Hydrogeophysics - Seismics Matthias Zillmer EOST-ULP p. 1
Table of contents SH polarized shear waves: Seismic source Case study: porosity of an aquifer Seismic velocities for porous media: The Frenkel-Biot-Gassmann theory Partial saturation of the pore space (air+water) Acquisition of near surface seismic data: Optimum window/offset technique Synthetic seismogram modeling p. 2
S-wave vibroseis source peak force: 450 N frequencies: 5 320 Hz depth of reflectors: 100 m depth of receivers in borehole (VSP): 200 m p. 3
S-wave vibroseis source Vibroseis technique A sweep signal of e.g. 10 s duration is generated with a linear increase in frequency from 10 to 100 Hz. There is a short time of 2 s, where one is recording reflections. This seismic trace is stored and later correlated with the sweep, which gives an impulse signal (Klauder wavelet) with the frequency bandwidth of the sweep. p. 4
S-wave vibroseis source Advantages of the S-wave vibroseis source compared to the P-wave sledgehammer seismic source: 1. The S-wave velocity is an important parameter. In combination with the P-wave velocity it can be used to determine the porosity. 2. The source signal is reproducable. 3. Smaller wavelength and better resolution than P-waves. 4. SH-waves can be generated with the source oriented perpendicular to the seismic line. At discontinuities they are not converted to P-waves, so that the wavefield is more simple than the P-SV wavefield. Problems: 1. The SH-source generates Love surface waves with larger amplitudes than the SH reflections. p. 5
Case study: Jarvis and Knight Aquifer heterogeneity from SH-wave seismic impedance inversion Kevin D. Jarvis and Rosemary J. Knight, Geophysics 67 (2002) Method VSP (penetrometer) measurements to determine the waveform and an initial velocity model at 3 VSP positions. Inversion of SH-wave reflection amplitudes 2D S-wave velocity model use an empirical formula to determine the porosity of the sand aquifer p. 6
Case study: Area Frazer River delta, British Columbia, Canada p. 7
Case study: Method generate SH-waves with a sledgehammer all sediments are water saturated; the water table is < 1m depth S-waves have better vertical resolution than P-waves in the saturated zone: λ p 4 = v p 4f = 1600 m/s 4 100 Hz = 4 m, λ s 4 = v s 4f = 200 m/s 4 100 Hz = 0.5 m S-waves are not sensitive to fluid saturation. large contrast in v s, if lithology changes or if porosity / void ratio changes (?) Construct a velocity model from the transmitted wave at 3 VSP locations. Extract the seismic signal from the VSP data. Perform waveform inversion to convert SH wave reflection amplitudes to S-wave velocities. p. 8
Case study: Model known from previous investigations p. 9
Case study: Data seismogram sections p. 10
Case study: Data time migrated seismic section p. 11
Case study: S-wave velocity from VSP scaled S wave velocities from VSP p. 12
Case study: 2D input velocity 2D input velocity model based on 3 VSPs. p. 13
Case study: 2D output velocity p. 14
Case study: 2D scaled output velocity p. 15
Case study: Void ratio porosity 48-53 %! p. 16
elastic moduli and seismic velocities body waves in isotropic elastic medium P compressional wave v p = λ + 2µ ρ = K + 4 3 µ ρ S shear wave v s = µ ρ 2 elastic constants (Lamé parameter) λ, µ and density ρ, bulk modulus K λ = K + 2 3 µ p. 17
elastic moduli, Hooke s law isotropic elastic medium t ik = λδ ik ε ll + 2µε ik t ik stress tensor and ε ik strain tensor fluid medium (no shear resistance) p pressure, V volume µ = 0, λ = K, t ik = pδ ik p = K( ) V V, Cp = ( ) V V, C = 1 K C compressibility, K incompressibility = bulk modulus p. 18
model of porous medium solid + voids (fluid or gas filled) K s 30 GPa bulk modulus of the solid constituent K f 2 GPa bulk modulus of the fluid constituent K dry 0.1 GPa bulk modulus of the unsaturated frame/skeleton/matrix What is the bulk modulus of the fluid saturated medium? and the same for the shear modulus: µ s, µ f = 0, µ dry, µ p. 19
Porosity φ two-phase medium: solid grains + pore fluid total volume: V = V s + V f porosity is the volume fraction occupied by the fluid: φ = V f V volume of solid phase: 1 φ = V s V, void ratio: e = V f V s = φ 1 φ mass: m = m s + m f, density: ρ = (1 φ)ρ s + φρ f p. 20
Gassmann s equations: 1. form K bulk modulus of the fluid saturated material K = K dry + α 2 ( α φ K s + φ K f ) 1 or α 2 K K dry = α φ K s + φ K f α = 1 K dry K s φ porosity α Biot-Willis constant p. 21
