我怎么得到纵波和横波的速度不使用旅行时间图?- 江南体育网页版- - - - -地球科学堆江南电子竞技平台栈交换 最近30从www.hoelymoley.com 2023 - 07 - 10 - t21:04:21z //www.hoelymoley.com/feeds/question/16518 https://creativecommons.org/licenses/by-sa/4.0/rdf //www.hoelymoley.com/q/16518 3 我怎么得到纵波和横波的速度不使用旅行时间图? nelaaam //www.hoelymoley.com/users/15470 2019 - 03 - 20 - t02:49:09z 2019 - 03 - 20 - t12:03:16z < p >我想编写一个程序,确定地震的震级和震中。从< a href = " http://www.dartmouth.edu/ ears5 /救济/ EQ_distance.html”rel = " nofollow noreferrer " > http://www.dartmouth.edu/ ears5 /施舍EQ_distance.html < / >,可以计算中心的距离与< / p > < p > <跨类= " math-container " > $ d = (ts-tp) / (1 / vs) - (1 / vp) $ < / span > < / p > < p >但我不是很确定什么vs和副总裁的值。从旅行时间图Vs和副总裁随距离传感器的地震。因为我有3个传感器与给定的纬度和经度,从中我可以得到滞后时间,有无论如何我可以从这些变量估计Vs和副总裁?< / p > < p >否则,还有其他我可以从震中的距离传感器吗? < / p > //www.hoelymoley.com/questions/16518/-/16524 # 16524 3 Erik回答的我怎么得到纵波和横波的速度不使用旅行时间图? 埃里克 //www.hoelymoley.com/users/12155 2019 - 03 - 20 - t08:39:01z 2019 - 03 - 20 - t12:03:16z < p >我认为是可能的4台是的,而不是三个。< / p > < p > < >强的假设(大约)均匀的速度我们得到以下问题< /强>。Assuming that $v_p$ and $v_s$ are constants between the Earthquake and all your receivers yields the following system: \begin{align} d &= \sqrt{\Delta x^2 + \Delta y^2 + \Delta z^2}=\text{3 knowns, 3 unknowns},\quad \text{for} \left\{ \begin{array}{rl} \Delta x &= x_\text{earthquake}-x_\text{receiver} \\ \Delta y & = y_\text{earthquake} - y_\text{receiver} \\ \Delta z & = z_\text{earthquake} - z_\text{receiver} \end{array} \begin{split} \end{split}\right.,\\ \Delta t & = t_s - t_p = \text{measured},\\ p &= \left(\frac{1}{v_s} - \frac{1}{v_p} \right) = \text{1 unknown}. \end{align} Restating the equation of your question then gives the forward problem: $$ \Delta t = p d.$$ For example, for $v_p=2000$ m/s and $v_s=1200$ m/s, we find $p=1/3000$ and can compute e.g. with $d = 600$ that $\Delta t = 600/3000 =0.2$ s.

Now, we must set=up the inverse problem. You generally need at least as many equations as unknowns. In this case we have 4 unknowns (the velocity and the $(x,y,z)$ earthquake location). That means that we need 4 (unique) equations. I think that the simplest way of obtaining 4 unique equations is to combine 4 measurements: $$ p\begin{pmatrix} d_1 \\ d_2 \\ d_3 \\ d_4 \end{pmatrix} = \begin{pmatrix} \Delta t_1 \\ \Delta t_2 \\ \Delta t_3 \\ \Delta t_4 \end{pmatrix}, $$ Denoting with $x_{1,2,3,4}$ and $y_{1,2,3,4}$ the latitude and longitude of the receivers, and assuming measurements at the surface, we obtain: $$ p\begin{pmatrix} \sqrt{(x_\text{earthquake}-x_1)^2 + (y_\text{earthquake}-y_1)^2 + z_\text{earthquake}^2} \\ \sqrt{(x_\text{earthquake}-x_2)^2 + (y_\text{earthquake}-y_2)^2 + z_\text{earthquake}^2} \\ \sqrt{(x_\text{earthquake}-x_3)^2 + (y_\text{earthquake}-y_3)^2 + z_\text{earthquake}^2 } \\ \sqrt{(x_\text{earthquake}-x_4)^2 + (y_\text{earthquake}-y_4)^2 + z_\text{earthquake}^2} \end{pmatrix} = \begin{pmatrix} \Delta t_1 \\ \Delta t_2 \\ \Delta t_3 \\ \Delta t_4 \end{pmatrix}. $$

Finally, we must solve the inverse problem. Unfortunately, the system is non-linear (the unknowns are 'hidden' in the root of the square and can't be separated). You must therefore use some non-linear solver. For example, in MATLAB you can do this

% True earthquake location x_earthquake=0; y_earthquake=0; z_earthquake=1000; % True station locations x_1 = 1000; y_1 = 1000; x_2 = 500; y_2 = -300; x_3 = -400; y_3 = -100; x_4 = -10; y_4 = 800; X = [x_1;x_2;x_3;x_4]; Y = [y_1;y_2;y_3;y_4]; % True velocity structure p0 = 1/3000; % Forward equation (F(1)=x_eartquake, F(2)=y_earthquake, F(3)=z_earthquake, F(4)=p. t =@(F) F(4) * sqrt( (F(1)-X).^2 + (F(2)-Y).^2 + F(3).^2); % True recordings measured_times = t([x_earthquake,y_earthquake,z_earthquake,p0]); % Misfit function (=0 at optimum) G =@(F) t(F) - measured_times; % Invert %options = optimoptions('fsolve','FiniteDifferenceType','central'); % using these will give better results in MATLAB %F_inv = fsolve( G, [1000,1000,1000,0.1],options) F_inv = fsolve( G, [1000,1000,1000,0.1]) x_earthquake_inv = F_inv(1) y_earthquake_inv = F_inv(2) z_earthquake_inv = F_inv(3) p_inv = F_inv(4)

If you copy this into https://octave-online.net/, for example, it will find an earthquake at (0,0,1000) and p=1/3000, with some small errors due to the non-linear solver.
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