rotating the axis of the reflector by the dip angle . This rotates the hyperbola on the travel-time curve by = tan-1(– 2 h 1 sin ) and has equation

Example: V 1 = 1500, h = 45 m, = 8° Helpful Hint: Reflect does not model dipping layers, but the Table 4 -6 Excel spreadsheet does!