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地震學 1935

《地震規模的儀器標度》

查爾斯·芮希特

給每一次地震一個數字——它最大那一擺的對數。

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In depth · the introduction

1935 年以前,你可以說一次地震「很猛」——卻說不出這一次比那一次更大。芮希特,把搖晃變成了一個數字。

把這個想法拆開看

地震的搖晃,離震源近就強、遠就弱,所以「這裡晃得多厲害」,講的既是地震、也是你站在哪兒。芮希特要的是一個屬於地震本身的數字。他的妙招:從地震儀劃下的那道曲線裡把它讀出來,再校正臺站離震源有多遠。

難處在於地震的差別極大——地面也許只動了千分之一毫米,也許動了整整一公尺。為馴服這個範圍,他用了對數:每升一級,地動就是十倍。這就是為什麼一次 M7 並非比 M6 大一點點——它是十倍的搖晃、約三十倍的能量。

它從哪裡來

芮希特是加州理工學院(帕薩迪納)一位年輕的物理學家,正在為南加州數百次被一套新建的、相同型號地震儀網記錄下來的小地震編目。受命發表這份目錄時,他需要一個公平的辦法給每次地震定大小。幾年前,日本地震學家和達清夫已經表明:把搖晃對距離作圖,就能給地震排序;芮希特與資深地震學家賓諾·古登堡共事,把這一想法做成了一套乾淨、對數、可重複的標度。「規模」這個詞,他借自天文學。

它為何重要

地震第一次能在同一條誠實的軸上比較——跨越國家、年代與不同的儀器。於是人們得以統計每種大小的地震多久發生一次,標出危險地震聚集在何處,並建立起決定我們如何設計樓房、橋梁與水壩的地震危險性科學。一個數字,成了地震科學與公眾報道共同的骨架。

就像星星的亮度

芮希特這個詞,取自看星星的人。天文學家用「星等」給恆星定亮度,每升一級是固定的亮度倍數,於是一顆暗星和一顆熾星能並排放在同一把短尺上。芮希特給地震如法炮製:每一級是十倍的搖晃,於是一陣勉強有感的微顫,和一場撕裂大陸的破裂,在數字上只隔幾格——紙面上很近,實情裡卻差著百萬倍。

上方是一道模擬的伍德-安德森地震圖,下方是一把對數振幅標尺。一個規模滑桿把記錄到的波包拉得更高,並讓一個標記沿標尺移動;標尺上等間距的規模刻度(M0 到 M9)所對應的振幅,每一級乘以十——1 微米、10 微米,一直到 1 公里。讀數給出 100 公里處的峰值振幅、以焦耳計的輻射地震能量,及其等效的 TNT 噸數。

它落在何處

芮希特的標度,接上了一脈學人——他們學著從地球的顫動與岩層裡讀懂它:從赫頓、萊爾在懸崖裡讀出深時(兩位都在本館中),到韋格納、赫斯拼出移動的大陸。規模,給了這門科學一個數字。今天的「芮氏規模」通常已是矩規模,公眾口中的「芮氏」也悄悄成了古登堡與金森的工作——但「用一個對數的數字,對應一次地震」這個想法,是他的。

The original document
Original source text
Charles F. Richter · Bulletin of the Seismological Society of America, 25(1): 1–32 · 1935
Magnitude, not intensity
Richter begins by separating two ideas everyday language runs together. Intensity — as in the Mercalli scale — measures how strongly the ground shook at one place; it is large near the source, fades with distance, and depends on local soil and buildings. He wanted instead a number for the shock itself: the same whoever measures it, wherever they stand. For it he borrowed a word from astronomy — magnitude.
The definition
The magnitude of any shock is taken as the logarithm of the maximum trace amplitude, expressed in microns, with which the standard short-period torsion seismometer would register that shock at an epicentral distance of 100 kilometers.
In plain terms: take the largest swing the standard instrument would draw at a fixed reference distance of 100 km, and read off its base-10 logarithm. A magnitude-0 shock is pinned to a one-micron trace — a thousandth of a millimetre; a magnitude-3 shock draws a millimetre; a magnitude-6 shock, a full metre. Every whole step is a tenfold jump in the trace.
The standard instrument and the distance correction
Two practical devices make the number repeatable. The standard recorder is the Wood–Anderson torsion seismometer (free period about 0.8 second, magnification about 2800), so any station can be reduced to a common yardstick. And because no station sits exactly 100 km from the source, Richter built an empirical table — the quantity −log A₀ — giving the trace a magnitude-0 shock would make at each distance, fitted from many Southern California earthquakes recorded at once across his network. Subtracting it removes distance and leaves a property of the source.
[ … ]
Richter is careful about the scale's reach: the corrections are calibrated to Southern California and to this instrument, and the zero point is a convention, set near the smallest shocks his network could record. He offers the scale as a practical, provisional tool — not a law of nature. The full thirty-two-page paper, with the distance table and worked examples, is at the source below.
Seismological Laboratory, Pasadena, California · 1935