September 27, 2013

Hirayama (1934): The first scientific paper on Magnetotellurics(English translation: H. Toh, Kyoto Univ.)

地電流及び地磁気変化の間の関係に就いて(1)On the Relations between the Variations of Earth
Potential Gradient and Terrestrial Magnetism.(1)By M. HIRAYAMA.

平	  山	  	  	  操１．緒	  	  	  言	 1. Introduction	  地電流は從來各地にて測定せられ，地磁氣，The telluric currents have been measured at
空中電氣，太陽黑點及び氣象要素等との關係 many places on the earth so far. There haveについても其の研究が少くなく，就中地磁氣 been not a few studies on their relation to theとの關係の密接なことは周知の事で，G. B. geomagnetic field, the atmospheric electricity,Airy(2), W. Ellis(3)等によりて地電流の東西分 the sunspot number or various meteorological
力及び南北分力の變化は夫々地磁氣の南北 factors etc. In particular, the relation to the
分力及び東西分力の變化に酷似してゐるこ geomagnetic field is known to be very close. G.とが注意され，S. Chapman, T. T. Whitehead(4) B. Airy(2), W. Ellis(3) and so on noted that
は地磁氣の鉛直分力の變化より地電位差の variations of the east-west and north-south
東西分力及び南北分力を計算し，又先般 S. E. components of the telluric current are veryForbush(5) は地電位差の鉛直分力の急激な變 similar to those of the north-south and east-west
化は概ね同時に，地磁氣の水平分力の變化を components of the geomagnetic field,伴つていることを指摘して居る．其の他 W. respectively.
S. Chapman and T. T.
van Bemmelen(6), L. A. Bauer 等の研究がある． Whitehead(4) calculated the east-west andnorth-south components of the geoelectric
potential difference from variations of thevertical geomagnetic component. Recently, S.
E. Forbush(5) also pointed out that rapid
variations of the vertical geoelectric component
are often associated with the simultaneous
variations of the horizontal geomagneticcomponent.
The studies by W. van(6)
Bemmelen , L. A. Bauer and so on can be listed
as the research on the relation as well.
(1) 中央氣象薹彙報(1) Bulletin of the Central Meteorological Observatory(2) G. B. Airy: Phil. Trans. R. S. vol. 158, (1868) 465. 原文未讀(2) G. B. Airy: Phil. Trans. R. S. vol. 158, (1868) 465. The text unread.

(3) W. Ellis: Proc. R. S. vol. 52 (1892), p. 191. 原文未讀(3) W. Ellis: Proc. R. S. vol. 52 (1892), p. 191. The text unread.

(4) S. Chapman and T. T. Whitehead: Transact. Cambridge Phil. Soc. 22,(4) S. Chapman and T. T. Whitehead: Transact. Cambridge Phil. Soc. 22,

Nr 25, 463, 1922.

Nr 25, 463, 1922.

(5) S. E. Forbush: Terr. Magn. vol. 38, No. 1, 1933.

(5) S. E. Forbush: Terr. Magn. vol. 38, No. 1, 1933.

(6) W. van Bemmelen: Proc. K. Akad. Amsterdam 1908. 原文未讀(6) W. van Bemmelen: Proc. K. Akad. Amsterdam 1908. The text unread.

1	  當觀測所に於ては昨年八月以來，地電位差及び地磁氣の變化を連續記録させてゐるが，その記象紙を見るに，地電位差の南北分力は，其の感度が東西分力に比して甚だ小さい爲め，地磁氣との關係も見出し難いが，東西分力の変化は降雨，降雪の際の如き狹範圍の變化を除けば，第一圖に其の一例を示せる如く殆ど悉く相對應し，地磁氣の水平分力が増大すると地電位差は東が高くなつてゐる．	  依つて筆者は過去一ヶ年の材料により，兩者の變化の間に介在する關係を求めんと試みた

Variations of the geoelectric potentialdifference and the geomagnetic field have beenrecorded continuously at this observatory sincelast August. The chart records show that therelation between the geoelectric andgeomagnetic fields is difficult to recognize inthe north-south geoelectric component, because
its sensitivity is very small compared with thatof the east-west component.
However,variations of the east-west geoelectriccomponent almost always correspond to thoseof the geomagnetic field as an example shownin Fig. 1, except for very limited periods at thetime of rain- or snow-fall. If the horizontal
geomagnetic component increases, the east
geoelectic potential gets higher.
The author, therefore, tried to reveal therelation between them using the data of the past
one year.	  この圖は昭和八年七月七日の記象紙の一部で，兩者の變Fig. 1 A part of the chart record on July 7, 1933.

