Geoacoustic modeling for acoustic propagation in ...

Volume 23

http://acousticalsociety.org/

169th Meeting of the Acoustical Society of America Pittsburgh, Pennsylvania 18-22 May 2015

Acoustical Oceanography: Paper 2pAO3

Geoacoustic modeling for acoustic propagation in mud ocean-bottom sediments William L. Siegmann Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY; [email protected]

Allan D. Pierce PO Box 339, East Sandwich, MA; [email protected] This paper reviews research since 2007 developed at BU and RPI, with leadership by the late W.M. Carey, on acoustic properties of mud. Marine mud consists primarily of clay mineral platelets, comprised of crystalline layers and usually carrying charge because of isomorphous substitution. Because of resulting electrical forces, the physical nature of mud is considerably different from sandy sediments. In particular as platelets settle under gravity, electrical forces repel face-to-face contact, while strong van der Waals forces permit edge-toface attachment. This platelet aggregation results in card-house structures, for which a tentative quantitative model has been analyzed (J. O. Fayton, RPI Ph.D. thesis, 2013). The model preserves basic physics of platelet interactions and leads to low shear speed predictions that are consistent with observations. Reasonably accurate compressional sound speed estimates follow from the Mallock-Wood formula; improved estimates result from including an electrostatic correction (2pAO5, this session). The basic physical concepts and semiempirical formulas determined for compressional and shear attenuations and their frequency dependencies in sandy sediments do not apply to mud, nor do assumptions underlying the often cited Biot theory for poroelastic media. A summary is provided of physical and geoacoustic mud properties for which measurements are needed.

Published by the Acoustical Society of America © 2016 Acoustical Society of America [DOI: 10.1121/2.0000220] Received 17 June 2016; Published 14 July 2016 Proceedings of Meetings on Acoustics, Vol. 23 005003 (2016)

Page 1

Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 71.174.147.17 On: Fri, 09 Sep 2016 12:15:22

W. L. Siegmann and A. D. Pierce

Geoacoustic modeling in mud sediments

This presentation is a review of the developments and status of the card-‐house theory of high porosity marine mud as of May 2015. The card-‐house research was initiated in 2007 by Allan Pierce and William Carey at BU, joined later by William Siegmann at RPI, and continued after Dr. Carey’s passing in 2012. It was delivered by William Siegmann in a Special Session on Acoustics of Fine Grained Sediments: Theory and Measurement, at the Acoustical Society of America meeting in Pittsburgh. This presentation is not a broadly based review of mud geoacoustics, but rather a focused description of the ongoing evolution and contributions from the card-‐house theory. Required measurements (both field and laboratory) for confirmation or modification of the theory are summarized, along with research directions for geoacoustic mud modeling. For a comprehensive review of the physical, chemical, and geoacoustic properties of mud, two valuable references are Jackson & Richardson (2007) and Bennett, Bryant, & Hulbert (1991). The dominant physical, chemical, and electrical characteristics of seabed mud are essential to understanding and modeling its geoacoustic features. The simplest physical model is a suspension that neglects the details of mechanisms that could cause the constituent clay particles to aggregate. In the following slides, the suspension consists of only clay particles in water, although the model and its results can be extended to include additional components such as bubbles and organic matter.

Figure 1. Primary constituents of seabed mud, and a simple suspension model. One advantage of the suspension model is that determination of its predictions is convenient. The following figures show clay-‐particle quantities in brown and mud quantities in purple.

Proceedings of Meetings on Acoustics, Vol. 23 005003 (2016)

Page 2




Figure 2. Relation between porosity and mud and platelet densities in the suspension model. Using a suspension model for a mud sample presupposes that it has a significant volume fraction of water. Estimates can be obtained for the porosity, although it is unclear at the start how large its value should be for the model to be useful. Another important estimate from the suspension model is for the compressional sound speed.

Figure 3. Relation between compressional speed ratio, porosity, and platelet density from the suspension model.


Page 3




The formula for the compressional speed ratio has the anticipated behavior with respect to variations of mud property parameters. A recent experiment by Ballard, Lee, & Muir (2014) shows close agreement with estimates from the formula. For field data, a comprehensive summary for silicielastic sediments is contained in Table 5.1 of Jackson & Richardson (2007). Part of these data is for sediments consisting of all or mostly clay, providing an opportunity to test compressional speed ratio estimates from the suspension model.

