Geoacoustic Modeling for Acoustic ... Special Session on Acoustics of Fine Grained Sediments: .... Marine mud first-principles physical model including.
Geoacoustic Modeling for Acoustic Propagation in Mud Sediments William L. Siegmann Rensselaer Polytechnic Institute Allan D. Pierce Boston University 171st Meeting, Acoustical Society of America Pittsburgh, PA, 17 May 2015 Special Session on Acoustics of Fine Grained Sediments: Theory and Measurements – Paper 2pAO3
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About This Presentation – • Review of continuing developments and status of card-house model for marine mud • Not a broad-based review of mud geoacoustics – Focus: describe ongoing evolution and extensions of contributions initiated by William M. Carey
• Required measurements (field and laboratory) • Geoacoustic mud model research directions 2
Resources for Marine Mud
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Seabed Mud Constituents • Primary: seawater, clay minerals – Also: silt, organics, bubbles … – Clay particles have electrical charge
Image: Hillel, Fundamentals of Soil Physics (1980)
Simplest physical model • “Idealized mud”: only two components (W, S) • Simplest model: a suspension of platelets and aggregates held together by van der Waals forces − What can be extracted from this model, with no details of aggregation mechanism?
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Suspension Model: Porosity • Physical parameters include – Density 𝜌𝑠 , 𝜌𝑤
– Bulk modulus 𝐵𝑠 , 𝐵𝑤 ; shear modulus GS
• Mud density 𝜌𝑚 = 𝜌𝑤 𝛽 + 𝜌𝑠 (1 – 𝛽)
(platelet quantities)
(mud quantities)
− Mud porosity 𝛽 = volume fraction of water − Define density ratios R𝜌𝑚 = (𝜌𝑚⁄𝜌𝑤 ) , R𝜌𝑠 = (𝜌𝑠⁄𝜌𝑤 ) Rewrite R𝜌𝑚 = 𝛽 + (1 − 𝛽)R𝜌𝑠 (*) – Measure two of R𝜌𝑠 , 𝑅𝜌𝑚 , 𝛽 estimate third from (*) • Example: 𝛽 = 0.9, R𝜌𝑠 = 2.65, R𝜌𝑚 = 1.165
• For muddy sediments, 𝛽 relatively high ( > 0.65) 5 WHY?
Suspension Model: cpm • Compressional speed cpm
[Mallock (1910), Wood (1941)]
Formula designed for two-component suspensions R𝑐𝑝𝑝 =
𝛽 + 1 − 𝛽 R𝜌𝑠 𝛽 + 1 − 𝛽 R𝐵𝑠 −1
−1/2
(**)
Neglect small bulk moduli ratio (𝐵𝑤�𝐵𝑠 ) = RB-1 for mud
–
Typical mud parameter values: Rcpm ≈ 0.98
–
• Rcpm = (
𝑐𝑝𝑝
�𝑐𝑤 )
as R𝜌𝑠
or as 𝛽
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• (**) consistent with available data (more needed) – Laboratory measurements • •
–
[Ballard, Lee, Muir (2014)]
Data cpm = 1458.5 m/s vs. formula cpm = 1460 m/s Sound speed difference ~ 0.1%
Data from 8 sites (clay/silty clay) [J&R (2007), Table 5.1]
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Table 5.1 [Jackson & Richardson (2007)]
Rcpm
β
ρm
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Rcpm: Data vs. Mallock-Wood Calculations
• Average of measurements and average of Mallock-Wood calculations differ by ~ 1% (~ 15 m/s) • Small but systematic difference between two sets of results 8 • PLEASE SEE 2pAO5
Shear Wave Speed csm • Shear speed csm small (insufficient mud data now) – Field data [Jackson &
Richardson (2007), Fig. 5.16]:
𝛽 ~ 0.9 csm~ 8 m/s 𝛽 ~ 0.68 – 0.75 csm ~ 15 – 30 m/s – Lab data [Ballard, Lee, Muir (2014)] Pure kaolinite 𝛽 ~ 0.76
csm ~ 6.9 ± 0.7 m/s
MECHANISM?
