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Seismic Wave Propagation

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LL F L F = k * L/L (Hooke’s Law) k = Young’s modulus Rand quartzite strain Elastic Materials

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Acoustic Waves F = Mass*Acceleration (Newton rules!) u u+ du x x + dx A F(x) F (x+dx) Net force = F(x+dx) – F(x) = F = [ *A*dx] *acc F/ x = * acc * A] but F = k * u/ x (Hookes law) and S = F/A, so K * u/ x x = * u 2 / t 2 i.e. wave equation where V= (k ) 1/2

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Seismic Wave Equation k * u/ x x = * u 2 / t 2 or d 2 u/dx 2 = ( /k) du 2 /dt 2 which has solutions of the form u = A e +ikt + Be -ikt

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Seismic Waves Body Surface

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Rayleigh Waves

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Seismic Wave Speeds MaterialP wave Velocity (m/s)S wave Velocity (m/s) Air332 Water1400-1500 Petroleum1300-1400 Steel61003500 Concrete36002000 Granite5500-59002800-3000 Basalt64003200 Sandstone1400-4300700-2800 Limestone5900-61002800-3000 Sand (Unsaturated)200-100080-400 Sand (Saturated)800-2200320-880 Clay1000-2500400-1000 Glacial Till (Saturated)1500-2500600-1000

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Seismic Velocities

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Wave Simulations Colorado School of Mines Tutorial Colorado School of Mines Tutorial Body waves in half space

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Huygen’s Principle

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Snell’s Law* (acoustic) *Fermat’s Least Time Principle

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Snell’s Law (elastic) sin 1 = sin 2 = sin 3 Vp 1 Vp 2 Vs 3

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Critical Refraction sin i c = sin (90º) V 1 V 2 sin i c = V 1 V 2

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Seismic Refraction Waves passing from slow to fast medium

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Snell’s Law

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Reflection & Refraction 0 200 400 T, msec Direct Reflected Refracted Distance, km

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Refraction: Two Layers

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Engineering Quad 1/27/00 12 gauge source 1m geophone spacing, 1 m minimum offset Travel Time Curve (Shotpoint Gather

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Refraction: 3 layer case

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Refraction: Dipping Layer

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Refraction: Hidden Layers

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Refraction: Lateral Offset

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Refraction: Many Layers

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Refraction: Multiple Layers

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Refraction: Linear V(z)

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Refraction: + Gradients V z z x x t

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Refraction: - Gradients V zz t x x LVZ Low velocity zone

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Diffraction

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Reflection: Basic Geometry T 2 = X 2 + ( 2Z/V) 2 V 2 T 2 = X 2 + T 0 2 V 2

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Reflection Hyperbola

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Reflection from Dipping Layer

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SHOT * Reflection display convention

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Sample shot gathers offend split spread

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