“ 12 elephants dancing in unison” (LITHOPROBE, CANADA) A vibrator truck Vibroseis images from the Lithoprobe Project, Canada www.lithoprobe.ca Introduction to Geophysics-KFUPM
Introduction to Geophysics-KFUPM Fig. 5.23 of Lillie
Reflection and Transmission <ul><li>The relative proportions are determined by the acoustic impedance – the product of density ( ρ ) and velocity ( v ): </li></ul><ul><li>Generally speaking, the greater its acoustic impedance is resulted from the “ harder ” the rock. </li></ul><ul><li>Maximum transmission of seismic energy requires a matching of acoustic impedances. </li></ul><ul><li>The total energy of a transmitted and reflected ray must equal the energy of the incident ray, due to partitioning energy as: </li></ul><ul><li>Incident Amplitude = Reflected Amplitude + Transmitted Amplitude </li></ul>Introduction to Geophysics-KFUPM From Kearey, Brooks, and Hill, 2002
Reflection and Transmission It becomes for a normally incident ray: <ul><li>A negative value of R indicates a 180 o phase change in the reflected ray. </li></ul>Introduction to Geophysics-KFUPM <ul><li>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 ( A 1 ) of reflected ray and the amplitude ( A 0 ) of the incident ray: </li></ul>T 12 = 2I 1 / (I 1 +I 2 ) T 21 = 2I 2 / (I 2 +I 1 ) Transmission Coefficients
Example: Air-water reflection ρ air =0; Vp=330 m/s ρ water =1; Vp=1500m/s R AirWater = (I Water -I Air ) / (I Air +I Water ) R AirWater = (I Water -0) / (0+I Water ) R AirWater = 1 Introduction to Geophysics-KFUPM Air Layer 1 Layer 2
ρ air =0; Vp=330 m/s ρ water =1; Vp=1500m/s Example: Water-air reflection R WaterAir = (I Air -I Water ) / (I Air +I Water ) R WaterAir = -1 ( A negative reflection coefficient) Introduction to Geophysics-KFUPM Air Water Layer 1 Layer 2
Introduction to Geophysics-KFUPM <ul><li>The input seismic signal is a specific waveform with a certain amplitude ( A i ). </li></ul><ul><li>b) The seismic response to an interface has the same waveform as the input signal, scaled to the amplitude of the reflection coefficient ( A r ); it appears at two way travel time ( T ) dependent on the thickness ( h ) and velocity ( V 1 ) of the material above the interface. </li></ul>Fig. 5.25 of Lillie
Introduction to Geophysics-KFUPM b) Seismic response for reflection at interface with positive reflection coefficient c) Seismic response for negative reflection coefficient Fig. 5.26 of Lillie a) Input minimum phase and zero phase seismic signals
Introduction to Geophysics-KFUPM High Frequency Input
Introduction to Geophysics-KFUPM Low Frequency Input
Convolution <ul><li>Earth as a Filter of Seismic Energy </li></ul><ul><li>G(t) * F(t) = H(t) </li></ul><ul><li>Source Earth = Seismogram </li></ul><ul><li>Wavelet Ref. Coeff. </li></ul>Introduction to Geophysics-KFUPM
Source and Earth Response <ul><li>Mathematical Description of Filter </li></ul><ul><li>Convolution </li></ul>Introduction to Geophysics-KFUPM See pp. 353 of Reynolds, 2002
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