a-value: rename T to scaling_factor to allow for more flexibility and…

… avoid stupid names

seismostats/analysis/estimate_a.py

@@ -10,17 +10,19 @@ def estimate_a(magnitudes: np.ndarray,
                mc: float | None = None,
                m_ref: float | None = None,
                b_value: float | None = None,
-               T: float | None = None,
+               scaling_factor: float | None = None,
                ) -> float:
     """Estimate the a-value of the Gutenberg-Richter (GR) law.
 
     N = 10 ** (a - b * (m_ref - mc)) (1)
 
     where N is the number of events with magnitude greater than m_ref, which
-    occurred in the time interval T. T should be given as a float- to begit
-    precise, it should be the time interval scaled to the time-unit of interest.
-    E.g., if the number of events per year are of interest, T should be the
-    number of years in which the events occurred.
+    occurred in the timeframe of the catalogue. The scaling_factor should be 
+    given as a float- to be precise, and most of the time stands for the time 
+    interval scaled to the time-unit of interest. E.g., if the number of events 
+    per year are of interest, scaling_factor should be the number of years in 
+    which the events occurred. The a-value can also be scaled by volume or area 
+    using scaling_factor.
 
     If only the magnitudes are given, the a-value is estimated at the lowest
     magnitude in the sample, with mc = min(magnitudes). Eq. (1) then simplifies
@@ -33,8 +35,9 @@ def estimate_a(magnitudes: np.ndarray,
         m_ref:      Reference magnitude for which the a-value is estimated. If
                 None, the a-value is estimated at mc.
         b_value:    b-value of the Gutenberg-Richter distribution
-        T:          Relative length of the time interval in which the events
-                occurred (relative to the time unit of interest, e.g., years)
+        scaling_factor:  Scaling factor. For example: Relative length of the time 
+                interval in which the events occurred (relative to the time unit 
+                of interest, e.g., years)
 
     Returns:
         a: a-value of the Gutenberg-Richter distribution
@@ -57,8 +60,8 @@ def estimate_a(magnitudes: np.ndarray,
                 "b_value must be provided if m_ref is given")
         a = a - b_value * (m_ref - mc)
 
-    # scale to reference time-interval
-    if T is not None:
-        a = a - np.log10(T)
+    # scale to reference time-interval / volume / area ...
+    if scaling_factor is not None:
+        a = a - np.log10(scaling_factor)
 
     return a