1. Pendahuluan
Analisis ini bertujuan untuk mengkaji hubungan antara parameter
geofisika bawah permukaan (amplitudo spektral maksimum, frekuensi
dominan, dan anomali gravitasi residual) dengan jumlah kejadian gerakan
tanah dan longsor (GT + L) melalui pembentukan Geophysical
Susceptibility Index (GSI).
2. Data
data <- data.frame(
Subdistrict = c(
"Banjarmangu","Pagetan","Pejawaran","Watumalang",
"Wanayasa","Kalibening","Batur","Karangkobar","Kejajar"
),
Total_Events = c(5,5,3,5,4,2,1,0,0),
Max_Ao = c(4.0,7.5,7.5,7.5,7.5,4.0,7.5,5.0,4.0),
Median_Fo = c(1.5,1.75,2.5,2.25,1.75,1.35,1.75,4.0,3.5),
Avg_Residual = c(-4.5,-7.0,-0.5,-5.5,5.0,7.5,6.0,1.0,4.5)
)
knitr::kable(data, caption = "Data Parameter Geofisika dan Kejadian Longsor")
Data Parameter Geofisika dan Kejadian Longsor
| Subdistrict |
Total_Events |
Max_Ao |
Median_Fo |
Avg_Residual |
| Banjarmangu |
5 |
4.0 |
1.50 |
-4.5 |
| Pagetan |
5 |
7.5 |
1.75 |
-7.0 |
| Pejawaran |
3 |
7.5 |
2.50 |
-0.5 |
| Watumalang |
5 |
7.5 |
2.25 |
-5.5 |
| Wanayasa |
4 |
7.5 |
1.75 |
5.0 |
| Kalibening |
2 |
4.0 |
1.35 |
7.5 |
| Batur |
1 |
7.5 |
1.75 |
6.0 |
| Karangkobar |
0 |
5.0 |
4.00 |
1.0 |
| Kejajar |
0 |
4.0 |
3.50 |
4.5 |
3. Penentuan Rank Parameter Geofisika
rank_ao <- c("7.5"=7, "5"=4, "4"=2)
rank_fo <- c(
"4"=1, "3.5"=2, "2.5"=3, "2.25"=4,
"1.75"=6, "1.5"=8, "1.35"=9
)
rank_res <- c(
"7.5"=1, "6"=2, "5"=3, "4.5"=4,
"1"=5, "-0.5"=6, "-4.5"=7, "-5.5"=8, "-7"=9
)
data$Rank_Ao <- rank_ao[as.character(data$Max_Ao)]
data$Rank_1_Fo <- rank_fo[as.character(data$Median_Fo)]
data$Rank_Neg_Residual <- rank_res[as.character(data$Avg_Residual)]
knitr::kable(data, caption = "Data dengan Ranking Parameter")
Data dengan Ranking Parameter
| Subdistrict |
Total_Events |
Max_Ao |
Median_Fo |
Avg_Residual |
Rank_Ao |
Rank_1_Fo |
Rank_Neg_Residual |
| Banjarmangu |
5 |
4.0 |
1.50 |
-4.5 |
2 |
8 |
7 |
| Pagetan |
5 |
7.5 |
1.75 |
-7.0 |
7 |
6 |
9 |
| Pejawaran |
3 |
7.5 |
2.50 |
-0.5 |
7 |
3 |
6 |
| Watumalang |
5 |
7.5 |
2.25 |
-5.5 |
7 |
4 |
8 |
| Wanayasa |
4 |
7.5 |
1.75 |
5.0 |
7 |
6 |
3 |
| Kalibening |
2 |
4.0 |
1.35 |
7.5 |
2 |
9 |
1 |
| Batur |
1 |
7.5 |
1.75 |
6.0 |
7 |
6 |
2 |
| Karangkobar |
0 |
5.0 |
4.00 |
1.0 |
4 |
1 |
5 |
| Kejajar |
0 |
4.0 |
3.50 |
4.5 |
2 |
2 |
4 |
4. Perhitungan Geophysical Susceptibility Index (GSI)
data$GSI <- data$Rank_Ao +
data$Rank_1_Fo +
data$Rank_Neg_Residual
knitr::kable(data, caption = "Data dengan GSI")
Data dengan GSI
| Subdistrict |
Total_Events |
Max_Ao |
Median_Fo |
Avg_Residual |
Rank_Ao |
Rank_1_Fo |
Rank_Neg_Residual |
GSI |
| Banjarmangu |
5 |
4.0 |
1.50 |
-4.5 |
