California
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PmP phase identification using waveform stacking method (`Richards-Dinger & Shearer, 1997 <https://doi.org/10.1029/97JB00883>`_)
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.. figure:: /photos/Richards_Shear_1997_method.png
   :alt: PmP phase identification through waveform stacking.
   :width: 100.0%
   :align: center

   By stacking waveforms within reflection point bins, it is possible to measure the U-shape curve, 
   i.e., the PmP-first P differential traveltimes with respect to distances. 
   Then the U-shape curves can be fitted with two free parameters: Moho depth and P-wave velocity in the uppermost mantle.


**Technical workflow:**

1. Aligning the collected event waveforms to the first-P arrivals;
2. Based on regional 1D HK model (`Hadley & Kanamori, 1977 <https://doi.org/10.1130/0016-7606(1977)88%3C1469:SSOTTR%3E2.0.CO;2>`_),
   conducting the focal depth correction to the aligned waveforms, making the PmP arrivals solely 
   dependent on the epicentral distances; 
3. Binning the waveforms based on the reflection points;
4. Stacking the waveforms within each bin to enhance the PmP signals; 
5. Measuring the differential traveltimes and fitting the U-shape curves to 
   estimate the Moho depth and P-wave velocity in the uppermost mantle.


**Results of Moho depth and uppermost mantle P-wave velocity estimation in Southern California:**

.. figure:: /photos/Richards_Shear_1997_result.png
   :alt: Moho depth and uppermost mantle P-wave velocity estimation results.
   :width: 100.0%
   :align: center