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N ABSTRACT OF THE THESIS OF BURLIE ALLEN BRUNSON for the degree of DOCTOR OF PHILOSOPHY in OCEANOGRAPHY presented on JUNE 23, 1983. Title: SHEAR WAVE ATTENUATION IN UNCONSOLIDATED IMENTS Redacted for privacy Abstract approved: Johnson Shear wave attenuation measurements were made using ceramic bimorph transducers to excite trans- verse vibrations in a cylindrical column of uncon- solidated sediment. Three different water-saturated sediments were used in an attempt to determine the effects of grain shape and sorting on the frequency dependence of attenuation. The mean grain size of the sediments was held constant while the grain shape and size distributions were varied. The sediment assem- blages used in the attenuation measurements included a moderately-sorted angular quartz sand, a well- sorted angular quartz sand, and well-sorted spherical glass beads. The moderately-sorted sand showed the greatest attenuation over the measurement frequency range of 1 to 20 kHz. The well-sorted sand and the glass beads showed generally lower attenuation with the beads being the least lossy propagation medium. All three sediments showed evidence of viscous attenu- ation due to fluid-to-grain relative motion. This mechanism leads to a non-linear relationship between attenuation and frequency. Sediment physical properties were measured for use as inputs to a theoretical attenuation model based on the Biot theory of propagation of waves in porous media. The model allowed attenuation versus frequency predictions to be made for each of the three sediment assemblages. The resultant comparisons between the measured and predicted attenuations demonstrated the importance of using measured model inputs obtained under controlled laboratory conditions when theoret- ical model capabilities are being evaluated. The model comparison shed significant light on the ability of this particular model to predict shear wave attenuation in non-ideal sediments. Shear Wave Attenuation in Unconsolidated Laboratory Sediments by Burlie Allen Brunson A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Completed June 23, 1983 Commencement June 1984 APPROVED: Redacted for privacy 1iProf,Tsor of Oceanography in Charge of Major Redacted for privacy Dean of School of Oceanogr Redacted for privacy Dean of Graduat1choo1 Date thesis is presented June 23, 1983 Typed by Lesley J. Rackowski for Burlie Allen Brunson ACKNOWLEDGEMENTS I would like to thank all those who have gener- ously given of their time and energy to see this project through. In particular, I would like to express my gratitude to my committee chairman, Dr. Richard K. Johnson. During the last two years, I have had the plea- sure of.working with two very fine men. Each has been a source of encouragement during the difficult times. I would like to thank Dr. Raymond C. Cavanagh and Dr. Ronald L. Spooner for their encouragement. Without financial support, a project like this would be impossible. I greatly appreciate the support afforded by the Office of Naval Research and the Naval Ocean Research and Development Activity. A special debt of gratitude is due Lesley J. Rackowski for sacrificially giving of her time to type the manuscript. Finally, I sincerely thank my wife, Lois, for her continuing encouragement and understanding through- out the course of this project. TABLE OF CONTENTS Page I. INTRODUCTION 1 II. OBSERVATIONAL CONSIDERATIONS Background 9 Observational Techniques 9 Shear Wave Observations 12 Speeds 12 Attenuation 18 Summary of Current Understanding 31 III. THEORETICAL CONSIDERATIONS Background Viscoelastic Models 38 The Kelvin-Voigt Model 38 The Hamilton Viscoelastic Model 39 Physical Sediment Models 43 Introduction Scattering Models 44 Suspension Models 45 The Biot-Stoll Physical Sediment Model Theory vs. Observations 61 IV. LABORATORY ACOUSTIC EXPERIMENTS 64 Background 64 Experiment Design Considerations 65 Propagation Medium 65 Wave Type 67 Frequency Range 68 Transducers 70 Measurement Technique 70 Frequency Control Interference Effects summary Sediment Acoustic Properties 78 Measurements Shear Wave Transducers Shear Wave Measurement System 84 Operational Measurement Procedures 90 Summary V. PHYSICAL PROPERTIES MEASUREMENTS 98 Background 98 Sediment Properties Measurements 98 Grain Size Distribution 99 Permeability 104 Porosity 109 Page Grain Specific Gravity 110 Summary 111 VI. SEDIMENT PROPERTIES 112 Introduction 112 Grain Size Distribution 112 Porosity 115 Permeability 117 Frame Shear Modulus (Real Part) 127 Frame Logarithmic Decrement 130 Pore Size Parameter 133 Structure Factor 135 Summary 146 VII. SHEAR WAVE DATA PRESENTATION AND ANALYSIS 147 Background 147 Shear Speed Measurements 147 Shear Attenuation Measurements 152 Spherical Beads (40/45) 