update

.gitignore

@@ -8,3 +8,5 @@ results*
 fm_data
 hash_results
 hash.log
+picks*
+hashpy2*

docs/README.md

@@ -30,7 +30,7 @@ The class will be a combination of lectures and hands-on exercises. We will use
 | 10/09 | [Earthquake Location & Relative Location](https://ai4eps.github.io/EPS207_Observational_Seismology/lectures/06_location_and_relocation.html) |
 | 10/16 | [Earthquake Statistics](https://ai4eps.github.io/EPS207_Observational_Seismology/lectures/07_statistics.html) |
 | 10/23 | [Focal Mechanism & Moment Tensor](https://ai4eps.github.io/EPS207_Observational_Seismology/lectures/08_focal_mechanism_and_momemt_tensor/) |
-| 10/30 | [Focal Mechanism & Moment Tensor]() |
+| 10/30 | [Focal Mechanism Inversion](https://ai4eps.github.io/EPS207_Observational_Seismology/lectures/09_focal_mechanism/) |
 | 11/06 | [Ambient Noise]() |
 | 11/13 | [Seismic Tomography]() |
 | 11/20 | [Full-waveform Inversion]() |

docs/lectures/09_focal_mechanism.md

@@ -0,0 +1,80 @@
+---
+marp: true
+paginate: true
+theme: gaia
+backgroundColor: #fff
+---
+
+# Focal Mechanism Inversion
+
+Notebooks: [codes/focal_mechanism.ipynb](codes/focal_mechanism/)
+
+---
+
+### Fault plane
+
+![w:500](./assets/Screenshot%202023-10-29%20at%2014.36.58.png)
+
+![bg right:55% 80%](./assets/Screenshot%202023-10-29%20at%2014.55.02.png)
+
+---
+
+### Focal Mechanism Beachball
+
+<!-- ![](./assets/Screenshot%202023-10-29%20at%2014.49.33.png) -->
+
+![w:400](./assets/Screenshot%202023-10-29%20at%2014.58.03.png)
+
+![bg right:50% 80%](./assets/Screenshot%202023-10-29%20at%2014.53.33.png)
+
+--- 
+
+### Radiation pattern
+
+![h:500](./assets/Screenshot%202023-10-29%20at%2014.38.56.png)
+
+![bg right:50% 80%](./assets/Screenshot%202023-10-29%20at%2015.04.01.png)
+
+<!-- footer: "Kumar et al. (2016)" -->
+
+---
+
+### How to determine focal mechanism?
+
+**Review: [Inverse Problems in Geophysics](https://ai4eps.github.io/EPS207_Observational_Seismology/lectures/06_location_and_relocation.html#6)**
+
+- Forward function: [last lecture](https://ai4eps.github.io/EPS207_Observational_Seismology/lectures/08_focal_mechanism_and_momemt_tensor/#33-more-specific-example-of-a-fault-described-by-a-double-couple-source)
+- Objective/Loss function
+- Gradient
+- Optimizer
+
+---
+<style scoped>
+section {
+  font-size: 28px;
+}
+</style>
+
+### Focal mechanism from first motion polarity
+
+- FPFIT
+
+Objective/Loss function: 
+$$
+F^{i, j}=\frac{\sum_k \left\{| p_0^{j, k}-p_t^{i, k} \mid \cdot w_0^{j, k} \cdot w_t^{i, k}\right\}}{\sum_k\left\{w_0^{j, k} \cdot w_t^{i, k}\right\}}
+$$
+
+$P_0^{j, k} are P_t^{i, k}$ are the observed and theoretical first-motion polarity (0.5 for compression, -0.5 for dilatation).
+$w_t^{i, k}=[A(i, k)]^{1 / 2}$ is the square root of the normalized theoretical P-wave radiation amplitude $A(i, k)$ of earthquake $E^j$ recorded at the $k^{\text {th }}$ station for source model $M^i$.
+
+<!-- footer: "Reasenberg (1985)" -->
+
+---
+
+### Focal mechanism from first motion polarity
+
+- HASH
+
+![bg w:800](https://gsw.silverchair-cdn.com/gsw/Content_public/Journal/bssa/92/6/10.1785_0120010200/3/2270_01.jpeg?Expires=1701569826&Signature=m1vSnJ8ZiRXGIo78DsY0JEkKJ-dSi6hHsMj2VtVrvdqvNQy9xS9NOZDSWUyLMx4Bs0ray9g45EARu6F1qP9B8cmNgNQF5qj30O7H4DHKxHuFohN9YxQt0A7rRqKSVbUmZcUu3D5CdPCN8dxVVt2Bl2SyYC5Le8oFakbS4tcOw-NSFbztboZUitlMn4BuOGaznJARW3QuKZixGmNwdVgBxMPFG7qzZilkx3RNpRJVX6qcoU23tcR~sD61gKq4v1gyA6EcCu19qHQ~8Y-PbIjyuXoKA9x1WrfxoP0s6sgMsTjcETGDvU1uQKxkxrKZJNqdZtX5VuN1wL85Z-Hl6zPunw__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
+
+<!-- footer: "Hardebeck and Shearer (2002)" -->