From f5b7d483aee7266d929f09cb2c1e01e3994d1621 Mon Sep 17 00:00:00 2001 From: SEOGI KANG Date: Fri, 12 Sep 2014 14:09:23 -0700 Subject: [PATCH] Initial commit: - 2D acoustic time domain code - Sponge and PML boundary codition were used --- simpegseis/SeisAcousticTime.py | 458 +++++++++++++++++++++++++++++++++ simpegseis/__init__.py | 2 + simpegseis/theory.pdf | Bin 0 -> 543991 bytes 3 files changed, 460 insertions(+) create mode 100644 simpegseis/SeisAcousticTime.py create mode 100644 simpegseis/__init__.py create mode 100644 simpegseis/theory.pdf diff --git a/simpegseis/SeisAcousticTime.py b/simpegseis/SeisAcousticTime.py new file mode 100644 index 0000000..5b5f608 --- /dev/null +++ b/simpegseis/SeisAcousticTime.py @@ -0,0 +1,458 @@ +from SimPEG import * +from SimPEG.Utils import sdiag, mkvc, sdInv +import matplotlib.pyplot as plt +from time import clock + +class AcousticTx(Survey.BaseTx): + + + def __init__(self, loc, time, rxList, **kwargs): + + self.dt = time[1]-time[0] + self.time = time + self.loc = loc + self.rxList = rxList + self.kwargs = kwargs + + + def RickerWavelet(self): + + """ + Generating Ricker Wavelet + + .. math :: + + """ + tlag = self.kwargs['tlag'] + fmain = self.kwargs['fmain'] + time = self.time + self.wave = (1-2*np.pi**2*fmain**2*(time-tlag)**2)*np.exp(-np.pi**2*fmain**2*(time-tlag)**2) + return self.wave + + def Wave(self, tInd): + + """ + Generating Ricker Wavelet + + .. math :: + + """ + tlag = self.kwargs['tlag'] + fmain = self.kwargs['fmain'] + time = self.time[tInd] + self.wave = (1-2*np.pi**2*fmain**2*(time-tlag)**2)*np.exp(-np.pi**2*fmain**2*(time-tlag)**2) + return self.wave + + def getq(self, mesh): + + txind = Utils.closestPoints(mesh, self.loc, gridLoc='CC') + q = sdiag(1/mesh.vol)*np.zeros(mesh.nC) + q[txind] = 1. + + return q + +class AcousticRx(Survey.BaseRx): + + def __init__(self, locs, **kwargs): + self.locs = locs + + # Question: Why this does not work? + # def getP(self): + # print 'kang' + # return mesh.getInterpolationMat(self.locs, 'CC') + + @property + def nD(self): + """ The number of data in the receiver.""" + return self.locs.shape[0] + + def getP(self, mesh): + P = mesh.getInterpolationMat(self.locs, 'CC') + return P + + + +class SurveyAcoustic(Survey.BaseSurvey): + """ + **SurveyAcousitc** + + Geophysical Acoustic Wave data. + + """ + + def __init__(self, txList,**kwargs): + self.txList = txList + Survey.BaseSurvey.__init__(self, **kwargs) + + def projectFields(self, u): + data = [] + + for i, tx in enumerate(self.txList): + Proj = tx.rxList[0].getP(self.prob.mesh) + data.append(Proj*u[i]) + return data + + +class AcousticProblemSponge(Problem.BaseProblem): + """ + + """ + surveyPair = SurveyAcoustic + Solver = Solver + storefield = True + verbose = False + stability = False + sig = False + + def __init__(self, mesh, **kwargs): + Problem.BaseProblem.__init__(self, mesh) + self.mesh.setCellGradBC('dirichlet') + Utils.setKwargs(self, **kwargs) + + def setSpongeBC(self, npad, dt, bcflag="all"): + #TODO: performance of abosrbing + self.bcflag = bcflag + ax = self.mesh.vectorCCx[-npad] + ay = self.mesh.vectorCCy[-npad] + if bcflag == 'all': + indy = np.logical_or(self.mesh.gridCC[:,1]<=-ay, self.mesh.gridCC[:,1]>=ay) + indx = np.logical_or(self.mesh.gridCC[:,0]<=-ax, self.mesh.gridCC[:,0]>=ax) + elif bcflag =='up': + indy = self.mesh.gridCC[:,1]<=-ay + indx = np.logical_or(self.mesh.gridCC[:,0]<=-ax, self.mesh.gridCC[:,0]>=ax) + elif bcflag =='left': + indy = self.mesh.gridCC[:,1]<=-ay + indx = self.mesh.gridCC[:,0]>=ax + elif bcflag =='right': + indy = self.mesh.gridCC[:,1]<=-ay + indx = self.mesh.gridCC[:,0]<=-ax + else: + raise Exception("Not implented!!") + tempx = np.zeros_like(self.mesh.gridCC[:,0]) + tempx[indx] = (abs(self.mesh.gridCC[:,0][indx])-ax)**2 + tempx[indx] = tempx[indx]-tempx[indx].min() + tempx[indx] = tempx[indx]/tempx[indx].max() + tempy = np.zeros_like(self.mesh.gridCC[:,1]) + tempy[indy] = (abs(self.mesh.gridCC[:,1][indy])-ay)**2 + tempy[indy] = tempy[indy]-tempy[indy].min() + tempy[indy] = tempy[indy]/tempy[indy].max() + temp = tempx+tempy + temp[temp>1.] = 1. + + f = 1.- temp*0.1 + self.sig = (1.-f)/f*2./dt + + + def stabilitycheck(self, v, time, fmain): + + self.dxmin = min(self.mesh.hx.min(), self.mesh.hy.min()) + self.topt = self.dxmin/v.max()*0.5 + self.dt = time[1]-time[0] + self.fmain = fmain + self.wavelen = v.min()/self.fmain + self.G = self.wavelen/self.dxmin + + if self.dt > self.topt: + print "Warning: dt is greater than topt" + self.stability = False + elif self.G < 16.: + print "Warning: Wavelength per cell (G) should be greater than 16" + self.stability = False + else: + print "You are good to go:)" + self.stability = True + + print ">> Stability information" + print (" dt: %5.2e s")%(self.dt) + print (" Optimal dt: %5.2e s")%(self.topt) + print (" Cell per wavelength (G): %5.2e")%(self.G) + print (" Optimal G: %5.2e")%(16.) + + def fields(self, v): + + if self.bcflag =='up': + self.mesh.setCellGradBC(['dirichlet', ['dirichlet', 'neumann']]) + elif self.bcflag =='left': + self.mesh.setCellGradBC([['neumann', 'dirichlet'], ['dirichlet', 'neumann']]) + elif self.bcflag =='right': + self.mesh.setCellGradBC([['dirichlet', 'neumann'], ['dirichlet', 'neumann']]) + + Grad = self.mesh.cellGrad + Div = self.mesh.faceDiv + AvF2CC = self.mesh.aveF2CC + rho = 0.27*np.ones(self.mesh.nC) + mu = rho*v**2 + DSig = sdiag(self.sig) + Drhoi = sdiag(1/rho) + MfmuiI = sdiag(1/(AvF2CC.T*(1/mu))) + + if self.stability==False: + raise Exception("Stability condition is not satisfied!!") + elif self.sig is False: + print "Warning: Absorbing boundary condition was not set yet!!" + start = clock() + print ">> Start Computing Acoustic Wave" + print (">> dt: %5.2e s")%(self.dt) + print (">> Optimal dt: %5.2e s")%(self.topt) + print (">> Main frequency, fmain: %5.2e Hz")%(self.fmain) + print (">> Cell per wavelength (G): %5.2e")%(self.G) + + + if self.storefield==True: + P = [] + #TODO: parallize in terms of sources + ntx = len(self.survey.txList) + for itx, tx in enumerate(self.survey.txList): + print (" Tx at (%7.2f, %7.2f): %4i/%4i")%(tx.loc[0], tx.loc[0], itx+1, ntx) + pn = np.zeros(self.mesh.nC) + p0 = np.zeros_like(pn) + un = np.zeros(self.mesh.nF) + u0 = np.zeros_like(un) + time = tx.time + dt = tx.dt + p = np.zeros((self.mesh.nC, time.size)) + q = tx.getq(self.mesh) + for i in range(time.size-1): + sn = tx.Wave(i+1) + s0 = tx.Wave(i) + pn = p0-dt*DSig*p0+Drhoi*dt*(Div*un+(sn-s0)/dt*q) + p0 = pn.copy() + # un = u0 - dt*sdiag(AvF2CC.T*self.sig)*u0 + dt*MfmuiI*Grad*p0 + un = u0 + dt*MfmuiI*Grad*p0 + u0 = un.copy() + p[:,i+1] = pn + + P.append(p) + elapsed = clock()-start + print (">>Elapsed time: %5.2e s")%(elapsed) + + return P + + elif self.storefield==False: + + Data = [] + + ntx = len(self.survey.txList) + for itx, tx in enumerate(self.survey.txList): + print (" Tx at (%7.2f, %7.2f): %4i/%4i")%(tx.loc[0], tx.loc[0], itx+1, ntx) + pn = np.zeros(self.mesh.nC) + p0 = np.zeros_like(pn) + un = np.zeros(self.mesh.nF) + u0 = np.zeros_like(un) + time = tx.time + dt = tx.dt + data = np.zeros((time.size, tx.nD)) + q = tx.getq(self.mesh) + Proj = tx.rxList[0].getP(self.mesh) + for i in range(time.size-1): + sn = tx.Wave(i+1) + s0 = tx.Wave(i) + pn = p0-dt*DSig*p0+Drhoi*dt*(Div*un+(sn-s0)/dt*q) + p0 = pn.copy() + # un = u0 - dt*sdiag(AvF2CC.T*self.sig)*u0 + dt*MfmuiI*Grad*p0 + un = u0 + dt*MfmuiI*Grad*p0 + u0 = un.copy() + data[i,:] = Proj*pn + + Data.append(data) + + return Data + +class AcousticProblemPML(Problem.BaseProblem): + """ + + """ + surveyPair = SurveyAcoustic + Solver = Solver + storefield = True + verbose = False + stability = False + sigx = False + + def __init__(self, mesh, **kwargs): + Problem.BaseProblem.__init__(self, mesh) + self.mesh.setCellGradBC('dirichlet') + Utils.setKwargs(self, **kwargs) + + def setPMLBC(self, npad, dt, bcflag="all"): + #TODO: performance of abosrbing + self.bcflag = bcflag + ax = self.mesh.vectorCCx[-npad] + ay = self.mesh.vectorCCy[-npad] + if bcflag == 'all': + indy = np.logical_or(self.mesh.gridCC[:,1]<=-ay, self.mesh.gridCC[:,1]>=ay) + indx = np.logical_or(self.mesh.gridCC[:,0]<=-ax, self.mesh.gridCC[:,0]>=ax) + elif bcflag =='up': + indy = self.mesh.gridCC[:,1]<=-ay + indx = np.logical_or(self.mesh.gridCC[:,0]<=-ax, self.mesh.gridCC[:,0]>=ax) + elif bcflag =='left': + indy = self.mesh.gridCC[:,1]<=-ay + indx = self.mesh.gridCC[:,0]>=ax + elif bcflag =='right': + indy = self.mesh.gridCC[:,1]<=-ay + indx = self.mesh.gridCC[:,0]<=-ax + else: + raise Exception("Not implented!!") + tempx = np.zeros_like(self.mesh.gridCC[:,0]) + tempx[indx] = (abs(self.mesh.gridCC[:,0][indx])-ax)**2 + tempx[indx] = tempx[indx]-tempx[indx].min() + tempx[indx] = tempx[indx]/tempx[indx].max() + tempy = np.zeros_like(self.mesh.gridCC[:,1]) + tempy[indy] = (abs(self.mesh.gridCC[:,1][indy])-ay)**2 + tempy[indy] = tempy[indy]-tempy[indy].min() + tempy[indy] = tempy[indy]/tempy[indy].max() + + fx = 1.-tempx*0.1 + fy = 1.-tempy*0.1 + self.sigx = (1-fx)/fx*2./dt + self.sigy = (1-fy)/fy*2./dt + + def stabilitycheck(self, v, time, fmain): + + self.dxmin = min(self.mesh.hx.min(), self.mesh.hy.min()) + self.topt = self.dxmin/v.max()*0.5 + self.dt = time[1]-time[0] + self.fmain = fmain + self.wavelen = v.min()/self.fmain + self.G = self.wavelen/self.dxmin + + if self.dt > self.topt: + print "Warning: dt is greater than topt" + self.stability = False + elif self.G < 16.: + print "Warning: Wavelength per cell (G) should be greater than 16" + self.stability = False + else: + print "You are good to go:)" + self.stability = True + + print ">> Stability information" + print (" dt: %5.2e s")%(self.dt) + print (" Optimal dt: %5.2e s")%(self.topt) + print (" Cell per wavelength (G): %5.2e")%(self.G) + print (" Optimal G: %5.2e")%(16.) + + def fields(self, v): + + if self.bcflag =='up': + self.mesh.setCellGradBC(['dirichlet', ['dirichlet', 'neumann']]) + elif self.bcflag =='left': + self.mesh.setCellGradBC([['neumann', 'dirichlet'], ['dirichlet', 'neumann']]) + elif self.bcflag =='right': + self.mesh.setCellGradBC([['dirichlet', 'neumann'], ['dirichlet', 'neumann']]) + + Grad = self.mesh.cellGrad + AvF2CC = self.mesh.aveF2CC + AvF2CCv = self.mesh.aveF2CCV + rho = 0.27*np.ones(self.mesh.nC) + mu = rho*v**2 + Divvec = sp.block_diag((self.mesh.faceDivx, self.mesh.faceDivy)) + Mrhocc = sp.block_diag((sdiag(rho), sdiag(rho))) + Mmuifvec = sdiag(AvF2CC.T*(1/mu)) + Msigf = sdiag(AvF2CCv.T*np.r_[self.sigx, self.sigy]) + Msigcc = sp.block_diag((sdiag(self.sigx), sdiag(self.sigy))) + MrhoccI = sdInv(Mrhocc) + MmuifvecI = sdInv(Mmuifvec) + Ivec = sp.hstack((sdiag(np.ones(self.mesh.nC)), sdiag(np.ones(self.mesh.nC)))) + + if self.stability==False: + raise Exception("Stability condition is not satisfied!!") + elif self.sigx is False: + print "Warning: Absorbing boundary condition was not set yet!!" + start = clock() + print ">> Start Computing Acoustic Wave" + print (">> dt: %5.2e s")%(self.dt) + print (">> Optimal dt: %5.2e s")%(self.topt) + print (">> Main frequency, fmain: %5.2e Hz")%(self.fmain) + print (">> Cell per wavelength (G): %5.2e")%(self.G) + + + if self.storefield==True: + Phi = [] + #TODO: parallize in terms of sources + ntx = len(self.survey.txList) + for itx, tx in enumerate(self.survey.txList): + print (" Tx at (%7.2f, %7.2f): %4i/%4i")%(tx.loc[0], tx.loc[0], itx+1, ntx) + phi = np.zeros((self.mesh.nC, tx.time.size)) + phin = np.zeros(self.mesh.nC*2) + phi0 = np.zeros_like(phin) + un = np.zeros(self.mesh.nF) + u0 = np.zeros_like(un) + time = tx.time + dt = tx.dt + q = tx.getq(self.mesh) + qvec = np.r_[q, q]*1/2 + + for i in range(time.size-1): + sn = tx.Wave(i+1) + s0 = tx.Wave(i) + phin = phi0-dt*(Msigcc*phi0)+dt*MrhoccI*(1/dt*(sn-s0)*qvec+Divvec*un) + phi0 = phin.copy() + un = u0 - dt*Msigf*u0 + dt*MmuifvecI*Grad*(Ivec*phi0) + u0 = un.copy() + phi[:,i+1] = Ivec*phi0 + Phi.append(phi) + elapsed = clock()-start + print (">>Elapsed time: %5.2e s")%(elapsed) + + return Phi + + elif self.storefield==False: + + Data = [] + + ntx = len(self.survey.txList) + for itx, tx in enumerate(self.survey.txList): + print (" Tx at (%7.2f, %7.2f): %4i/%4i")%(tx.loc[0], tx.loc[0], itx+1, ntx) + phi = np.zeros((mesh.nC, time.size)) + phin = np.zeros(mesh.nC*2) + phi0 = np.zeros_like(phin) + un = np.zeros(mesh.nF) + u0 = np.zeros_like(un) + time = tx.time + dt = tx.dt + p = np.zeros((self.mesh.nC, time.size)) + q = tx.getq(self.mesh) + qvec = np.r_[q, q]*1/2 + for i in range(time.size-1): + sn = tx.Wave(i+1) + s0 = tx.Wave(i) + phin = phi0-dt*(Msigcc*phi0)+dt*MrhoccI*(1/dt*(sn-s0)*qvec+Divvec*un) + phi0 = phin.copy() + un = u0 - dt*Msigf*u0 + dt*MmuifvecI*Grad*(Ivec*phi0) + u0 = un.copy() + data[i,:] = Proj*(Ivec*phi0) + + Data.append(data) + + elapsed = clock()-start + print (">>Elapsed time: %5.2e s")%(elapsed) + + return Data + +if __name__ == '__main__': + + time = np.linspace(0, 0.04, 2**9) + dt = time[1]-time[0] + options={'tlag':0.0025, 'fmain':400} + rx = AcousticRx(np.vstack((np.r_[0, 1], np.r_[0, 1]))) + tx = AcousticTx(np.r_[0, 1], time, [rx], **options) + survey = SurveyAcoustic([tx]) + wave = tx.RickerWavelet() + cs = 0.5 + hx = np.ones(150)*cs + hy = np.ones(150)*cs + mesh = Mesh.TensorMesh([hx, hy], 'CC') + prob = AcousticProblemPML(mesh) + prob.pair(survey) + prob.setPMLBC(30, dt, bcflag='all') + prob.storefield = True + v = np.ones(mesh.nC)*2000. + prob.stabilitycheck(v, time, 100.) + U = prob.fields(v) + icount = 220 + extent = [mesh.vectorCCx.min(), mesh.vectorCCx.max(), mesh.vectorCCy.min(), mesh.vectorCCy.max()] + fig, ax = plt.subplots(1, 1, figsize = (5,5)) + ax.imshow(np.flipud(U[0][:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'binary') + plt.show() + diff --git a/simpegseis/__init__.py b/simpegseis/__init__.py new file mode 100644 index 0000000..ad29a07 --- /dev/null +++ b/simpegseis/__init__.py @@ -0,0 +1,2 @@ +from SeisAcousticTime import * + diff --git 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