ALBERT

Notes: Our purpose is to give a short summary of the theory of synthetic seismograms, including all multiple reflections and to show the method of their construction with the use of an electronic computer.The waves to be considered in reflection seismic being approximately plane and horizontal it is generally admitted that in most cases the propagation phenomena can be described with the equation 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR315:GPR_315_mu1"/〉 (u, displacement; V(z), velocity; p, density). Moreover, for all practical purposes, the velocity V (z) is not a continuous function of the depth z. In fact, the earth can be divided up into more or less thin layers, with constant velocity inside each layer and sudden variations at each interface. It is therefore reasonable to substitute to the single equation (1) a series of simple propagation equations with constant coefficients 〈displayedItem type="mathematics" xml:id="mu2" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR315:GPR_315_mu2"/〉 provided a set of boundary conditions is adjoined to them in order to ensure the continuity of displacement and tension.As with all seismic problems, this is essentially a transient system and a very convenient method to resolve equation (2) is to resort to the Laplace transformation, by writing 〈displayedItem type="mathematics" xml:id="mu3" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR315:GPR_315_mu3"/〉 Then the general integral of (2) is: 〈displayedItem type="mathematics" xml:id="mu4" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR315:GPR_315_mu4"/〉 A and B being two constants. This expression is valid inside of a layer, including the two faces. If the propagation velocity in an adjoining layer is V we get an equation similar to (4), say (4′), but with different constants C and D. At a point on the interface, both expressions are valid. Consequently, if we take three points M, P and N into consideration, respectively at the depths z– V T, z and z + V T, we can write four expressions (4) and(4′). The continuity of the tension gives a fifth expression. The constants A, B, C and D can be eliminated from these equations. The result of the elimination is 〈displayedItem type="mathematics" xml:id="mu5" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR315:GPR_315_mu5"/〉 is the reflection coefficient. Going back to the original functions we find a recurrence expression with four terms 〈displayedItem type="mathematics" xml:id="mu6" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR315:GPR_315_mu6"/〉 In order to make use of this expression, we set out from curve 〈displayedItem type="mathematics" xml:id="mu7" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR315:GPR_315_mu7"/〉 which divides the plane Ozt into two domains:1) a domain contiguous to the axis Oz where u is identical to zero;2) the remainder of the plane where for z = o, u(t, o) =s(t)–“the signal”–is given in a narrow interval in the proximity of the origin.The numerical calculation is carried out at the intersection points of two sets of straight lines:1) equidistant parallels to Oz (with spacing x) and2) parallels to Ot through the intersection of the curve T with the straights of the first family.Computations having been carried out for all points (z, t) of the second domain, they lead finally to the values of the function u at the surface, u(t, o), outside the interval where the signal is given. This function u(t, o) is the requested synthetic seismogram.The shape of the signal enters into the calculations. As a matter of fact it is always necessary to try several signals, hence to construct several synthetic seismograms. However, the operation consisting in the modification of the response is simpler than the calculation of the initial film. This leads to the notion of the synthetic impulse seismogram, which is constructed by assuming that the signal is a pure impulse. This impulse seismogram being calculated, it is easy to construct as many synthetic records as there are signals to be taken into account.

Notes: A filtered seismic trace often appears as an almost sinusoidal curve. The reflected energy arrivals are superimposed and interfere with the continuous oscillations of the trace, and are therefore often difficult to distinguish. This is the chief difficulty in picking reflections. The situation is similar to that met with in gravimetry when a strong regional anomaly conceals small local anomalies. However, a regional anomaly is regular and broad, and owing to these two characteristics it can be removed. In reflection seismology batches of energy may also be concealed by oscillations of a continuous character. The main difference lies in the fact that the background of continuous seismic vibrations is not static, as is the case in gravimetry, but variable with time. However, a fairly constant physical quantity corresponds to these vibrations, which are composed partly of noise, partly of undesired secondary reflections. This quantity is the energy of motion of the surface layer of the ground. It is this troublesome energy that we intend to remove, in order to keep only the useful, actually reflected, energy.These remarks clearly demonstrate the importance of an investigation of the energy contained in the surface layer of the ground. After showing that, in the simplest case, the density of this energy can be expressed almost exactly by the formula u ′2−uu′′in which u′ is the velocity of a ground particle, we show how the non-linear filtering defined by this formula can be realized, and we provide a few examples.

Notes: Summary The data presented characterize nitrogen composition and biochemical changes in transplants from the human embryo and adult man skin. As compared to adult, the human embryo skin contains more water soluble nitrogen substances, viz., residual and polypeptide nitrogen, free amino acids, as well as cystine and lysine. Protein disintegration of the skin characterized by autolysis, proteolysis, and hydrolysis coefficients is much more rapid in the human embryo than in the adult. Redistribution of nitrogen substances during the embryonic skin disintegration is attended by a considerable rise in the free amino acid content. High lability of proteins in the embryonic skin, as well as a high content of proteolytic enzymes in the latter, provides for intensive protein disintegration and resynthesis which is conductive to a more rapid desquamation of necrotic tissues, and to a more rapid healing of the skin defect. This shows the expediency of using the embryonic skin in homoplasty.