It is

化の相對應して居るのが注意され，又十七時と十八時の間

noteworthy that variations of the geomagnetic fieldに於て三十分位の週期に，三分位の週期が重疊し，その振(upper) and the geoelectric field (lower) correspond

幅の比が週期により著しく異なる好例を示す．

well with each other.

From 17 through 18 GMT,

variations of about 3-min period are superimposedon those of about 30-min period.

It is a good

example of the intense period dependence of theamplitude ratio of the geoelectric field to thegeomagnetic field.

２．調査の方法及び結果	 
2. Method of Investigation and the Results	  記象紙に現はれる變化を週期的及び非週
Variations appeared in the chart records
期的の二變化に分け，前者にありては一群の were classified into periodic and aperiodic
週期的變化があるとき，其等の平均の振 v a r i a t i o n s . T h e a m p l i t u d e a n d p e r i o d2

of the former were determined as the respective
averages of a series of periodic variations.
Those of the latter were regarded as the averagesof AB and BC for amplitude, and the timeinterval AC for period (see Fig. 2). The
amplitudes and periods thus defined were readfrom the chart records. However, there were
not a few aperiodic variations that were difficult
to distinguish them from periodic variations as
manifested in Fig. 2. The close resemblance ofthe two emerged especially in the variations withperiods longer than 60 min.

幅及び週期を夫々其の振幅及び週期とし，後者にては，振幅としては AB，BC の平均を，又 time interval AC を週期と考へ，（第二圖參照），これ等を記象紙より讀み取った．然し
非週期的變化と雖も，第二圖の如く週期的變化とも看做されるやうなものも少くなく，六十分以上の變化には殊に多かつた．

Fig. 2 (No captions were given in the original text.)
Variations of the geoelectric potential	  又通常の日の記象紙では一粍が地磁氣では三分，地電位差では四分になつて居るので，difference and the geomagnetic field have been
三分以下の短い週期の變化は早廻しにした recorded continuously at this observatory sincelast August. The chart records show that the
ものより求めた．（毎月四日間，國際日に早relation
betweenthegeoelectricand廻しにしたものは一分が）地磁氣及び地電位
geomagnetic fields is difficult to recognize in the差共に四粍である．）
north-south geoelectric component, because its	  又地電位差の東西分力の日變化を見るに， sensitivity is very small compared with that of
地磁氣の水平分力，鉛直分力の日變化に似て the east-west component. However, variations
居り，水平分力に對しては若干の位相差があ of the east-west geoelectric component almost
るが，鉛直分力に對しては殆ど位相差が認め always correspond to those of the geomagnetic
られず極めて類似せる變化を示して居るこ field as an example shown in Fig. 1, except forvery limited periods at the time of rain- orと第三圖の通りである．それで記象紙より直snow-fall.
If the horizontal geomagnetic
接讀み取れない位の長い週期（約二時間以component increases, the east geoelectic上）の變化は，極めて靜穏な日を選んで調和 potential gets higher.
分析をなし補足した．
The author, therefore, tried to reveal therelation between them using the data of the past
one year.
3Fig. 3 This figure shows the averaged daily variations ofJanuary 5 and February 17.

3. Theoretical Calculation
The chart records of the geoelectric
potential difference showed that its east-westcomponent was mostly accompanied bysimultaneous short-period variations of thehorizontal geomagnetic component withnegligible variations in other geomagnetic
components, while the declination and thedownward geomagnetic component also varied
simultaneously at longer periods especially fordaily variations. I, therefore, proceeded to mycalculation by assuming the east-west
geoelectric component being induced solely by
thoseofthenorthward
geomagneticcomponent(7) (here I also assumed that thegeographical north and the geomagnetic northwere identical.). I applied the results of mycalculation to relatively short periods (shorterthan 80 minutes).

３．理論的計算	 	  地電位差の記象紙を見るに，東西分力の比較的長い週期の變化殊に日變化に於ては，同時に地磁氣の鉛直分力及び偏角の變化も見られるが，短い週期の變化にては水平分力の變化のみで他の要素の變化は顯著でないことが多い．依つて地電位差の東西分力の變化は地磁氣の南北分力（地理學上の北と磁力の指す北とが一致するものとする．）即ち水平分力の變化のみによって誘起される (7) ものとして計算し，其の結果と比較的短い週期（八十分以下）の場合に適用して見た．	  (7) 寺田博士は地磁氣の短週期變化に於ける南北分力と鉛直分力	  	  (7) Dr. Terada calculated the amplitude ratios and phase differencesの比及び位相差を説明するに際しこれ等の變化は地中の電流に依	  	  between the northward and downward components of the short-periodるものとして計算されてゐる．	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  geomagnetic variations assuming them being induced in the Earth.
T. Terada: Journ. Coll. Sci. Tokyo Imp. Univ. Vol. XXXVII, Art. 9. 	  	 4T. Terada: Journ. Coll. Sci. Tokyo Imp. Univ. Vol. XXXVII, Art. 9.