Gassmann s equations: 2. form K = K dry 1 αb B = 1 K dry 1 K s 1 K dry 1 K s + φ ( 1 K f 1 K s ) B Skempton s coefficient p. 22
Gassmann s equations: 3. form K K s K = K dry K s K dry + K f φ(k s K f ) The second Gassmann equation: µ = µ dry µ shear modulus of the fluid saturated material. The saturated shear modulus equals the unsaturated modulus, which implies that it does not depend on the fluid type. p. 23
Frenkel s equations poro-elastic medium (Frenkel 1944, Biot 1954) the slow second P-wave is strongly attenuated for ω ω c. there are two waves propagating in the saturated medium: 1 P-wave and 1 S-wave ( ) 1 K dry + α 2 α φ K s + φ K f + 4 v p = ρ 3 µ dry, v s = µdry which e.g. implies a small decrease in S-wave velocity at the water table v s,wet = µ ρ = µ < v s,dry = (1 φ)ρ s + φρ f µ ρ dry = ρ µ (1 φ)ρ s p. 24
Critical porosity For most porous rocks there is a critical porosity φ c that separates their mechanical and acoustic behaviour into two distinct domains: For porosities lower than φ c the mineral grains are load-bearing, whereas for porosities greater than φ c the rock becomes a suspension in which the fluid phase is load-bearing (K dry = 0). The value of φ c depends on rock type, e.g. 0.4 for sand. p. 25
Critical porosity (Saturated) Elastic modulus as a function of porosity. p. 26
Aggregat of spheres elastic moduli of a dense packing of spheres Hertz (1882) - Mindlin (1949): K dry = [ C 2 (1 φ) 2 µ 2 ] 1/3 s 18π 2 (1.0 ν s ) 2P µ dry = 5 4ν s 5(2 ν s ) [ 3C 2 (1 φ) 2 µ 2 ] 1/3 s 2π 2 (1.0 ν s ) 2 P K dry µ dry = 5(2 4ν s) 3(5 4ν s ) 0.7 0.8 v p 1.4 v s in dry medium v(z) z 1/6 p. 27
Air+Water saturated soil The pore fluid is a mixture of air and water. The bulk modulus of the mixture of a fluid and a gas is computed with the Reuss-average (iso-stress in the mixture): 1 K f = S w K w + 1 S w K g S w is the water saturation of the pore space (volume fraction of water). ρ f = S w ρ w + (1 S w )ρ g p. 28
Air+Water saturated soil Vp [km/s] 7 6 5 4 3 2 1 0 0 10 20 30 100 70 8090 The P-wave velocity is a function of porosity and water saturation. Critical porosity 40 % Suspension domain = unconsolidated rock domain: A very small amount of gas in the pore fluid strongly reduces the P-wave velocity (but has no influence on the S-wave velocity). 40 50 60 porosity [%] 70 80 90100 40 5060 10 2030 water saturation [%] p. 29
Oil+Water saturated rock Domenico (1974) The difference of properties between oil and water is smaller than of oil and gas. Elastic moduli increase with pressure=depth. p. 30
Optimum window/offset technique Hunter et al., Shallow seismic reflection mapping, Geophysics 49 (1984) p. 31
Optimum window section Band-pass filtering, Static corrections based on first arrival refractions, Normal Move Out correction, Stacking. Major disadvantage: Non-linear streching of NMO distorts wide-angle reflections, so that no correlation possible. p. 32
Optimum offset section Offset: 46 m, spacing 3 m The best field conditions have been found where the near-surface overburden is fine-grained and water-saturated; frequencies in the 300-400 Hz range can be transmitted to considerable depths. The worst field conditions occur when the near-surface materials are coarse-grained and have a low moisture content; at these sites one may be forced to drop the low-cut filters to 50 Hz to allow transmission from depth, at the expense of resolution. p. 33
Seismograms: model p. 34
Seismograms: angles max. angles of reflected P-waves: water table reflections: 1 96 m θ < tan 20 m 80 bedrock reflection: 1 96 m θ < tan 80 m 50 critical angles and offsets head waves: sinθ 1 v 1 = sinθ 2 v 2, sinθ c v 1 = 1 v 2 water table: θ c 10, r c 3.5 m bedrock: θ c 20, r c 30 m p. 35
Seismograms: traveltimes f = 100 Hz; T = 0.010 s T p (r=96m) T s (r=96m) Rayleigh(r=96m) soundwave(r=96m) 0.274 s 0.384 s 0.42 s 0.282 s R pp (1,r=0) 0.057 s R pp (2,r=0) 0.091 s R ps (1,r=0) 0.069 s R ps (2,r=0) 0.236 s R ss (1,r=0) 0.080 s R ss (2,r=0) 0.380 s p. 36
Seismograms 0 0.1 0.1 0.2 0.2 time [s] time [s] 0 source-receiver offset [m] 10 20 30 40 50 60 70 80 90 0.3 0.4 source-receiver offset [m] 10 20 30 40 50 60 70 80 90 0.3 0.4 Ux Uz without stress-free surface p. 37
Seismograms 0 0.1 0.1 0.2 0.2 time [s] time [s] 0 source-receiver offset [m] 10 20 30 40 50 60 70 80 90 0.3 0.4 source-receiver offset [m] 10 20 30 40 50 60 70 80 90 0.3 0.4 Ux Uz with stress-free surface p. 38