diff --git a/lib/potential/gkernel_triangle2d.cpp b/lib/potential/gkernel_triangle2d.cpp
index b26d516..fca6b8e 100644
--- a/lib/potential/gkernel_triangle2d.cpp
+++ b/lib/potential/gkernel_triangle2d.cpp
@@ -42,6 +42,8 @@ typedef void (*gkernel_triangle2d_ptr)(gctl::matrix<double> &out_kernel, const g
 
 void gkernel_triangle2d_vz(gctl::matrix<double> &out_kernel, const gctl::array<gctl::triangle2d> &ele, 
 	const gctl::array<gctl::point2dc> &obsp, gctl::verbose_type_e verbose);
+void gkernel_triangle2d_vx(gctl::matrix<double> &out_kernel, const gctl::array<gctl::triangle2d> &ele, 
+	const gctl::array<gctl::point2dc> &obsp, gctl::verbose_type_e verbose);
 void gkernel_triangle2d_vzx(gctl::matrix<double> &out_kernel, const gctl::array<gctl::triangle2d> &ele, 
 	const gctl::array<gctl::point2dc> &obsp, gctl::verbose_type_e verbose);
 void gkernel_triangle2d_vzz(gctl::matrix<double> &out_kernel, const gctl::array<gctl::triangle2d> &ele, 
@@ -65,6 +67,9 @@ void gctl::gkernel(matrix<double> &out_kernel, const array<triangle2d> &ele,
 		case Vz:
 			triangle_kernel = gkernel_triangle2d_vz;
 			break;
+		case Vx:
+			triangle_kernel = gkernel_triangle2d_vx;
+			break;
 		case Tzx:
 			triangle_kernel = gkernel_triangle2d_vzx;
 			break;
@@ -92,6 +97,8 @@ typedef void (*gobser_triangle2d_ptr)(gctl::array<double> &out_obs, const gctl::
 
 void gobser_triangle2d_vz(gctl::array<double> &out_obs, const gctl::array<gctl::triangle2d> &ele, 
 	const gctl::array<gctl::point2dc> &obsp, const gctl::array<double> &rho, gctl::verbose_type_e verbose);
+void gobser_triangle2d_vx(gctl::array<double> &out_obs, const gctl::array<gctl::triangle2d> &ele, 
+	const gctl::array<gctl::point2dc> &obsp, const gctl::array<double> &rho, gctl::verbose_type_e verbose);
 void gobser_triangle2d_vzx(gctl::array<double> &out_obs, const gctl::array<gctl::triangle2d> &ele, 
 	const gctl::array<gctl::point2dc> &obsp, const gctl::array<double> &rho, gctl::verbose_type_e verbose);
 void gobser_triangle2d_vzz(gctl::array<double> &out_obs, const gctl::array<gctl::triangle2d> &ele, 
@@ -116,6 +123,9 @@ void gctl::gobser(array<double> &out_obs, const array<triangle2d> &ele, const ar
 		case Vz:
 			triangle_obser = gobser_triangle2d_vz;
 			break;
+		case Vx:
+			triangle_obser = gobser_triangle2d_vx;
+			break;
 		case Tzx:
 			triangle_obser = gobser_triangle2d_vzx;
 			break;
@@ -130,6 +140,7 @@ void gctl::gobser(array<double> &out_obs, const array<triangle2d> &ele, const ar
 }
 
 double gkernel_triangle2d_vz_sig(gctl::triangle2d *ele_ptr, gctl::point2dc *op_ptr);
+double gkernel_triangle2d_vx_sig(gctl::triangle2d *ele_ptr, gctl::point2dc *op_ptr);
 double gkernel_triangle2d_vzx_sig(gctl::triangle2d *ele_ptr, gctl::point2dc *op_ptr);
 double gkernel_triangle2d_vzz_sig(gctl::triangle2d *ele_ptr, gctl::point2dc *op_ptr);
 
