About the results about deepwave

[ar4]

Greetings,

I ran your code and obtained a receiver_amplitudes of shape [250, 300, 2], as expected, and the result looked plausible. To be certain, I have pasted the code that I ran, and attached the output that I received. Does this code produce a receiver_amplitudes of shape [250, 300, 1] for you? If so, did you receive any warning messages while running it?

import deepwave as dp
import numpy as np
import torch as tr

data = np.ones([201, 301], np.float32)*2500

dx = 10 # 10m in each dimension
dt = 0.004 # 4ms --- Sampling Interval
nz = np.shape(data)[0]
ny = np.shape(data)[1]
nt = int(1 / dt) # 1s --- Sampling freq
r_spacing = dx*(ny-1)
s_spacing = dx
ymax = (ny-1)*dx
num_shots = int(np.floor(ymax / s_spacing))
coord_receivers = tr.linspace(0,ymax,2)
num_receivers_per_shot = int(len(coord_receivers))
num_sources_per_shot = 1
num_dims = 2
peak_freq = 4
peak_source_time = 1/peak_freq

model = tr.tensor(data)

"""
source and receiver position --- x_s -> Tensor of shape [num_shots, num_sources_per_shot, num_dimensions]
--- x_r -> Tensor of shape [num_shots, num_receivers_per_shot, num_dimensions]
"""

x_r = tr.zeros(num_shots,num_receivers_per_shot,num_dims)
for j in range(num_receivers_per_shot):
  x_r[:,j,1] = coord_receivers[j] #receiver potition

x_s = tr.zeros(num_shots, num_sources_per_shot, num_dims)
for j in range(num_sources_per_shot):
  x_s[:,0,1] = tr.linspace(ymax/2, ymax, num_shots) #sources potition
  x_s[:,0,0] = 100#tr.linspace(0,(nz-1)*dx, len(x_s[:,0,1])) #depth

source_amplitudes = (dp.wavelets.ricker(peak_freq, nt, dt,
peak_source_time).reshape(-1, 1, 1).repeat(1, num_shots, num_sources_per_shot))

prop = dp.scalar.Propagator({'vp': model}, dx)
receiver_amplitudes = prop(source_amplitudes, x_s, x_r, dt)

[Ge0sz]

What was the input shape to print it like this? you used plt.imshow()? the shape of result is [nt, num_shots, num_receivers_per_shot], yes?

[ar4]

I think you are asking what command I used to create the two plots in my previous message. I used plt.imshow(receiver_amplitudes[...,0]) and plt.imshow(receiver_amplitudes[...,1]) to produce them, plotting the data recorded by each of the two receivers.

[Ge0sz]

so in our example x is the shot of each source and y the time, yes?

[ar4]

Yes.

[Ge0sz]

also, instead of x_s[:,0,0] = 100 for depth, can i use , x_s[:,0,0] = tr.linspace(0,(nz-1)*dx, len(x_s[:,0,1])) in order to have for each source different depth? the shots are made one after the other and not simultaneously ,yes?

[ar4]

That should work, although note that the source will be moved to the nearest cell - if the cell size is 10x10m then a source located at (5, 5)m will be moved to (10,10)m, for example.

I am not sure what you are referring to when you ask about simultaneous shots. I can think of two possibilities:

1. The num_sources_per_shot refers to how many sources will be used in each shot. If you wish for each shot to only contain one source (so no simultaneous sources) then this should be set to 1. It is set to 1 in the example code above, so the data in receiver_amplitudes[:,0,:] will only involve the source located at x_s[0,0,:], for example.
2. You may also be asking about whether parallel processing is used to perform the propagation in parallel. It is.

[Ge0sz]

Perfect, thank you!

[Ge0sz]

How can i increase the duration of the time of recording? by increasing 'nt'?

[ar4]

Yes.

…

On Sat, 27 Mar 2021 at 22:41, Ge0sz ***@***.***> wrote: How can i increase the duration of the time of recording? by increasing 'nt'? — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#26 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACMJSKRBFJ54BWISXKAAAQDTFZNLBANCNFSM4ZYLBZTQ> .

[Ge0sz]

the coordinates -position of receiver and source should be in real distance or pixel?

[ar4]

The documentation says "The coordinates are specified in the same units as dx and are with respect to the origin of the model." - i.e., real distance. You can also see this in the examples, e.g., where the source coordinates are set using x_s = torch.Tensor([[[0, 20 * dx]]])

…

On Sun, 28 Mar 2021 at 16:26, Ge0sz ***@***.***> wrote: the coordinates -position of receiver and source should be in real distance or pixel? — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#26 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACMJSKWGSB6M6XRJVUWYUNTTF5KENANCNFSM4ZYLBZTQ> .

[Ge0sz]

The result is the total displacement or there is a specific orientation for example horizontal-vertical? Thanks again :)

[ar4]

The package currently uses the scalar wave equation. I think the values can therefore be best interpreted as being related to differential pressure.

[Ge0sz]

so it's acceleration?

[ar4]

Acceleration is usually a vector.

[Ge0sz]

pressure is also a vector

[ar4]

I think pressure is normally a scalar: https://en.wikipedia.org/wiki/Pressure#Scalar_nature

[Ge0sz]

ok, can you suggest any way to calculate displacement?

[ar4]

I think displacement is inversely proportional to the spatial derivative of pressure. If you need vertical displacement at a specific position, for example, you could probably record the wavefield at a few adjacent cells in the vertical direction around that position and use these to calculate the vertical derivative there.

[ar4]

Not inversely proportional - I meant proportional with a negative coefficient.

[Ge0sz]

You mean: ΔP=-x , where ΔP the differential pressure and x the displacement? Also, how can i separate the vertical or horizontal component if the pressure is scalar?

[ar4]

By "differential pressure" I mean excess pressure - the difference from the pressure in the unperturbed state. I believe displacement is proportional to the negative spatial derivative of the differential pressure. If you want vertical displacement, you calculate the vertical derivative of the differential pressure, whereas if you want horizontal displacement then you calculate the horizontal derivative of the differential pressure.

[ar4]

Did you get the result that you wanted?

[Ge0sz]

I wanted to ask, if its scalar and it depicts the total, how can calculate the displacement in a direction for example vertically?

[ar4]

I will try to clarify what I said: With Deepwave, you can record the (differential/excess) pressure at grid cells that you specify as receiver locations. I think the displacement in a direction can be approximately calculated using the negative spatial derivative of the pressure in that direction. If you want the vertical displacement at the point (y,z), you can therefore place receivers at (y,z-1) and (y,z+1) to record the pressure at those two points and then use these recordings to calculate the vertical derivative, and thus vertical displacement, there (vertical displacement at (y,z) is approximately proportional to p(y,z+1)-p(y,z-1)). The derivative can be calculated more accurately by using a higher accuracy finite difference approximation (using more receivers). Does that make sense?

[Ge0sz]

Now yes! Thanks again