The recurrence interval (
R) of earthquakes from a given fault-segment is related to the long-term slip-rate (
S) and the displacement accompanying an earthquake (
D). The relation is expressed as
R=
D/
S [WALLACE (1970)], when aseismic fault creep is disregarded.
D has a relation with the earthquake magnitude
M as log
D(meter)=0.6
M-4.0 for Japanese inland earthquakes. Then, the relation
R to
M is expressed as log
R=0.6
M-4.0-log
S.
It is proposed here that a given fault-segment has a constant value in
D through time during late Quaternary period. Values
D and
M may be different between different faults or segments, but there is a proper value
D0 or
M0 for a given fault or its segment. Historic records on Japanese earthquakes seem consistent with this assumption.
D0 or
M0 is obtained from data of historic earthquakes or from a unit offset of geologic references.
Fault length
L is proportional to a dimension of strain domain, and it represents the maximum magnitude from the fault. The relation of
L to earthquake magnitude
M is log
L(kilometer)=0.6
M-2.9 for Japanese inland earthquakes. Then, maximum magnitude
ML from a fault is expressed as
ML=(1/0.6)log
L+4.85.
When a given fault or its segment has no earthquake during at least
t years up to the present, the accumulated earthquake energy during
t years is expressed as
Mt=(1/0.6)log(
t·
S)+6.67.
Thus, a probable maximum magnitude
Mmax from a given fault or its segment is expressed as
Mt<
Mmax<
ML. Examples of the above procedure and its result are described.
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