@@ -174,7 +185,31 @@ void gkernel_triangle2d_vz(gctl::matrix<double> &out_kernel, const gctl::array<g
 #pragma omp parallel for private (j) schedule(guided)
 		for (j = 0; j < e_size; j++)
 		{
-			out_kernel.at(i, j) = gkernel_triangle2d_vz_sig(ele.get(j), obsp.get(i));
+			out_kernel[i][j] = gkernel_triangle2d_vz_sig(ele.get(j), obsp.get(i));
+		}
+	}
+	return;
+}
+
+void gkernel_triangle2d_vx(gctl::matrix<double> &out_kernel, const gctl::array<gctl::triangle2d> &ele, 
+	const gctl::array<gctl::point2dc> &obsp, gctl::verbose_type_e verbose)
+{
+	int i, j;
+	int o_size = obsp.size();
+	int e_size = ele.size();
+
+	out_kernel.resize(o_size, e_size);
+
+	gctl::progress_bar bar(o_size, "gkernel_vx");
+	for (i = 0; i < o_size; i++)
+	{
+		if (verbose == gctl::FullMsg) bar.progressed(i);
+		else if (verbose == gctl::ShortMsg) bar.progressed_simple(i);
+
+#pragma omp parallel for private (j) schedule(guided)
+		for (j = 0; j < e_size; j++)
+		{
+			out_kernel[i][j] = gkernel_triangle2d_vx_sig(ele.get(j), obsp.get(i));
 		}
 	}
 	return;
@@ -198,7 +233,7 @@ void gkernel_triangle2d_vzx(gctl::matrix<double> &out_kernel, const gctl::array<
 #pragma omp parallel for private (j) schedule(guided)
 		for (j = 0; j < e_size; j++)
 		{
-			out_kernel.at(i, j) = gkernel_triangle2d_vzx_sig(ele.get(j), obsp.get(i));
+			out_kernel[i][j] = gkernel_triangle2d_vzx_sig(ele.get(j), obsp.get(i));
 		}
 	}
 	return;
@@ -222,7 +257,7 @@ void gkernel_triangle2d_vzz(gctl::matrix<double> &out_kernel, const gctl::array<
 #pragma omp parallel for private (j) schedule(guided)
 		for (j = 0; j < e_size; j++)
 		{
-			out_kernel.at(i, j) = gkernel_triangle2d_vzz_sig(ele.get(j), obsp.get(i));
+			out_kernel[i][j] = gkernel_triangle2d_vzz_sig(ele.get(j), obsp.get(i));
 		}
 	}
 	return;
@@ -246,7 +281,31 @@ void gobser_triangle2d_vz(gctl::array<double> &out_obs, const gctl::array<gctl::
 #pragma omp parallel for private (i) schedule(guided)
 		for (i = 0; i < o_size; i++)
 		{
-			out_obs.at(i) += gkernel_triangle2d_vz_sig(ele.get(j), obsp.get(i)) * rho[j];
+			out_obs[i] += gkernel_triangle2d_vz_sig(ele.get(j), obsp.get(i)) * rho[j];
+		}
+	}
+	return;
+}
+
+void gobser_triangle2d_vx(gctl::array<double> &out_obs, const gctl::array<gctl::triangle2d> &ele, 
+	const gctl::array<gctl::point2dc> &obsp, const gctl::array<double> &rho, gctl::verbose_type_e verbose)
+{
+	int i, j;
+	int o_size = obsp.size();
+	int e_size = ele.size();
+
+	out_obs.resize(o_size, 0.0);
+
+	gctl::progress_bar bar(e_size, "gobser_vx");
+	for (j = 0; j < e_size; j++)
+	{
+		if (verbose == gctl::FullMsg) bar.progressed(j);
+		else if (verbose == gctl::ShortMsg) bar.progressed_simple(j);
+
+#pragma omp parallel for private (i) schedule(guided)
+		for (i = 0; i < o_size; i++)
+		{
+			out_obs[i] += gkernel_triangle2d_vx_sig(ele.get(j), obsp.get(i)) * rho[j];
 		}
 	}
 	return;
@@ -270,7 +329,7 @@ void gobser_triangle2d_vzx(gctl::array<double> &out_obs, const gctl::array<gctl:
 #pragma omp parallel for private (i) schedule(guided)
 		for (i = 0; i < o_size; i++)
 		{
-			out_obs.at(i) += gkernel_triangle2d_vzx_sig(ele.get(j), obsp.get(i)) * rho[j];
+			out_obs[i] += gkernel_triangle2d_vzx_sig(ele.get(j), obsp.get(i)) * rho[j];
 		}
 	}
 	return;
@@ -294,7 +353,7 @@ void gobser_triangle2d_vzz(gctl::array<double> &out_obs, const gctl::array<gctl:
 #pragma omp parallel for private (i) schedule(guided)
 		for (i = 0; i < o_size; i++)
 		{
-			out_obs.at(i) += gkernel_triangle2d_vzz_sig(ele.get(j), obsp.get(i)) * rho[j];
+			out_obs[i] += gkernel_triangle2d_vzz_sig(ele.get(j), obsp.get(i)) * rho[j];
 		}
 	}
 	return;
@@ -328,6 +387,34 @@ double gkernel_triangle2d_vz_sig(gctl::triangle2d *ele_ptr, gctl::point2dc *op_p
 	return -2.0e+8*GCTL_G0*sum;
 }
 
+double gkernel_triangle2d_vx_sig(gctl::triangle2d *ele_ptr, gctl::point2dc *op_ptr)
+{
+	double sum;
+	double A, B, C;
+	double Aa, Ab, Ba, Bb, Ca, Cb;
+
+	sum = 0.0;
+	for (int n = 0; n < 3; n++)
+	{
+		Aa = (ele_ptr->vert[n]->y - op_ptr->y)*(ele_ptr->vert[(n+1)%3]->x - op_ptr->x) -
+			 (ele_ptr->vert[(n+1)%3]->y - op_ptr->y)*(ele_ptr->vert[n]->x - op_ptr->x);
+		Ab = pow(ele_ptr->vert[(n+1)%3]->y - ele_ptr->vert[n]->y,2) +
+			 pow(ele_ptr->vert[(n+1)%3]->x - ele_ptr->vert[n]->x,2);
+		A = Aa/Ab;
+
+		Ba = atan2(ele_ptr->vert[n]->y - op_ptr->y, ele_ptr->vert[n]->x - op_ptr->x);
+		Bb = atan2(ele_ptr->vert[(n+1)%3]->y - op_ptr->y, ele_ptr->vert[(n+1)%3]->x - op_ptr->x);
+		B = (ele_ptr->vert[(n+1)%3]->y - ele_ptr->vert[n]->y)*(Ba - Bb);
+
+		Ca = pow(ele_ptr->vert[(n+1)%3]->x - op_ptr->x,2) + pow(ele_ptr->vert[(n+1)%3]->y - op_ptr->y,2);
+		Cb = pow(ele_ptr->vert[n]->x - op_ptr->x,2) + pow(ele_ptr->vert[n]->y - op_ptr->y,2);
+		C = 0.5*(ele_ptr->vert[(n+1)%3]->x - ele_ptr->vert[n]->x)*(log(Ca) - log(Cb));
+
+		sum += A*(B+C);
+	}
+	return -2.0e+8*GCTL_G0*sum;
+}
+
 double gkernel_triangle2d_vzx_sig(gctl::triangle2d *ele_ptr, gctl::point2dc *op_ptr)
 {
 	double sum;