Factors in the Behavior of Ground Water in a Ghyben-Herzberg System 
Chester K. Wentworth 1 
INTRODUCTION 
The hydrostatic relationship between 
fresh ground water and sea water along 
coasts and in many islands has been recog¬ 
nized for about 60 years, since the work of 
Badon Ghyben (1889) and of Herzberg 
(1901). It has been studied in various parts 
of the world but perhaps nowhere are there 
more data concerning it than in Hawaii. In 
the course of the Pacific war the occurrence 
of ground water on many islands has been of 
crucial importance and the concept of a 
Ghyben-Herzberg lens has become widely 
circulated. 
Rain falling on the surface of an ideally 
permeable circular island in the ocean is in 
part absorbed into the ground. This water 
percolates downward and accumulates at the 
surface of the salt water at sea level. The 
fresh water builds up to a height above sea 
level determined by its amount and by the 
permeability of the island rock, and also 
presses downward until it extends about 40 
times as far below sea level as it does above 
sea level. The upper surface of such a 
ground-water body can be shown to be a 
domed one, and the lower surface is deeply 
curved because of the ratio of 1 to 40. The 
fresh-water body thus approximates the 
form of a double convex lens, with the cir¬ 
cular edge coinciding with the circular coast 
(Fig. 1). This is the Ghyben-Herzberg 
lens, and the model on which the theory 
rests. In many places, owing to differences 
in rock structure, only a portion or sector of 
the lens will be developed, but the principle 
applies equally well. 
1 Geologist, Board of Water Supply, Honolulu, 
Hawaii. Manuscript received February 6, 1947. 
The Ghyben-Herzberg balance is not by 
any means universal along ocean coasts and 
one may presume that it is well exemplified 
along only a small fraction of continental 
coasts. Otherwise it would probably be bet¬ 
ter known. Its somewhat limited occurrence 
is due to the requirement of rocks within a 
certain range of permeability, sufficient rain¬ 
fall, and lack of specialized structure in the 
rocks. The rock structure must in the main 
be fairly homogeneous and be isotropically 
permeable if a well-characterized Ghyben- 
Herzberg system is to develop. 
Fig. 1 . Section through an ideal permeable 
island in the ocean, showing the form of the fresh¬ 
water body known as the Ghyben-Herzberg lens. 
Owing to scale limitations the bottom of the lens 
is shown only about 10 times as thick as the top 
part, instead of the 40-fold relation that occurs in 
nature. 
In Hawaii, the principle of balance has 
become well known because of its remark¬ 
able development in the Honolulu-Pearl 
Harbor areas and in a few other localities on 
Oahu (Alexander, 1908; Andrews, 1909; 
Palmer, 1927: 17-20). It is not present or 
at least is scarcely demonstrable along about 
half of the windward coast because the rock 
is of low permeability and unsuitable struc¬ 
ture. It is also much less developed on most 
of the other islands of Hawaii. Practical im- 
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