Making seismic frequency measurements in the laboratory: construction of a system for measurement of the dynamic bulk modulus of rock at seismic frequencies

地震波在地球上传播的周期从远震的几秒到测井的几毫秒不等，典型的地震勘探发生在大约5赫兹到250赫兹的狭窄频率范围内。这些“低”频率与“高”频率形成对比，“高”频率通常约为1兆赫（10^6赫兹），几乎所有的P波和S波速度和衰减的实验室测量都使用高频。这是一个严重的问题，因为观测到的这些岩石的地震速度和衰减，特别是那些含有孔隙流体的岩石，很大程度上取决于频率。这种频率依赖性被称为速度色散，当我们使用主要使用超声波（MHz）频率开发的物理性质框架时，色散限制了我们正确解释地震（5 Hz至250 Hz）和测井（20 kHz）观测结果的能力。我们建议通过开发一种新系统来克服这一限制，使我们能够在实验室中对真实地震频率下的地震特性（特别是动态压缩性）进行测量。该方法将采用“强制振荡”技术来测量岩石样品在受到小的振荡压力变化时体积的变化。通过分析单元内产生的压力，不仅可以确定与给定频率下地震速度直接相关的参数，还可以确定相应的地震衰减。这种方法长期以来一直被聚合物科学家用来研究塑料的详细特性。虽然将常规超声实验室测量与地震观测相比较的问题是众所周知的，但全世界只有少数小组进行这些测试，而且所有这些小组都是测量互补剪切特性。该系统将是地球科学和多孔介质研究领域中唯一能够在实际应力和孔隙压力条件下直接获得这种频率下的动态压缩率（或体积模量）的系统。这些信息将使我们能够对现有的波传播理论进行新的基本测试，并更多地了解地震频率下实际岩石的非弹性特性。

Seismic waves travel in the earth with periods from many seconds for teleseisms to milliseconds in  logging,  typical seismic exploration occurs over a narrow range of frequencies from about 5 Hz to 250 Hz. These 'low' frequencies contrast with the 'high' frequencies, typically of about 1 MHz (10^6 Hz), employed in almost all laboratory measurements of P and S wave velocities and attenuation.  This is a serious problem as the observed seismic velocities and attenuations of such rocks, and particularly those rocks hosting pore fluids, can depend strongly on frequency. This frequency dependence is known as velocity dispersion, and the dispersion limits our abilities to properly interpret seismic (5 Hz to 250 Hz) and well logging  (20 kHz) observations when we use a physical property framework developed primarily using ultrasonic (MHz) frequencies.  We propose to overcome this limitation by developing a new system to allow us to make make measurements in the laboratory of the seismic properties (specifically the dynamic compressibility) at truly seismic frequencies.  The method will employ a 'forced oscillation' technique to measure the changes in the volume of the rock samples while they are subject to small oscillating pressure variations. By analysis of the resulting pressures within the cell, one is able to determine not only parameters that directly relate to the seismic velocity at a given frequency but also the corresponding seismic attenuation.  This method has long been used by polymer scientists to study the detailed characteristics of plastics. Although the problems with comparing conventional ultrasonic laboratory measurements to seismic observations is well known, there are only a small number of groups worldwide carrying out these tests and all of these groups are measuring complementary shear properties.  This proposed system will be the only one within the geoscience and porous media research communities capable of directly obtaining the dynamic compressibiltiy (or bulk modulus) at such frequencies under realistic conditions of stress and pore pressure. This information will allow us to  both carry out new fundamental tests of existing theories of wave propagation and to learn more about the anelastic properties of real rocks at seismic frequencies.