Processes altering seismic amplitudes (Reynolds, 1998) Seismic amplitudes Affected by • Reflection and transmission at an interface • Geometrical spreading • Absorption • Receiver response • Measurement system Geometrical spreading Energy proportional to: r1 Plane wave: constant Cylindrical wave: ~ 1/r Spherical wave: ~ 1/r2 r2 Energy is proportional to (Amplitude)2 ⎛ E (r1 ) ⎞ ⎟⎟ Attenuation due to geometrical spreading: 10* log⎜⎜ ⎝ E (r2 ) ⎠ 10 Absorption Transformation of Energy into Heat Amplitude: A = A0e − αx α = Absorption coefficient Energy is proportional with A2 Quality factor Q= 2π E = 2π = ∆E / E ∆E 2π Part of energy, that is lost in a cycle Relation between Q and α αv αλ = = Q πf π Absorption is frequency dependent πf α= Qv Common Earth materials 0.25 < α < 0.75 (dB/λ) 300 > Q > 50 π Q= αλ Note: exp(-αx) Question 1: • • • • • 20 Hz seismic wave Travels with km/s Propagates for 1000 m through Medium: absorption coefficient 0.25 dB/λ What is the wave attenuation in dB due solely to absorption????? Answer: λ=v/f= 250 m: absorption: 4*0.25=1 dB Question 2: • Wave with λ=100 m propagates through homogeneous medium • Between two detectors at radial distances of km and km the wave amplitude is attenuated by 10 dB • Calculate contribution of geometrical spreading to this value of attenuation and, thus, determine the absorption coefficient of the medium in dB/ λ 10 dB in 1000 m: dB/ λ Geometrical spreading: 20 10log (A0/A)= 20 10log (2)=6dB/ 1km = 0.6 dB/ λ ⇒ absorption coefficient: 1-0.6=0.4 dB/ λ! ...Seismic amplitudes Affected by • Reflection and transmission at an interface • Geometrical spreading • Absorption... dependent πf α= Qv Common Earth materials 0.25 < α < 0.75 (dB/λ) 300 > Q > 50 π Q= αλ Note: exp (- x) Question 1: • • • • • 20 Hz seismic wave Travels with km/s Propagates for 1000 m through Medium:... Geometrical spreading: 20 10log (A0/A)= 20 10log (2)=6dB/ 1km = 0.6 dB/ λ ⇒ absorption coefficient: 1-0 .6=0.4 dB/ λ!