Assumption 1. Horizontal layers of constant velocity

Assumption 2. Normal incidence of plane P wave = No shear waves

Assumption 3. Stationary source waveform

Assumption 4. No noise

Assumption 5. Known source waveform

Assumption 6. Random reflectivityWhite process – Appendix B(B8)Autocorrelation = amplitude spectrum

Assumption 7. Minimum-phase wavelet

Deconvolution

Deconvolution SummaryAssumption 1,2,3 ： formulating the convolutional model of the 1-

D seismogram

)()()()( tntetwtx

Assumption 4 ： eliminates the unknown noise

)()()( tetwtx

Assumption 5 ： determine deconvolution

Assumption 6 ： the basis for statistical deconvolution

Assumption 7 ： provides a minimum-phase

Convolution model

x(t) ： recorded seismogram (known)w(t) ： basic seismic wavelet (known)* ： convolution

e(t) ： earth’s impulse response (unknown)

n(t) ： random ambient noiseexternal noises – wind, environment,

geophone coupling to groundinternal noises – recording instrument

)()()()( tntetwtx