Figure 4. Summary of sediment physical and geoacoustic properties from 57 silicielastic sites [Table 5.1, Jackson & Richardson (2007)]. Properties in the Table which have been discussed are compressional speed ratio (col. 3), porosity (%, col. 6), and mud density (g cm-‐3, col. 7). Note that the data are ordered by mean grain size (φ log units, col. 5), and that attenuation (dB m-‐1, col. 4) tends to increase with mean grain size. The compressional speed ratio from the eight samples of predominantly clay data, boxed in green in Fig. 4, and the suspension model are compared versus porosity in Fig. 5. Note that additional data from Table 5.1, that is, data samples below the green box in Fig. 4 which are not primarily clay, may also be compared with corresponding model predictions. The upshot is that the agreement for the additional samples is comparable to those for the original eight, provided that the porosity is larger than 65%. It appears that high porosity sediments, even if not entirely or mostly clay, can have compressional speed ratios that are consistent with predictions of the suspension model. It is important to add that the comparisons in Fig. 5 reveal systematic differences between data and model estimates, of the order of 1%. Although this percentage is small, it represents significant sound speed ratio differences. A presentation by Pierce & Siegmann (2015) in the same session as this one provides a physically-‐based hypothesis for these differences. The hypothesis relies on specifying the interaction mechanism of the clay particles, and consequently is beyond the framework of the simple suspension model.


Page 4




Figure 5. Comparison between compressional speed ratio versus porosity from measurements (green) and the Mallock-‐Wood suspension model (magenta).

In contrast to the compressional speed data, observed shear speed values are very small for high porosity mud sediments. The suspension model cannot provide an explanation for this fact. For example, it is not a result of elasticity of the platelets, which are relatively rigid because of a high shear modulus.

Figure 6. Status of field and laboratory data showing small shear speed versus porosity from data; the Mallock-‐Wood suspension model predicts much larger shear speeds.


Page 5




A different mud structure model, including a particle aggregation mechanism, is needed to account for the small shear modulus. One such is an aggregation structure based on clay platelets with net negative charges in the presence of positive seawater ions. Detailed considerations by Pierce & Carey (2008) lead to a platelet model with its flat surfaces having distributed lateral quadrupoles that cause aggregation into card-‐house structures.

Figure 7. Key principles of the card-‐house structure model of mud.

Because the marine mud of interest has high porosity, one can ask whether card-‐house structures have relatively large values of this parameter. The answer to this question leads to one of the quantitative successes of the card-‐house model.

Figure 8. Estimates of porosity from the card-‐house structure model of mud.


Page 6




Detailed specification of the physics of the platelet aggregation mechanism in card-‐house structures is essential to develop other quantitative estimates from the model. It is important to mention that soil scientists were aware for decades of card-‐house aggregates in mud. However, a quantitative and physically-‐based determination of the quadrupole interaction mechanism is a relatively new contribution on which all recent progress is based.

Figure 9. Specification of the electric quadrupole moment density Eq. (4) is critical for modeling platelet aggregation into card-‐house structures. An effective Stern layer is formed by the positive ions attracted to a negatively-‐charged platelet surface. Using Eq. (4) a sequence of increasingly detailed models (A through D) were developed to produce estimates for the shear speed in high porosity marine mud.


Page 7




Figure 10. The first physics-‐based Model A for the interaction between two clay mineral platelets. Calculation of the interaction energy V as a function of interaction angle is lengthy, and the result is in Pierce & Carey (2008).

Figure 11. Model B accounts for quadrupoles distributed over the platelet surface, rather than a quadrupole charge concentrated at one location. Because this model allows platelet edges to come in physical contact with platelet faces, a singular shear modulus arises due to ignoring the finite size of ions attracted to the charged surface. Model C accounts for the thickness of the ion interaction layer and produces a finite value for the shear modulus. These models omit the platelet elasticity, which might influence the shear modulus two-‐platelet interactions. Model D shows that this mechanism has negligible effects. The final shear speed result in Eq. (5) produces values that are sensitive to values of only three of its parameters.


Page 8




Figure 12. Predictions from the final formula for shear speed, Eq. (5), are relatively sensitive to the values of three of its six parameters.

The ranges of shear speed values from Eq. (5) are shown in Fig. 13 for typical ranges of property values of two common minerals, kaolinite and smectite, from Fayton (2013). Values for kaolinite are shown in red, and values for smectite are shown in blue. Along with ranges of values, some representative values for the parameters are shown.

Figure 13. Parameter values for properties of two clay minerals are provided. The ranges of values (column 3) and representative values (column 2) of physcial interest are shown in rows 2-‐4. These values are used in Eq. (5) to produce ranges of shear speed estimates (column 4) and repersentative shear speed estimates (row 5). These estimates are close to those from field data in Fig. 6 (Jackson & Richardson (2007)) and from laboratory measurements (Ballard, et al. (2014)). A list of achievements of the card-‐house model as of mid-‐2015 is provided next. It is emphasized that this model has an entirely different basis from the well-‐known model of Biot (1956) for poro-‐elastic materials. In the latter, contact forces play the key role in particle interactions, while in the former, electrical and Van der Waals forces are critical in interactions. Geoacoustic consequences of this fundamental difference arise in the corresponding estimates for both compressional and shear wave speeds as well as compressional and shear wave attenuations.


