seismic refraction method lecture 21

$: Seismic refraction method lecture 21$
Seismic Refraction Method

Overview

Prepared byDr. Amin Khalil

Overview

Types and Properties of seismic waves

Seismic waves at an interface

Basic laws for seismic refraction

T-X graph (travel time distance curve

Interpretation & Modeling

TYPES AND PROPERTIES OF SEISMIC WAVES• There are two types of elastic body wave in a solid:– P-Waves: compression waves– S-waves: shear waves

• P-waves are the faster and are usually the ones studied in simple seismic methods.

• Other waves (surface waves) also exist but are much slower. It is these waves that do the damage in earthquakes.

• We will focus our attention on P-waves from now on.

Compressional (“P”) WaveIdentical to sound wave – particle motion

is parallel to propagation direction.

Animation courtesy Larry Braile, Purdue University

Shear (“S”) WaveParticle motion is perpendicularto propagation direction.

Animation courtesy Larry Braile, Purdue University

Velocity of Seismic WavesDepends on density elastic moduli

34

K

Vp

Vs

where K = bulk modulus, = shear modulus, and = density.

Velocity of Seismic Waves

Bulk modulus = resistance to compression = incompressibility

Shear modulus = resistance to shear = rigidity The less compressible a material is, the greater its p-wave velocity, i.e., sound travels about four times faster in water than in air. The more resistant a material is to shear, the greater its shear wave velocity.

RIGIDITY

It a measure of how the medium resist the change in shape. Hence, rigidity in fluids and fluid-like media is zero. This mean that no shear wave (S-waves) are travelling in fluids.

This property help in the identification that the outer core is liquid like shell.

Surface waves in an elastic solid

Overview







What happen when seismic waves encounters an interface?!!!

We start by defining some important phenomena:

1- Seismic wave propagation in a media is dependent on elastic impedance Z. The elastic impedance Z is defined by:

Z= vWhere:

densityv= seismic velocity

At an interface

Seismic waves exhibit number of actions named collectively as energy partition at an interface. The seismic waves are reflected, refracted and converted from P to S and from S to P. The reflection is governed by the reflection coefficient which represent the percentage of the energy that will be reflected.

Energy Partition

21

12

zzzzR

REFLECTION Coefficient is defined by:

Where Z1 and Z2 are the impedances for the first and second layer respectivley.

Overview






Basic laws:

Snell Law

Reciprocity law

Snell’ law

This law control the refraction of seismic energy at an interface:

2

1

2

1

)sin()sin(VV

ii

Where i1 and i2 are the incident and refracted angles and V1 and V2 are velocities of the first layer and second layer respectively.

Primarily, refraction method depends on the hypothesis that velocity increases with depth. This is because refracted waves to be recorded by an array of geophones on the surface should be critically refracted, i.e. The refraction angle be 90o , in this case the refracted energy propagate parallel to interface with the speed of the faster second layer. This type of propagation is called head waves. Head waves itself acts as seismic rays incident at the interface with 90o angle and refraction back to the surface is then taking place(see fig.)

source geophone

V1

V2

ic

ic

Ic is the angle of critical refraction and is given by:

Ic =sin-1 (V1 /V2 )

Snell’s LawIf V2>V1, then as i increases, r increases faster

Principal of Reciprocity

• The travel time of seismic energy between two points is independent of the direction traveled, i.e., interchanging the source and the geophone will not affect the seismic travel time between the two.

END

seismic refraction method lecture 21

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