163 Angular Sand (40/45) 165 Angular Sand (unsieved) 167 Grain Shape Effects 171 Grain Sorting Effects 175 Summary 181 VIII. SHEAR WAVE MODEL PRESENTATION AND ANALYSIS 182 Introduction 182 The Shear Wave Model 182 Permeability Sensitivity 193 Pore Size Parameter Sensitivity 195 Structure Factor Sensitivity 197 Biot/Stoll Shear Wave Model-to-Data 198 Comparisons Spherical Bead (40/45) Data Versus 202 Model Angular Sand (40/45) Data Versus 210 Model Angular Sand (Unsieved) Data 221 Versus Model IX. CONCLUSIONS 231 X. BIBLIOGRAPHY 234 LIST OF FIGURES Figure Page IV-1 Shear Wave Transducer (Exploded) 80 IV-2 Shear Wave Transducer (Cross-Section) 81 IV-3 Shear Wave Sensor System 85 IV-4 Shear Wave Measurement Instrumentation 87 Block Diagraiu IV-5 Received Level Versus Separation for 95 Well-Sorted Angular Sand at 4 kHz V-i Variable Head Permeameter (Cross- 106 Section) VI-1 Grain Size Distributions for Sediments 114 Used in Shear Wave Measurements VI-2 Permeability Versus ø3iu-ø2 for 120 Moderately-Sorted Angular Sand Vu-i Shear Wave Speed Data (Saturated 149 Samples) VII-2 Received Level Versus Separation for 156 Well-Sorted Spherical Beads at 10 kHz VII-3 Received Level Versus Separation for 157 Well-Sorted Angular Sand at 10 kHz VII-4 Received Level Versus Separation for 158 Moderately-Sorted Angular Sand at 10 kHz VII-5 Received Level Versus Separation for 159 Well-Sorted Angular Sand at 1 kHz VII-6 Received Level Versus Separation for 160 Well-Sorted Angular Sand at 10 kHz VII-7 Received Level Versus Separation for 161 Well-Sorted Angular Sand at 20 kHz VII-8 Attenuation Versus Frequency for Well- 164 Sorted Spherical Beads (40/45) LIST OF FIGURES (Cont.) Figure Page VII-9 Attenuation Versus Frequency for 166 Well-Sorted Angular Sand.(40/45) Vil-lO Attenuation Versus Frequency for 168 Moderately-Sorted Angular Sand (Unsieved) Vu-il Attenuation Comparison Between 172 Saturated Well-Sorted Angular Sand and Spherical Beads VII-12 Attenuation Comparison Between 178 Saturated Well-Sorted and Moderately- Sorted Angular Sands VIII-1 Biot-Stoll Model Attenuation Predic- 189 tions for Base Case Sand with Theo- retical Upper and Lower Bounds VIII-2 Attenuation Predictions Showing Con- 192 tributions of Frame and Viscous Losses to Total Sediment Losses for Base Case VIII-3 Sensitivity of Biot-Stoll Model 194 Attenuation Predictions to Variations in Permeability VIII-4 Sensitivity of Biot-Stoll Model 196 Attenuation Predictions to Variations in Pore Size Parameter VIII-5 Sensitivity of Biot/Stoll Model 199 Attenuation Predictions to Variations in the Structure Factor VIII-6 Comparison of Biot-Stoll Model 203 Attenuation Predictions to Bead (40/45) Data for Optimum Value of Pore Size Parameter and Structure Factor VIII-7 Comparison of Frame, Viscous, and Total 205 Attenuation Predictions to Bead (40/45) Data VIII-8 Comparison of Pore Size Parameter 207 Effects on Attenuation Predictions for Saturated Beads (40/45) LIST OF FIGURES (Cont.) Figure Page VIII-9 Comparison of Biot-Stoll Model 212 Attenuation Predictions to Angular Sand (40/45) Data for Optimum Value of Pore Size Parameter and Structure Factor Vill-lO Comparison of Frame, Viscous, and 214 Total Attenuation Predictions to Angular Sand (40/45) Data Vill-il Comparison of Pore Size Parameter 216 Effects on Attenuation Predictions for Saturated Angular Sand (40/45) VIII-12 Comparison of Permeability Estimate 218 Effects on Attenuation Predictions for Saturated Angular Sand (40/45) VIII-13 Comparison of Bict-Stoll Model 222 Attenuation Predictions to Angular Sand (Unsieved) Data for Optimum Value of Pore Size Parameter and Structure Factor VIII-14 Comparison of Frame, Viscous, and 225 Total Attenuation Predictions to Angular Sand (Unsieved) Data VIII-15 Comparison of Permeability Estimate 226 Effects on Attenuation Predictions for Saturated Angular Sand (Unsieved) VIII-l6 Comparison of Pore Size Parameter 229 Effects on Attenuation Predictions for Saturated Angular Sand (Unsieved) LIST OF TABLES Table Page 111-1 Biot/Stoll Physical Parameters 60 V-i Grain Size Scales for Sands 100 VI-1 Sediment Properties 113 VI-2 Kozeny-Carman Factors for Laboratory 121 Sed irnents VI-3 Permeability Observations and Estimates125 for Laboratory Sediments VI-4 Measured Dry Frame Speed, Attenuation, 129 and Logarithmic Decrement at 10 kHz VI-5 Pore Size Parameter Estimates Using 136 Three Different Methods, a(crn) VI-6 Structure Factor Estimates Derived 141 From Sediment Formation Factors Vu-i Shear Speed and Modulus at 10 kHz, 150 Wet and Dry Sediments VII-2 Shear Wave Attenuation in Water- 154 Saturated Laboratory Sediments VIII-1 Base Sediment Physical Properties 190 VIII-2 Physical Properties of Laboratory 201 Sediments (Measured and Derived from
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