– Platelet elasticity leads to csm ~ 102 - 103 m/s
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Card-House Structural Model • Explaining shear speed requires model with realistic platelet interaction mechanism – Mineral platelets small: length L ~ 10-6 m, thin: h = thickness, δ = h/L ~ 10-1 – 10-2
Kaolinite particle [Lambe (1951)]
• Platelets in sea water are quadrupole slabs – Repel face to face – Attach end to face
}
• Platelets aggregate card houses because of because attractive van der Waals forces overcome electrical forces
Card-House Model: Porosity • Card-house structures consistent with high 𝛽
– Estimates 𝛽 ~ 0.9 from inverting Eqs. (*) and (**) – Estimate 𝛽 ≈ 1 – 3δ analytically for “ideal” card house [Pierce & Carey (2008)]
– Randomly generated card houses
[Fayton (2013)]
• Constructed physically-based model “rules” to grow aggregates • Calculated average 𝛽 over realizations: δ: 10-3 10-1 𝛽: 0.99 0.61 • Sanity check: aggregate sizes vs. 𝛽 compare with observations [Huang (1993)
Quantitative success for card-houses
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Card-House Model: Key Step • Card-house structures and their platelet interactions are not new [Image: Lambe (1958), in McCarthy, Essentials of Soil Mechanics and Foundations, 7th Edition (2007)]
• Formula for platelet quadrupole moment/area q was first quantitative result [Pierce & Carey (2008)] q =
𝑒 𝑁𝐴 𝜌𝑠 χ 6
ℎ3
1+
3 κℎ
2
+
3 κℎ 2
– Parameter χ = cation “carrying” capacity of platelet { – 1/K = effective Stern layer thickness
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Card-House Model: Shear Speed (1) • Interaction Model A [Pierce & Carey (2008)] – Interacting platelets rotate rigidly in response to acoustic shear – One normally-oriented lateral quadrupole near center of each platelet – Calculate interaction energy V(ϕ) between two platelets – Upper-platelet displacement constrained by “torsional shear modulus Gm = τ /L3, spring constant” τ = Vϕϕ where τ = (cons) q /L csm = 𝐺𝑚⁄𝜌𝑚 – Result: csm small, possibly underestimates measured shear wave speeds 13
Card-House Model: Shear Speed (2) • Interaction Model B
[Fayton (2013)]
– Each platelet has surface distribution of lateral quadrupole elements – Calculate interaction energy V(ϕ) by quadruple integral over both platelets Gm = τ/L3 – Result: this idealized model predicts τ is infinite
• Interaction Model C
[Fayton (2013)]
– Account for interaction (Stern) layer of thickness d between platelets • d = K-1 ~ 0.45 nm
– Result: this improved model predicts τ is finite
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Card-House Model: Shear Speed (3) • Interaction Model D [Fayton (2013)] – Influence of platelet elasticity? •
Modifies platelet rigid rotation near Stern layer
– Result: negligible effect on csm
• Formula for shear speed (Model C) csm ≈
𝑒 𝑁𝐴 𝜌𝑠 χ 6
ℎ3
1+
3 κℎ
• Parameter variability
2
+
3 κℎ 2
– Less sensitive to 𝜌𝑠 , 𝛽, K values – More sensitive to h, L, χ values
1
2𝜋𝜋𝐿3 𝑑𝜌𝑚 −2
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Estimates for Shear Speed • Common clay minerals kaolinite and smectite • Low-sensitivity parameters fixed for calculations:
κ-1 = 0.45 nm, 𝛽 = 0.9, 𝜌𝑠 = 2640, 𝜌𝑠 = 2530 kg/m3 Representative Range of Range of csm PARAMETERS Value *
Values *
Platelet Thickness Kaolinite: 0.05 0.03 – 0.07 h ( microns ) Smectite: 0.0055 0.001 – 0.01 Platelet Width Kaolinite: 0.9 0.5 – 1.3 L ( microns ) Smectite: 0.9 0.5 – 1.3 Cation Exch. Capacity Kaolinite: 0.09 0.03 – 0.15 χ ( moles/kg ) Smectite: 1.2 0.8 – 1.5 Shear Speed Kaolinite: 13 Smectite: 0.25 csm ( m/sec )