	  先づ地表面を無限に廣い平面と考へ，x軸を北に，y 軸を西に，z 軸を鉛直下方にとり z の負側は眞空で，正側は一様な傳導率に，誘磁率µをもつ導體であると假定し，更に電氣力 E は x 軸に無關係，磁力 H は y，z軸に無關係であるとする．すると Ex = 0, Hy= Hz = 0 と考へたから，maxwell の基本方程式は次のやうになる．但し E 及び H の x, y, z成分を夫々Ex, Ey, Ez 及び Hx, Hy, Hz とする．

First, suppose the ground surface to be an
infinitely large plane, and take x-, y- and z-axis
to the northward, westward and downward
directions, respectively. Also assume that theupper half-space (z < 0) is occupied by vacuum,
while the lower (z > 0) is a uniform conductor	 	 	 (1), (2)より	 
where Ex, Ey, Ez and Hx, Hy, Hz are the x-, yand z-component of E and H, respectively.
Eqs. (1) and (2) are combined to give:

今 Hx∝e -pt+i(my+qt)+ z とするとSuppose Hx∝e -pt+i(my+qt)+ z, then it is readily
shown:

with a permeability of µ. I further assume thatthe electric field, E, is independent of x,
whereas the magnetic field, H, is independentof both y and z. It follows that Ex = 0, Hy = Hz= 0, which gives the following Maxwellequations;αα

If we write α = -( α ’ + i β ’), α ’ and β ’ arerespectively given by:となる．依つて(2)より

It follows from Eq. (2) that;

或は實數部分をとりor by taking the real parts of E and H;

但しwith5	 Hence, the amplitude ratios are given by:

故に振幅の比は	 	 	 If we consider the case of very weak decay (p =0), the former ratio becomes:	  今誘磁率 µ = 1 とし，κ の値としては地
表近くでは 10-13－10-14(emn)の間にて變化すると云ふ W. J. Rooney 及び O. H. Gish(8)の測定の結果を採用し 5×10-14emn と考へる．

Now I assume µ = 1, and consider κ =	 簡單に減衰しない場合（p = 0）を考へれば

5 x 10-14emu adopting the results ofmeasurements by W. J. Rooney and O. H.
Gish(8) who claimed that κ varied between 10-13and 10-14(emu) in the vicinity of the Earth’s
surface.
According to the record by S. E.
Forbush, the ratio of the downward geoelectriccomponent (Ez) to the northward geomagneticcomponent (Hx) is approximately 8 x 102
mV/km/γ . It follows from Eq. (9) that thewavelength λ (= 2π /m) becomes 1.3 x 104km.
If m is thus small, m4 is negligible comparedwith 16π 2κ 2µ2q2 so far as the period inconcern is not very long. On the other hand, if
1−
Eym = 0, Eq. (10) is reduced to∝ T 2 , which
Hx
Eyis close to the observed curve of∝ T − 0.4 .
Hx	  S. E. Forbush の record より地電位差の鉛直分力の振幅（Ez）と地磁氣の水平分力の振幅（Hx）との比を求めると，大略 8×10
mu/km/γ程度(9)である．依つて(9)式より波長λ（= 2π / m）は 1・3×104 粁となる．m がこの程度であるとすると，週期の餘り大きくない範圍では m4 は 16π 2κ 2µ2q2 に比して省略することが出來る．又他方に於て m = 01−Eとすると(10)式より y ∝ T 2 となり，實際
Hx
Eの曲線を表はす y ∝ T − 0.4 に近いものとな
Hx(9)

る．この點より考へても 16π 2κ 2µ2q2 が主項で m4 が補正項であると想像される．依つて(10)式を用ひ

Ey
Hx∝

This also supports that 16π 2κ 2µ2q2 is theleading term while m4 is the correcting term.

