Hello @Mayra Alvarez, in my oppinion it is too exaggerated when you do response spectrum analysis because the point of interest embedded under ground surface. The tank can be considered as if part of soil layer.

In general the answer of your question is yes and I explain more below about the conditions and applications to do a spectral response analysis for a water tank when it is supposed to be embedded in the soil. In water tanks embedded in soil, at least to some extent, for many cases, the conditions of embedment are complicated. For example, structures are not supported uniformly around their circumferences because of adjacent structures and cuts in the soil, such as for the connected pipes, etc. Water embedment has a significant effect on soil-structure interaction: in comparison with a surface foundation, both the water tank input motion and the water tank impedances change for an embedded water tank. For vertically propagating waves, a horizontal shear wave produces both a horizontal translation and rotation of the embedded massless foundation; a vertical compression wave produces a vertical translation and rocking of the embedded massless water tank. In general, the amplitude of a water tank input motion for embedded water tanks is less than that for surface water tanks, especially in the high-frequency range. Structural responses are thus reduced for embedded water tanks. For water tanks, during the seismic design of a soil-foundation-structure system, if the water tank is embedded under the soil surface, design response spectra at the control point under the soil surface. However, location of the water tank is not always known at the time when the design response spectrum is constructed. Thus, design response spectra at several depths of the site profile need to be established considering the free-field ground response; the effect of soil-structure interaction is not considered. Besides, because soil parameters usually exhibit large variabilities, it causes uncertainty of the design response spectra at various depths of the site profile. Thus, probabilistic design response spectrum at a control point under the soil surface may be required to accurately reflect the seismic hazards at corresponding locations.

I hope my answer is helpful and responded to your question.

Best of luck.

To complement the comments above - which I guess would be representative of a larger sample of opinions in terms of getting split opinions, I would just say,

Not worth undertaking, if your objective is to assessing structural damage of the tank itself or adjacent structures - very notionally you could think of the soil in the neighbourhood of the tank as a damping mechanisms, in the rare situation in which some isolation layer(s) are not added to prevent compressions on the tank.

But Yes (a big one), if you are after digging into fundamental science. The problem setting, as described above, would attract the attention of theorist.

Response spectrum analysis should be used to estimate the peak response (displacement, stress, etc.) of a structure to a particular base motion or force. That is on can apply it if all modes of vibration are subjected to the same excitation.

You can’t really say that an embed water tank is subjected to a single point excitation. Even if you ignore the effect of the base' size on the arrival of the seismic wave, i.e. assuming the base as a single point, you still need to consider the effect of excitation on the tank's sides. With no stretch of the imagination, you can say that every mode of an embedded water tank is subjected to the same excitation. For this reason, the response spectrum concept is not useful for wind or blast. However, a drastic approximation such as assuming the whole system as one single degree of freedom, then you can, but you wouldn't trust your answer.

The best solution for your problem is a time-domain dynamic direct integration analysis accounting for the soil-water-structure interaction. Software packages like Abaqus are suitable for this task.

The answer is yes. Spectral acceleration can be determined in any point in the depth of the earth and under ground structures can be calculated for this acceleration. But mostly this will not affect them so much.