2 |
8 |
7 |
17 |
| Pagetan |
5 |
7.5 |
1.75 |
-7.0 |
7 |
6 |
9 |
22 |
| Pejawaran |
3 |
7.5 |
2.50 |
-0.5 |
7 |
3 |
6 |
16 |
| Watumalang |
5 |
7.5 |
2.25 |
-5.5 |
7 |
4 |
8 |
19 |
| Wanayasa |
4 |
7.5 |
1.75 |
5.0 |
7 |
6 |
3 |
16 |
| Kalibening |
2 |
4.0 |
1.35 |
7.5 |
2 |
9 |
1 |
12 |
| Batur |
1 |
7.5 |
1.75 |
6.0 |
7 |
6 |
2 |
15 |
| Karangkobar |
0 |
5.0 |
4.00 |
1.0 |
4 |
1 |
5 |
10 |
| Kejajar |
0 |
4.0 |
3.50 |
4.5 |
2 |
2 |
4 |
8 |
5. Uji Korelasi Spearman
params <- c("Max_Ao","Median_Fo","Avg_Residual","GSI")
spearman_results <- data.frame(
Parameter = params,
rho = NA,
p_value = NA
)
for (i in seq_along(params)) {
test <- cor.test(
data$Total_Events,
data[[params[i]]],
method = "spearman",
exact = FALSE
)
spearman_results$rho[i] <- round(test$estimate,3)
spearman_results$p_value[i] <- round(test$p.value,4)
}
knitr::kable(spearman_results, caption = "Hasil Uji Korelasi Spearman")
Hasil Uji Korelasi Spearman
| Parameter |
rho |
p_value |
| Max_Ao |
0.343 |
0.3667 |
| Median_Fo |
-0.494 |
0.1770 |
| Avg_Residual |
-0.655 |
0.0553 |
| GSI |
0.957 |
0.0001 |
6. Uji Kendall Tau
kendall_results <- data.frame(
Parameter = params,
tau = NA,
p_value = NA
)
for (i in seq_along(params)) {
test <- cor.test(
data$Total_Events,
data[[params[i]]],
method = "kendall",
exact = FALSE
)
kendall_results$tau[i] <- round(test$estimate,3)
kendall_results$p_value[i] <- round(test$p.value,4)
}
knitr::kable(kendall_results, caption = "Hasil Uji Kendall Tau")
Hasil Uji Kendall Tau
| Parameter |
tau |
p_value |
| Max_Ao |
0.295 |
0.3339 |
| Median_Fo |
-0.400 |
0.1561 |
| Avg_Residual |
-0.471 |
0.0869 |
| GSI |
0.867 |
0.0018 |
7. Hubungan GSI dan Total Kejadian Longsor
plot(
data$GSI,
data$Total_Events,
xlab = "Geophysical Susceptibility Index (GSI)",
ylab = "Total Kejadian Longsor (GT + L)",
main = "Hubungan GSI dan Total Kejadian Longsor",
pch = 19,
col = "blue",
cex = 1.5
)
abline(lm(Total_Events ~ GSI, data = data), col = "red", lwd = 2)
text(
data$GSI,
data$Total_Events,
data$Subdistrict,
pos = 3,
cex = 0.7
)
8. Kesimpulan
Analisis menunjukkan bahwa GSI dapat merepresentasikan tingkat
kerentanan geofisika bawah permukaan, namun hubungan statistik dengan
jumlah kejadian longsor tidak menunjukkan signifikansi yang kuat,
sehingga GSI lebih tepat digunakan sebagai indikator potensi
kerentanan.
Ringkasan Hasil:
- Korelasi Spearman: Menunjukkan hubungan antara
parameter geofisika dengan kejadian longsor
- Korelasi Kendall Tau: Memberikan konfirmasi
tambahan terhadap hubungan tersebut
- GSI: Indeks gabungan yang mengintegrasikan ketiga
parameter geofisika