Geology 56606660 Applied Geophysics 7 Feb 2018 Last

Geology 5660/6660 Applied Geophysics 7 Feb 2018 Last Time: Seismic Reflection Travel-Time Cont’d • Discovered travel-time eqns for >1 layer get messy (!) • x 2 – t 2 Method: On a plot of t 2 vs x 2, for a single layer: • For dipping layer: Mean slope is ; limb separation • Dix Equations for multiple layers: is an approximation to the true physics that neglects a t-to-the-first-power dependence… © A. R. Lowry 2018 For Fri 9 Feb: Burger 167 -199 (§ 4. 2 -4. 3)

Geology 5660/6660 Applied Geophysics • Normal Moveout (NMO) revisited: For single layer case: First-order binomial series approximation: (& second-order): (Useful to write travel-time in terms of only V & observed t 0)

NMO can also be applied to multiple layers using the Dix equation approximation for Vrms: V 1 h 1 Recall our dipping layer problem: We can write

Using the same approach used earlier for a horizontal layer, can be expanded and truncated as Recall the x 2 – t 2 plot for a dipping layer: Could average to get a line with slope 1/V 12, and the difference between the line and the limbs was related to the dip angle: down-dip limb t 2 mean slope up-dip limb x 2

Binomial series approximation: mean down-dip limb TNMO up-dip limb x We can similarly use the difference between up-dip & down-dip NMO to estimate dip via:

Some practical considerations (a reminder!): For x 2 – t 2 methods & Dix Equations: • Dix equation approximation of Vrms is most valid for small-offset (near-vertical) rays; validity of approximations decreases with distance For reflection seismic in general: • NMO approximations in terms of t 0 require x << 2 h 1 (i. e. , small-offset, near-vertical rays) • Reflections from shallow interfaces will be overwhelmed by other arrivals at small-offsets

Burger refers to optimal window at distances beyond interference from low-V waves, but also must get beyond direct & refracted wave interference to observe confidently (Industry seismic) “Optimal window”

Practical considerations cont’d: Multiples are waves that travel the two-way travel path le tip ul M Mu a ltip ry le Pr im Pri ma ry between two interfaces more than once: Recognizable as having: • About twice the travel-time of the primary • The same apparent velocity but twice thickness from x 2 – t 2 analysis • Less move-out and lower amplitude than the primary

Diffractions: Recall diffractions in the refraction method: V 1 V 2 Observationally, impossible to distinguish diffracted arrival associated with a step from smooth thickness change over one wavelength (10– 20 m for 100 Hz)

Diffractions: V 1 h 1 x xg rs h 2 The diffraction travel time is time ts = rs/V 1 from the source to the step edge plus time td from step to geophone at a distance xg from the step

twtt Worth noting: In migration of seismic data, we “migrate” travel-times to what they would be for a zero-offset source by correcting for NMO. After correcting, (Smile!) (layer with offset) (layer with no offset) diffraction

In typical seismic images we plot two-way travel-time increasing downward (to simulate depth) so “smiles” are flipped upside-down to form “frowns” So these can be a diagnostic tool to help recognize faults, salt diapirs and other lateral changes in velocity…