Values
3 – 34 0.01 – 2 6 - 41 0.15 – 1 4 - 22 0.2 – 0.3
*[Mitchel & Soga (2007), Ma & Eggleton (1999); Bundy & Harrison (1986), Conley (1966)]
Rcsm field data fall in kaolinite range [Ballard et al. (2014)]: Kaolinite Rcsm measured ~ 6.9 ± 0.7 m/s, comparable with card-house formula ~ 6.1 m/s 16
• [J & R (2007)]: •
Card-House Achievements to Date • Marine mud first-principles physical model including platelet interactions − Porous and elastic but not Biot poro-elastic
• • • • •
Parameters expressed in terms of physical quantities Consistent with Mallock-Wood explanation for cpm < cw Explains mechanism for high 𝛽 Explains mechanism for small csm Produces csm estimates: – –
In range of values from available data compendium [J & R (2007)] Comparable with lab measurements [Ballard, et al. (2014)]
• Provides basis for understanding additional geoacoustic 17 properties of mud
Compressional Wave Attenuation αpm • Physical mechanisms under investigation • Measurements – UK bay [Wood & Weston (1964)] over 4-50 kHz
αpm ~ 0.066 (f/1000) dB/m
• Values larger than seawater, smaller than other sediments •
f dependence linear
άpm ~ 0.1 dB/λ
WHY?
– Shallow FL bay mud site [J&R (2007), Table 5.1, line 1] αpm ~ 0.097 (f/1000) dB/m (determined at 400 kHz)
– Laboratory data [Ballard et al. (2014)] αpm ~ 35-50 dB/m over 60-110 kHz with dependence ~ f 0.73 Extrapolates to αpm ~ 1.6 dB/m at 1 kHz
• More well-documented data strongly needed
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Shear Wave Attenuation αsm • Physical mechanisms uncertain • Ratio (αsm / αpm ) expected to be large because csm small: >1 >>1 – Fixed f
(αsm / αpm ) = (άsm / άpm ) (cpm / csm )
• Measurements – Field data [J & R (2007), Fig. 5.23] varies 15-60 dB/m at 1 kHz over 30 cm depth αsm ~ 90-235 dB/m – Lab data [Ballard et al. (2014)] over 150-350 Hz with dependence ~ f 1.46 Extrapolates to αpm ~ 1100 dB/m at 1 kHz
– Severe need for more well-documented mud data19
Measurements Needed for Modeling • Geoacoustic parameters: cpm , csm , αpm , αpm – Frequency and depth dependence
• Bulk properties: 𝛽, 𝜌𝑚 , temperature, pH • Constituent fractions: clay (& mineral types), silt, sand • Clay platelet properties: 𝜌𝑠 , χ , generic shapes – Distributions of h , L , surface area, roughness scale
• Microstructure properties: aggregate characteristics, permeability, resistivity, thermal conductivity • Bubbles: gas fraction, size distribution, generic shapes • Organic matter: volume fraction, types, characteristics • Layer interface depths – If multiple layers, all of the above
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Research Directions for Modeling • Develop quantitative model for interactions of mineral platelets in mud • Construct analytical models that explain observed attenuations αpm and αsm in mud • Derive quantitative models for depth and frequency dependence of mud geoacoustic properties • Develop a quantitative approach for predicting when bubbles occur in mud, and for their sizes and shapes • Investigate feasibility for quantitative modeling of organic matter effects on geoacoustic properties. • Investigate quantitative models for mud with multiple component constituents. 21
Sincere appreciation to the Ocean Acoustics Program of the Office of Naval Research for support of this research and PhD students
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