Introduction to Geophysics

Ali Onceloncel@kfupm.edu.

saDepartment of Earth SciencesKFUPM

Seismic Exploration: Fundamentals 1

V = k + ( )

p4/3

1. Nafe-Drake Curves suggesting that compressional wave velocity and density are directly proportional . The below equation:

Implies that P-wave velocity is inversely proportional

to density, Explain the paradox.

Homework, Due to Wednesday

Figure 3.10 of Lillie, 1999, modified f rom Birch, 1960Figure 3.10 of Lillie, 1999, modified f rom Birch, 1960

Sediments and sedimentary rock

I gneous and metamorphic rock

Homework due to Wednesday

1. Using the information in the below figures, Explain the anomalous positions of Vp and Vs for ice.

Previous Lecture

Elastic Coefficients and Seismic WavesBirc's LawNafe-Drake Curve Factors affecting P-wave and S-wave velocity Seismic velocities for Geological Materials Amplitude Changes of Particle Motions Wavefronts and RayPaths Seismic Trace Seismic Wave Types

Reminder: Seismic Velocity in a homogeneous medium

V=(appropriate elastic modulus/density)1/2

What is relationship of rock density to seismic velocity?

Inversely proportional to the square root of the density

V = = =k + ( ) + 2

p4/3

V = =s

From Tom Boyd’s WWW Site - http://talus.mines.edu/fs_home/tboyd/GP311/introgp.shtml

Elastic Moduli

= k - =2 σ E3 ( 1 + σ ) ( 1 - 2 σ )

Where Shear Modules Lame’s lambda constant E= Young’s module ρ= mass density σ = Poisson’s ratio

k = 2 2

Bulk Module is k

σ υ

Reminder: k and

Bulk Moduluswhere = dilatation = V/V and P = pressure

=k= (P/) Ratio of increase in pressure to associated volume change

shear stress = (F /A)

=shear stressshear strain

shear modulusshear strain = (l /L)

Force per unit area to change the shape of the material

Reminder: Poisson’s Ratio

Ratio Vp and Vs depends on Poisson ratio:

where

Poisson’s ratio varies from 0 to ½. Poisson’s ratio has the value ½ for fluids

LLxx =

WWyy =

σ= - (yy / xx)

Reminder: Seismic Velocities (P-wave)

Rock Velocities (m/sec)

pp. 18-19 of Berger

Reminder: Influences on Rock Velocities

• In situ versus lab measurements• Frequency differences• Confining pressure• Microcracks• Porosity• Lithology• Fluids – dry, wet• Degree of compaction

•……………

Huygen’s Principle

Fermat’s Principle

pp. 20 of Burger’s book.

•Travel time graph. The seismic traces are plotted according to the distance (X) from the source to each receiver. The elapsed time after the source is fired is the travel time (T).

Travel-Time Graph

T=X/VX distance from source to the receiver,

T total time from the source to the receiver

V seismic velocity of the P, S, or R arrival.

• Initial wave fronts for P, S and R waves, propagating across several receivers at increasing distance from the source.

Estimates of Seismic Velocity

•B) The slope of the travel time for each of the P,S, and R arrivals (see earlier figure) is the inverse of velocity.

A) The slope of line for each arrival is the first derivative (dT/dX).

A) A compressional wave, incident upon an interface at an oblique angle, is split into four phases: P and S waves reflected back into the original medium; P and S waves refracted into other medium.

Reflected/Refracted Waves

Model CalculationSimple, Horizontal Two Layers

Direct Wave?

Selected ray path (a) and travel-time curve 9b) for direct wave. The slope, or first derivative, is the reciprocal of the velocity (V1).

Direct WaveXV

tdirect

1

1

Model CalculationSimple, Horizontal Two Layers

Reflected Wave?

Model CalculationSimple, Horizontal Two Layers

Head Wave or Critically Refracted?

All Three Arrivals

Ray paths for direct, reflected, and critically refracted waves, arriving at receiver a distance (X) from the source. The interface separating velocity (V1) from velocity (V2) material is a distance (h) below the surface.

Ray paths

Snell’s Law- Critically Refracted Arrival

For a wave traveling from material of velocity V1 into velocity V2 material, ray paths are refracted according to Snell’s law.

i1 = angle of incidence

i2= angle of refraction

•Wave fronts are distorted from perfect spheres as energy transmitted into material of different velocity. Ray paths thus bend (“refract”) across an interface where velocity changes.

The angles for incident and refracted are measured from a line drawn perpendicular to the interface between the two layers.

Seismic Refraction

Behavior of Refracted Ray on Velocity Changes