Processes altering seismic amplitudes

Seismic amplitudes Affected by Reflection and transmission at an interface Geometrical spreading Absorption Receiver response Measurement system

Geometrical spreading Energy proportional to: r 1 Plane wave: constant r 2 Cylindrical wave: ~ 1/r Spherical wave: ~ 1/r 2 E/4\pi R^2 Energy is proportional to (Amplitude)2 Attenuation due to geometrical spreading:

Energy is proportional with A2 Absorption Transformation of Energy into Heat Amplitude: a = Absorption coefficient Energy is proportional with A2 Quality factor 2 p Part of energy, that is lost in a cycle Relation between Q and a

Absorption is frequency dependent

Common Earth materials 0.25 < a < 0.75 (dB/l) 300 > Q > 50 Note: exp(-ax)

Question 1: 20 Hz seismic wave Travels with 5 km/s Propagates for 1000 m. through Medium: absorption coefficient 0.25 dB/l What is the wave attenuation in dB due solely to absorption????? Answer: l=v/f= 250 m: absorption: 4*0.25=1 dB

Question 2: Wave with l=100 m propagates through homogeneous medium Between two detectors at radial distances of 1 km and 2 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/ l. 10 dB in 1000 m: 1 dB/ l Geometrical spreading: 20 10log (A0/A)= 20 10log (2)=6dB/ 1km = 0.6 dB/ l absorption coefficient: 1-0.6=0.4 dB/ l!