Spring GSC499 2008 Introduction to Seismology, Earthquakes and Earth Structure
Todays Class Today
Lecture: Scattering and Migration in Seismic Reflection
How do we correct for scattered and diffracted arrivals in seismic sections?
Reading: Chapter 7.3 and 7.4 Wednesday Morning: Reflection Seismology Examples Wednesday Afternoon Exam 1
Will cover all lecture and returned lab material Will start at 3 pm, maximum time: 4 hours Bring ruler, compass, pencils, calculator, etc.
04/28/08
Cal Poly Pomona
GSC499 Spring 2008 Introduction to Seismology, Earthquakes and Earth Structure
Diffracted Arrivals
Complicated structures will produced scattered and diffracted arrivals Accurate interpretation needs more sophisticated theory Velocity perturbations can be thought of as generating secondary seismic sources in response to the incident wavefield
04/28/08 Cal Poly Pomona
GSC499 Spring 2008 Introduction to Seismology, Earthquakes and Earth Structure
Huygens Principle Huygen
Consider a plane wave front: it can be thought to propagate through the constructive interference of secondary wavelets
Explains behavior of waves when passing through narrow opening
04/28/08 Cal Poly Pomona
1
GSC499 Spring 2008 Introduction to Seismology, Earthquakes and Earth Structure
Diffraction
= bending of the ray paths at the edges of the gap Degree of diffraction depends on the wavelength of the waves relative to the size of the opening
04/28/08 Cal Poly Pomona
GSC499 Spring 2008 Introduction to Seismology, Earthquakes and Earth Structure
The Exploding Reflector Reflector
Imagine that each point on a reflector generates a secondary source in response to the incident wavefield. First consider a single point scatterer in a zero-offset section. Minimum travel time is given by:
t0 = 2h/v
04/28/08 Cal Poly Pomona
GSC499 Spring 2008 Introduction to Seismology, Earthquakes and Earth Structure
The Exploding Reflector Reflector
More generally, the travel time as a function of horizontal distance, t(x), is given by:
t(x) = 2 SQRT(x 2+h2)/v
After re-arranging:
t2/t 02 - 4x 2/(v 2t02) = 1 Hyperbola with apex directly above the scattering point
04/28/08 Cal Poly Pomona
2
GSC499 Spring 2008 Introduction to Seismology, Earthquakes and Earth Structure
Comparison with NMO Hyperbola
Diffraction hyperbola
Is steeper Results from ray different geometry
NMO hyperbola: travel time for a reflection off a horizontal layer as a function of source-receiver distance Diffraction hyperbola: travel time as a function away from a point scatterer at depth for zero-offset data
04/28/08
Cal Poly Pomona
GSC499 Spring 2008 Introduction to Seismology, Earthquakes and Earth Structure
Artifacts
Consider a horizontal reflector, made up of a series of point scatterers
Each generates a diffraction hyperbola in a zero-offset section Huygens principle: sum coherently only at the main reflection: later arrivals cancel out However, if the reflector vanishes, its endpoint will produce a diffracted arrival that will create an artifact
04/28/08
Cal Poly Pomona
GSC499 Spring 2008 Introduction to Seismology, Earthquakes and Earth Structure
Migration
= technique for removing these artifacts from reflection data Simplest: diffraction summation migration
Assume that each point in a zero-offset section is the apex of a hypothetical diffraction hyperbola Replace value of time series at that point by average of data taken at pints along the hyperbola
04/28/08 Cal Poly Pomona
3
GSC499 Spring 2008 Introduction to Seismology, Earthquakes and Earth Structure
Migration
collapses diffraction artifacts into their true locations Can produce dramatic improvement in image quality Can be implement before CMP stacking
Pre-stack migrati...