Introduction to Geophysics

Ali Onceloncel@kfupm.edu.

saDepartment of Earth SciencesKFUPM

Seismic Reflection 4: Acquisiton, Processing, and Waveform Analysis

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Types of Velocities Average Velocity Root mean Square Velocity (RMS) Interval velocity

Previous LectureIn

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Example: Disk Formula

21

11

2,

n

iii

n

iinrms ttvv

v1=1500 m s-1

v2=2000 m s-1

v3=2345 m s-1

t1=2.14 s

t2=1.21 s

t3=1.13 s

What is vrms at the base of layer 3?

1-

21

222

s m 064.1882

13.121.114.2

)13.12345()21.12000()14.21500(

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Fig 5.21 of Lillie

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“12 elephants dancing in unison” (LITHOPROBE, CANADA)

A vibrator truck

Vibroseis images from the Lithoprobe Project, Canada

www.lithoprobe.ca

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Fig. 5.23 of Lillie

Reflection and Transmission

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02

•The relative proportions are determined by the acoustic impedance – the product of density (ρ) and velocity (v):

vI •Generally speaking, the greater its acoustic impedance is resulted from the “harder” the rock.

•Maximum transmission of seismic energy requires a matching of acoustic impedances.

•The total energy of a transmitted and reflected ray must equal the energy of the incident ray, due to partitioning energy as:

Incident Amplitude = Reflected Amplitude + Transmitted Amplitude

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Reflection and Transmission

0

1

A

AR

12

12

1122

1122

II

II

vv

vvR

It becomes for a normally incident ray:

•A negative value of R indicates a 180o phase change in the reflected ray.

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•Reflection coefficient R is a numerical measure of the amplitude and polarity of the wave reflected from an interface, relative to the incident wave. It is the ratio between the amplitude (A1) of reflected ray and the amplitude (A0 ) of the incident ray:

T12 = 2I1 / (I1+I2)

T21 = 2I2 / (I2+I1)

Transmission Coefficients

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112212 II

II

vv

vvR

Example: Air-water reflection

ρair =0; Vp=330 m/s

ρwater =1; Vp=1500m/s

RAirWater = (IWater-IAir) / (IAir+IWater)

RAirWater = (IWater-0) / (0+IWater)

RAirWater = 1

AirLayer 1

Layer 2

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ρair =0; Vp=330 m/s

ρwater =1; Vp=1500m/s

Example: Water-air reflection

RWaterAir = (IAir-IWater) / (IAir+IWater)

RWaterAir = -1 ( A negative reflection coefficient)

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2211

221121 II

II

vv

vvR

Air

Water

Layer 1

Layer 2

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a) The input seismic signal is a specific waveform with a certain amplitude (Ai).

b) b) The seismic response to an interface has the same waveform as the input signal, scaled to the amplitude of the reflection coefficient (Ar); it appears at two way travel time (T) dependent on the thickness (h) and velocity (V1) of the material above the interface.

Fig. 5.25 of Lillie

Fig. 5.26 of Lillie

a) Input minimum phase and zero phase seismic signals

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b) Seismic response for reflection at interface with positive reflection coefficient

c) Seismic response for negative reflection coefficient

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High Frequency Input

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Low Frequency Input

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Convolution

• Earth as a Filter of Seismic Energy

G(t) * F(t) = H(t)

Source Earth = Seismogram Wavelet Ref. Coeff. In

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Source and Earth Response

• Mathematical Description of Filter

• Convolution

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See pp. 353 of Reynolds, 2002