A self‐similar model for sedimentary rocks with application to the dielectric constant of fused glass beads

电介质 渗透(认知心理学) 球体 凝聚态物理 幂律 多孔性 电导率 沉积岩 材料科学 渗流阈值 物理 矿物学 几何学 电阻率和电导率 地质学 数学 复合材料 量子力学 统计 天文 古生物学 神经科学 生物
作者
Parongama Sen,C. M. Scala,Morrel H. Cohen
出处
期刊:Geophysics [Society of Exploration Geophysicists]
卷期号:46 (5): 781-795 被引量:955
标识
DOI:10.1190/1.1441215
摘要

We develop a theory for dielectric response of water‐saturated rocks based on a realistic model of the pore space. The absence of a percolation threshold manifest in Archie’s law, porecasts, electron‐micrographs, and general theories of formation of detrital sedimentary rocks indicates that the pore spaces within such rocks remain interconnected to very low values of the porosity ϕ. In the simplest geometric model for which the conducting paths remain interconnected, each grain is envisioned to be coated with water. The dielectric constant of the assembly of water‐coated grains is obtained by a self‐consistent effective medium theory. In the dc limit, this gives Maxwell’s relation for conductivity σ of the rock [Formula: see text], where [Formula: see text] is the conductivity of water. In order to include the local environmental effects around a grain, a self‐similar model is generated by envisioning that each rock grain itself is coated with a skin made of other coated spheres; the coating at each level consists of other coated spheres. The self‐consistent complex dielectric constant [Formula: see text] is given in this model in terms of that of water [Formula: see text] and of rock [Formula: see text], by [Formula: see text] for spherical particles. This gives, in the dc limit, [Formula: see text]. For nonspherical particles, the exponent m in Archie’s law [Formula: see text] is greater than 3/2 for the plate‐like grains or cylinders with axis perpendicular to the external field and smaller than 3/2 for plates or cylindrical particles with axis parallel to the external field. Artificial rocks with a wide range of porosities were made from glass beads. We present data on the glass bead rocks for dc conductivity and the dielectric constant at 1.1 GHz. The data follow the conductivity and the dielectric responses given by the self‐similar model. The present theory fails to explain the salinity dependence of [Formula: see text] at lower frequencies.
最长约 10秒,即可获得该文献文件

科研通智能强力驱动
Strongly Powered by AbleSci AI
更新
PDF的下载单位、IP信息已删除 (2025-6-4)

科研通是完全免费的文献互助平台,具备全网最快的应助速度,最高的求助完成率。 对每一个文献求助,科研通都将尽心尽力,给求助人一个满意的交代。
实时播报
昏睡的蟠桃应助liars采纳,获得150
1秒前
斯文败类应助荒野风采纳,获得10
1秒前
1秒前
hrzmlily完成签到,获得积分10
3秒前
顽主完成签到,获得积分10
4秒前
义气访曼完成签到 ,获得积分10
5秒前
时尚战斗机完成签到,获得积分10
5秒前
7秒前
亦玉完成签到,获得积分10
7秒前
Philadelphus完成签到,获得积分20
9秒前
9秒前
wsh完成签到 ,获得积分10
10秒前
luyue9406完成签到,获得积分10
10秒前
luochen完成签到,获得积分10
10秒前
酷波er应助奶黄包采纳,获得10
11秒前
ROMANTIC完成签到 ,获得积分10
11秒前
Hancock完成签到 ,获得积分10
12秒前
luyue9406发布了新的文献求助10
13秒前
Akim应助小王采纳,获得10
13秒前
甜蜜的楷瑞应助zqfxc采纳,获得10
15秒前
Hello应助花雨落123采纳,获得10
17秒前
18秒前
19秒前
柚仝完成签到 ,获得积分10
19秒前
贾明灵完成签到,获得积分10
19秒前
未来学术司马懿应助LIUYONG采纳,获得10
20秒前
Dops完成签到,获得积分10
22秒前
票子发布了新的文献求助10
23秒前
晚风完成签到 ,获得积分10
23秒前
坚强莺发布了新的文献求助10
23秒前
无奈曼云完成签到,获得积分10
24秒前
不会吹口哨完成签到,获得积分10
24秒前
易槐完成签到,获得积分10
25秒前
情怀应助和谐的梦蕊采纳,获得10
25秒前
26秒前
喜悦的飞机完成签到,获得积分10
27秒前
27秒前
27秒前
29秒前
忘川完成签到,获得积分10
29秒前
高分求助中
【提示信息,请勿应助】关于scihub 10000
Les Mantodea de Guyane: Insecta, Polyneoptera [The Mantids of French Guiana] 3000
徐淮辽南地区新元古代叠层石及生物地层 3000
The Mother of All Tableaux: Order, Equivalence, and Geometry in the Large-scale Structure of Optimality Theory 3000
Global Eyelash Assessment scale (GEA) 1000
Picture Books with Same-sex Parented Families: Unintentional Censorship 550
Research on Disturbance Rejection Control Algorithm for Aerial Operation Robots 500
热门求助领域 (近24小时)
化学 材料科学 医学 生物 工程类 有机化学 生物化学 物理 内科学 纳米技术 计算机科学 化学工程 复合材料 遗传学 基因 物理化学 催化作用 冶金 细胞生物学 免疫学
热门帖子
关注 科研通微信公众号,转发送积分 4038426
求助须知:如何正确求助?哪些是违规求助? 3576119
关于积分的说明 11374556
捐赠科研通 3305834
什么是DOI,文献DOI怎么找? 1819339
邀请新用户注册赠送积分活动 892678
科研通“疑难数据库(出版商)”最低求助积分说明 815029