Page 9




Figure 14. Achievements of the card-‐house theory. The status of understanding of compressional and shear wave attenuation in mud, and some experimental results, are indicated in Figs. 15 and 16.

Figure 15. Estimates of compressional attenuation αpm of mud are seen to vary over almost two orders of magnitude. Its dependence on frequency is uncertain but believed to be roughly linear.


Page 10




Figure 16. Estimates of shear attenuation αsm of mud are also seen to vary over almost two orders of magnitude. Little is known about its value and frequency dependence other than its value is expected to be large relative to αpm . In conclusion, Figs. 17 and 18 suggest measurements needed and research directions for improved modeling of mud.

Figure 17. Field and laboratory measurements needed for testing the card-‐house theory and for further improvements in modeling seabed mud.


Page 11




Figure 18. Research directions for improving current models and developing extended geoacoustic models of seabed mud. ACKNOWLEDGEMENTS Sincere appreciation to the Ocean Acoustics Program of the Office of Naval Research for encouragement and funding to support this research. REFERENCES Ballard, M. S., Lee, K. M., and Muir, T. G. (2014). “Laboratory P-‐ and S-‐wave measurements of a reconstituted muddy sediment with comparison to card-‐house theory,” J. Acoust. Soc. Am. 136, 2941-‐2946. Bennett, R. H., Bryant, W. R., and Hulbert, M. H., Eds. (1991). Microstructure of Fine-‐Grained Sediments (Springer-‐Verlag, New York), pp. 3-‐566. Biot, M. (1956). “Theory of deformation of a porous viscoelastic anistropic solid,” J. Appl. Phys. 27, 459-‐467. Bundy, W. M., and Harrison, J. L. (1986). “Nature and utility of hexamethylenediamine-‐ produced kaolin floc structure,” Clays Clay Miner. 34, 81-‐86. Conley, R. F. (1966). “Statistical distribution patterns of particle size and shape in the Georgia kaolins,” Proc. 14th National Conf. Clays and Clay Minerals, Berkeley, CA, 317-‐344.


Page 12




Fayton, J. O. (2013). Estimation of Geoacoustic Parameters of Marine Mud (Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, NY). Hillel, D. (1980). Fundamentals of Soil Physics (Academic Press, New York), p. 58. Huang, H. (1993). “Porosity-‐size relationship of drilling mud flocs: fractral structure,” Clays Clay Miner. 41, 373-‐379. Jackson, D. R., and Richardson, M. D. (2007). High-‐Frequency Seafloor Acoustics (Springer-‐ Verlag, New York), pp. 29-‐170. Lambe, T. W. (1951). Soil Testing for Engineers (Wiley, New York), p. 35. [See also Hall, C. E. (1950). “Fundamental study of clay: X, water films in monodisperse kaolinite functions,” J. Amer. Ceramic Soc. 37, 211-‐218.] Lambe, T. W. (1958). “The engineering behaviour of compacted clay”, ASCE JSMFD, 84, 1665-‐1-‐ 35. Ma, C., and Eggleton, R. A. (1999). “Cation exchange capacity of kaolinite,” Clays Clay Miner. 47, 174-‐180. Mallock, A. (1910). “The damping of sound by frothy liquids,” Proc. Royal Soc. London Series A, 84, 391-‐395. McCarthy, D. F. (2007). Essentials of Soil Mechanics and Foundations, 7th Ed. (Prentice Hall, New Jersey), p. 83. Mitchel, J. K., and Soga, K. (2007). Fundamentals of Soil Behavior (Wiley, New York), pp. 109-‐ 119. Pierce, A. D., and Carey, W. M. (2008). “Acoustical characteristics of muddy sediments,” Proc. Mtgs. Acoust. 5, 07002. Pierce, A. D., and Siegmann, W. L. (2015). “Tentative acoustic wave equation that includes relaxation processes for mud sediments in the ocean,” J. Acoust. Soc. Am. 137, 2282(A). Wood, A. B. (1941). A Textbook of Sound, 2nd Ed. (Macmillan, NY), pp. 360-‐363. Wood, A. B., and Weston, D. E. (1964). “The propagation of sound in mud,” Acoustica 14, 156-‐ 162.


Page 13
