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地震学 1935

《地震震级的仪器标度》

查尔斯·里克特

给每一次地震一个数字——它最大那一摆的对数。

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In depth · the introduction

1935 年以前,你可以说一次地震「很猛」——却说不出这一次比那一次更大。里克特,把摇晃变成了一个数字。

把这个想法拆开看

地震的摇晃,离震源近就强、远就弱,所以「这里晃得多厉害」,讲的既是地震、也是你站在哪儿。里克特要的是一个属于地震本身的数字。他的妙招:从地震仪划下的那道曲线里把它读出来,再校正台站离震源有多远。

难处在于地震的差别极大——地面也许只动了千分之一毫米,也许动了整整一米。为驯服这个范围,他用了对数:每升一级,地动就是十倍。这就是为什么一次 M7 并非比 M6 大一点点——它是十倍的摇晃、约三十倍的能量。

它从哪里来

里克特是加州理工学院(帕萨迪纳)一位年轻的物理学家,正在为南加州数百次被一套新建的、相同型号地震仪网记录下来的小地震编目。受命发表这份目录时,他需要一个公平的办法给每次地震定大小。几年前,日本地震学家和达清夫已经表明:把摇晃对距离作图,就能给地震排序;里克特与资深地震学家本诺·古登堡共事,把这一想法做成了一套干净、对数、可重复的标度。「震级」这个词,他借自天文学。

它为何重要

地震第一次能在同一条诚实的轴上比较——跨越国家、年代与不同的仪器。于是人们得以统计每种大小的地震多久发生一次,标出危险地震聚集在何处,并建立起决定我们如何设计楼房、桥梁与大坝的地震危险性科学。一个数字,成了地震科学与公众报道共同的骨架。

就像星星的亮度

里克特这个词,取自看星星的人。天文学家用「星等」给恒星定亮度,每升一级是固定的亮度倍数,于是一颗暗星和一颗炽星能并排放在同一把短尺上。里克特给地震如法炮制:每一级是十倍的摇晃,于是一阵勉强有感的微颤,和一场撕裂大陆的破裂,在数字上只隔几格——纸面上很近,实情里却差着百万倍。

上方是一道模拟的伍德-安德森地震图,下方是一把对数振幅标尺。一个震级滑块把记录到的波包拉得更高,并让一个标记沿标尺移动;标尺上等间距的震级刻度(M0 到 M9)所对应的振幅,每一级乘以十——1 微米、10 微米,一直到 1 千米。读数给出 100 公里处的峰值振幅、以焦耳计的辐射地震能量,及其等效的 TNT 吨数。

它落在何处

里克特的标度,接上了一脉学人——他们学着从地球的颤动与岩层里读懂它:从赫顿、莱尔在悬崖里读出深时(两位都在本馆中),到魏格纳、赫斯拼出移动的大陆。震级,给了这门科学一个数字。今天的「里氏震级」通常已是矩震级,公众口中的「里氏」也悄悄成了古登堡与金森的工作——但「用一个对数的数字,对应一次地震」这个想法,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