A method for determining absolute ultrasonic velocities and elastic properties of experimental shear zones

Abstract

Laboratory experiments are a vital tool for assessing elastic properties of rock and determining the underlying geomechanical processes that inform large scale, predictive models. In some cases, relative values of elastic properties are sufficient, but absolute values are necessary when comparing between locations and to address upscaling from lab to field settings. However, determining absolute values of ultrasonic velocity and elastic parameters in laboratory experiments is often complex and hampered by apparatus design. Moreover, measuring the evolution of elastic properties with shear deformation has proven especially difficult. Here, we describe a method that allows measurements of P- and S-wave velocity as a function of shear deformation under stresses of 10's of MPa. The approach includes rigorous calibration experiments and accounts for the evolution of impedance contrasts at sample interfaces as a function of strain. We describe our method by applying it to sheared layers that represent simulated fault zones composed of clay-quartz mixtures and fault rocks recovered from drilling. P-wave arrival times range from 10 to 20 μs and wave speeds are 2–4 km/s during shear of layers a few mm in thickness subject to normal stress of 25 MPa and shear strains >30. Travel time data for apparatus calibration are fit with rational functions and root mean square error is used to assess uncertainty. Wave speed varies systematically with shear stress and increases with shear strain due to comminution, compaction, internal strain localization and shear fabric development.

Introduction

Laboratory experiments have been used for decades to measure the mechanical and elastic properties of Earth materials, including rock, soil, sediment, and ice.^{6,7,12,15,20,22,23,36,38,}46, 47, 48^,50,55,57,60 The existing literature provides a sound basis for understanding variations in elastic properties in Earth's crust.^5,14,16, 17, 18^{,21,24,25,28,30,43,45,49,50,53,59} However, determination of ultrasonic wavespeed and its evolution during deformation has proven difficult, and only limited data are available to illuminate the evolution of micromechanical processes and the role of shear fabric in governing elastic properties, rock strength, and fault zone processes. Elastic properties measured via ultrasonic waves provide sensitive proxies for processes that are difficult to observe directly, including changes in porosity, contact stiffness, and the development of foliation and shear fabric.^{4,8,11,18,19,21,30,51} Absolute velocity and elastic property measurements of rock and sediment are also of particular value because they inform upscaling efforts and allow direct comparison with field data and theoretical models.

While relative changes in velocity can be retrieved without knowledge of the absolute wavespeed when changes in time of flight and sample thickness are small,^14,44 lab experiments often involve large changes in elastic properties as deformation progresses,^52,54 which necessitates information about absolute wavespeed and travel time. Obtaining calibrations for absolute travel times during shear is difficult for two main reasons: 1) Shear coupling at the rock interfaces requires rough surfaces and results in an impedance contrast –between the rock and loading platen–that evolves with shear during the experiment, and 2) The shear interface includes rock material that compacts and evolves independently from the bulk rock samples, and thus calibrations require independent measurement of the interface and its evolution with shear. A related challenge – particularly in small, thin or layered samples is that the travel time within the test specimen is on the order of a few μs. Thus, measurement of elastic wave speed requires travel time calibration and cross correlation techniques to evaluate subtle changes. Indeed, in many experimental configurations the time taken for signals to propagate through forcing blocks, platens, or other elements of the testing system constitute a large fraction of the total travel time, and must be measured and corrected with high accuracy.^6,9,16,17,30 Although there are a few studies that have reported absolute values of elastic wave properties, the methods have not been extensively described.

Here, we describe a method to obtain absolute elastic wave velocities during direct shearing experiments. The method provides instantaneous velocities under load, which can be used to track the evolution of friction, compaction, permeability and other rock properties with progressive deformation. We describe the method using data from friction experiments performed in a double direct shear configuration, on synthetic fault gouge composed of a range of mixtures of Ca-montmorillonite and quartz powder, as well as on marine sediment that represents the protolith for material entrained along the subduction plate boundary offshore Sumatra, obtained by drilling during International Ocean Discovery Program (IODP) Expedition 362 (McNeill, Dugan, Petronotis, & Expedition 362 scientists, 2017). The purpose of this paper is to describe our methods to: 1) calibrate arrival times of ultrasonic waves through rock samples and the laboratory deformation apparatus, 2) calculate absolute ultrasonic velocities and elastic moduli for a range of materials tested, and 3) present an empirical approach for generalizing our method for a variety of loading configurations, deformation apparatus, and materials.