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When an earthquake is sourced, the coulomb stresses that originate from the source (due to the P-wave) are bounded by two perpendicular planes, which make up the 2 planes in an earthquake focal mechanism. Both are mathematically equivalent. Thus, without independent knowledge of which plane sourced the earthquake, either could be the "fault". Therefore, the axillary plane represents the mathematical equivalent to the source of the earthquake and is represented in earthquake focal mechanisms for a variety of reasons (helps visualize the style of faulting, disambiguity, completeness, etc.)

It is extremely common for seismologists to calculate the focal mechanism without knowing which plane is the fault and which is the auxillary plane

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