µqより振幅の比を計4πκ

Hence, using

算すると次の通りである．

EyHx∝µqderived from Eq.
4πκ(10), the amplitude ratio is calculated asfollows:	  (8) W. J. Rooney and O. H. Gish: Earth-resistivity survey at(8) W. J. Rooney and O. H. Gish: Earth-resistivity survey at Huancayo．

Huancayo. Revu. Terr. Mag. 35, 61-72 (1930).	  	  	  	  	  	  	  	  	  	  	 Revu. Terr. Mag. 35, 61-72 (1930).	  (9) この値は僅かの data と而も rough を讀みとりから出したも(9) This value is based on not only few data but also rough reading, andので，非常に不確實ではあるが，大體の order を知るには差支へ

thus very uncertain.

ないと思ふ．

order estimation.

6

However, it is considered to be enough for rough*This tabulates periods in minute (the upper row) and the ratios Ey/Hxin mV/km/nT. No captions were given in the original text.	  この値を實際の値と比較し(10)式の展開式

To compare the tabulated values withthe observation, I derived the following valuesfor λ using the expanded form of Eq. (10);	 
by substituting the observed values for	 
Eyon
Hx
L.H.S. and the calculated values above for

Eyµqより左邊は實測値を，は上の計算
Hx4πκµq.
4πκ

値を用ひて λ の値を求めると次の如くである．

*This table shows periods in minute (the upper row) and thewavelengths in 103 km. No captions were given in the original text.

These values are very close to the	  この値は寺田博士が地磁氣の短週期變化
value of 1200km which Dr. Terada calculatedに於ける南北分力と鉛直分力との比より求from the ratio of the northward to downward
められた 1200 粁に甚だ近いものである．
components of the short-period geomagnetic	  今波長を 1600 粁と假定し，(10)式よりvariations.
Ey/Hx を計算して實測の結果と比較して見Now assuming the wavelength to beるに次に示せる如く甚だよく一致して居る． 1600km, comparison of the observation with
Ey/Hx calculated from Eq. (10) gives very good
agreement as follows:*This compares the calculated (the middle row) and observed (thebottom row) ratios Ey/Hx in mV/km/nT. The upper row shows periods
in minute. No captions were given in the original text.

The relation between the two,therefore, can be approximated by Eq. (10) in
the case of relatively short-period variations.
However, as for long-period variations such as
daily variations, Hy and Hz terms should befurther added to the fundamental equation,
whereas the Earth should be treated as a sphereat the same time.	  この様に比較的短い週期の變化にありては兩者の關係は略ゝ(10)式にて滿足されるであらうと考へられるが，日變化の如き長い週期の變化にありては，基本方程式に更に Hy, Hz の項を加へ，且つ地球を球と看做さねばならぬと思はれる．

7

４．結論	 4. Conclusions	  以上を要約すれば次の通りである．
Everything described above can be	  地電位差の東西分力の變化は地磁氣の水 summarized as follows:
平分力の變化と密接な關係があり，前者の後Variations of the east-west geoelectric者に對する變化の大きさの割合は，變化の緩 component are closely related with those of the
急によって異なり，大體に於て T -0.4 比例す horizontal geomagnetic component, and the ratioるものである．而してこれ等兩者の變化が of the former variation magnitude to the latter ismaxwell の基本方程式に依って結び付けられ dependent on their periods, i.e., approximatelyて居るものとして計算した結果はよく實際 proportional to T -0.4. The calculated ratiosと一致して居る．
assuming that those variations of the two	  終わりに臨み，お閲讀を賜つた岡田臺長先 components are tied with each other by the生並びに，終始有益なお助言に預かつた畠山 Maxwell equations coincide well with the actual
所長，お代読下された倉石先生に深く感謝致 observations.
します．	  	  	  	  	  	  	  	  	  	  	  	  	  （終）In the end, I would like to express my（昭和八年八月	  於臨時豊原地磁氣觀測所） sincere thanks to Dr. Okada, Head of the
Meteorological Observatory of Japan who
kindly made a critical review of the present
manuscript, Dr. Hatakeyama, Director of theToyohara Temporary Geomagnetic Observatory,
whose comments were very useful throughout
this study and Dr. Kuraishi who were helpful
enough to read through this paper.
(End)(August of 1933

Written at the Toyohara Temporary Geomagnetic Observatory)＊To cite Hirayama's (1934) original paper, use:
Hirayama, M. (1934), On the relations between the variations of Earth potential gradient and terrestrial
magnetism, J. Meteorol. Soc. Jpn. Ser. II, Vol. 12, No. 1, 16-22 (in Japanese with English abstract)．
To download, use https://www.jstage.jst.go.jp/article/jmsj1923/12/1/12_1_16/_pdf.
[His original paper in Japanese is included here by courtesy of Meteorological Society of Japan.]8