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The asthenosphere exists because the mantle's ability to deform is strongly dependent on temperature, pressure, composition, water and deformation mechanism. Cooling from the surface creates a strong lithosphere. Beneath it, hotter mantle deforms by material creep at much lower stress on geological timescales. The asthenosphere is predominantly solid weak rock, not a global ocean of magma. On the much shorter timescale of a seismic wave, it still supports S waves.

The hot shallow mantle can be close to its solidus. Water weakening of rocks and, in some settings, a small connected melt fraction can further lower effective viscosity. At greater depths, changes in pressure, homologous temperature, mineral structure and water storage modify the deformation laws; increasing depth does not imply indefinitely decreasing viscosity. Explaining a weak upper-mantle interval does not require every location to contain the same amount of melt.

There are several physically distinct boundaries to test. The thermal lithosphere-asthenosphere boundary describes a thermal transition, the mechanical boundary a contrast in long-term strength or viscosity, and the seismic lithosphere-asthenosphere boundary a change in seismic velocity or other wave properties. They need not have identical depths. A smooth geothermal gradient can explain broad thermal weakening, but a very sharp decrease of seismic velocity may require changes in melt fraction, hydration, composition or seismic anisotropy. A sharp shallow reflector within a craton might instead be an internal lithospheric boundary.^[ref]

Begin with a thermal null model. A half-space cooling model givesIf a thermal boundary corresponds to a fixed temperature $T_{\ast }$, its depth isso it deepens as the square root of plate age. Test that prediction against independently determined seafloor ages, bathymetry and heat flux. An oceanic plate cooling model adds finite thickness and basal heat supply, allowing the old-age depth to approach a finite value. For continents, include radiogenic heating, crustal thickness, the history of continental rifting or tectonic thickening, and advective heating by magma or mantle flow. A cold, dry craton and a recently extended volcanic region should not share the same thermal profile.

Then calculate the observable consequences of competing mechanisms rather than merely assigning a boundary to a map:

Compare models against the observed boundary depth and its sharpness, including uncertainty and resolution. An age–depth trend with matching heat flux favours thermal control; a sharp discontinuity that fails the thermal prediction but coincides with an electrical anomaly can support a melt- or hydration-related transition. Neither observation alone proves a unique cause. The spatially varying boundary is best understood as the result of thermal evolution interacting with composition, fluids and deformation history.

The along-strike rupture time is $L/v_r$, where $v_r$ is rupture velocity. Taking a representative crustal $v_r\simeq 3\mathrm{km}{\mathrm{s}}^{-1}$ gives about $2$ s for a $6$ km unilateral finite-source rupture. A different assumed rupture velocity changes this estimate. The local slip rise time at one patch is not specified and need not equal the whole-fault rupture time.

For comparable distance and ground conditions, the eastern observer lies in the forward rupture directivity direction. Radiation from successive patches arrives closer together, producing a shorter, more concentrated and generally larger-amplitude ground-velocity pulse. The western observer receives the contributions spread over a longer interval, generally with less concentrated shaking. This concerns pulse duration and amplitude; it does not imply an equally large permanent displacement at the eastern site.^[ref]

For distant observers approximately along strike, an elementary seismic travel time construction giveswhere $\beta$ is the shear-wave velocity. With $v_r=3$ and $\beta =3.5\mathrm{km}{\mathrm{s}}^{-1}$, these propagation contributions are about $0.29$ and $3.71$ s, respectively; finite local rise time broadens them. Double-couple radiation pattern, receiver geometry and local site response can change the observed amplitudes, so location east or west alone is not an unconditional intensity prediction.

A seismically inferred transition associated with the base of the lithosphere, often identified by a decrease in shear-wave velocity. Its depth and sharpness constrain combinations of temperature, composition, hydration, melt fraction and seismic anisotropy. A sharp discontinuity inside a craton can instead lie within its thick lithospheric mantle.^[ref]

The propagation speed of a shear elastic wave. In an ideal isotropic elastic medium it is $V_s=\sqrt{\mu /\rho }$, where $\mu$ is shear modulus and $\rho$ mass density. Seismic anisotropy, frequency-dependent relaxation and melt can complicate the inference from an observed shear-wave velocity to temperature or composition.